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Centered around dynamics, DCDS-B is an interdisciplinary journal focusing on the interactions between mathematical modeling, analysis and scientific computations. The mission of the Journal is to bridge mathematics and sciences by publishing research papers that augment the fundamental ways we interpret, model and predict scientific phenomena. The Journal covers a broad range of areas including chemical, engineering, physical and life sciences. A more detailed indication is given by the subject interests of the members of the Editorial Board.

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Preface to the special issue "Dynamics and control in distributed systems: Dedicated to the memory of Valery S. Melnik (1952-2007)"
Tomás Caraballo Garrido, Oleksiy V. Kapustyan, Pavlo O. Kasyanov, José Valero and Michael Zgurovsky
2019, 24(3) : ⅰ-ⅴ doi: 10.3934/dcdsb.20193i +[Abstract](211) +[HTML](78) +[PDF](112.13KB)
Abstract:
Stability analysis of a chemotherapy model with delays
Ismail Abdulrashid, Abdallah A. M. Alsammani and Xiaoying Han
2019, 24(3) : 989-1005 doi: 10.3934/dcdsb.2019002 +[Abstract](297) +[HTML](81) +[PDF](543.61KB)
Abstract:

A chemotherapy model for cancer treatment is studied, where the chemotherapy agent and cells are assumed to follow a predator-prey type relation. The time delays from the instant that the chemotherapy agent is injected to the instant that the treatment is effective are taken into account and dynamics of systems with or without delays are compared. First basic properties of solutions including existence and uniqueness, boundedness and positiveness are discussed. Then conditions on model parameters are established for different outcomes of the treatment. Numerical simulations are provided to illustrate theoretical results.

Periodic orbits for the perturbed planar circular restricted 3–body problem
Elbaz I. Abouelmagd, Juan Luis García Guirao and Jaume Llibre
2019, 24(3) : 1007-1020 doi: 10.3934/dcdsb.2019003 +[Abstract](205) +[HTML](74) +[PDF](374.87KB)
Abstract:

We characterize when the classical first and second kind of periodic orbits of the planar circular restricted \begin{document}$ 3 $\end{document}–body problem obtained by Poincaré, can be extended to perturbed planar circular restricted \begin{document}$ 3 $\end{document}–body problems. We put special emphasis when the perturbed forces are due to zonal harmonic or to a solar sail.

Pursuit differential-difference games with pure time-lag
Lesia V. Baranovska
2019, 24(3) : 1021-1031 doi: 10.3934/dcdsb.2019004 +[Abstract](202) +[HTML](86) +[PDF](380.23KB)
Abstract:

The analytical approach for solution of pursuit differential-difference games with pure time-lag is considered. For the pursuit local problem with the fixed time the scheme of the method of resolving functions and Pontryagin's first direct method are developed. The integral presentation of game solution based on the time-delay exponential is proposed at first time. The guaranteed times of the game termination are found, and corresponding control laws are constructed. Comparison of the times of approach by the method of resolving functions and Pontryagin's first direct method for the initial problem are made.

On the exact number of monotone solutions of a simplified Budyko climate model and their different stability
Sabri Bensid and Jesús Ildefonso Díaz
2019, 24(3) : 1033-1047 doi: 10.3934/dcdsb.2019005 +[Abstract](89) +[HTML](41) +[PDF](1986.81KB)
Abstract:

We consider a simplified version of the Budyko diffusive energy balance climate model. We obtain the exact number of monotone stationary solutions of the associated discontinuous nonlinear elliptic with absorption. We show that the bifurcation curve, in terms of the solar constant parameter, is S-shaped. We prove the instability of the decreasing part and the stability of the increasing part of the bifurcation curve. In terms of the Budyko climate problem the above results lead to an important qualitative information which is far to be evident and which seems to be new in the mathematical literature on climate models. We prove that if the solar constant is represented by \begin{document}$ \lambda \in (\lambda _{1}, \lambda _{2}), $\end{document} for suitable \begin{document}$ \lambda _{1}<\lambda _{2}, $\end{document} then there are exactly two stationary solutions giving rise to a free boundary (i.e. generating two symmetric polar ice caps: North and South ones) and a third solution corresponding to a totally ice covered Earth. Moreover, we prove that the solution with smaller polar ice caps is stable and the one with bigger ice caps is unstable.

Robustness of dynamically gradient multivalued dynamical systems
Rubén Caballero, Alexandre N. Carvalho, Pedro Marín-Rubio and José Valero
2019, 24(3) : 1049-1077 doi: 10.3934/dcdsb.2019006 +[Abstract](116) +[HTML](62) +[PDF](498.13KB)
Abstract:

In this paper we study the robustness of dynamically gradient multivalued semiflows. As an application, we describe the dynamical properties of a family of Chafee-Infante problems approximating a differential inclusion studied in [3], proving that the weak solutions of these problems generate a dynamically gradient multivalued semiflow with respect to suitable Morse sets.

Some remarks on an environmental defensive expenditures model
Tomás Caraballo, Renato Colucci and Luca Guerrini
2019, 24(3) : 1079-1093 doi: 10.3934/dcdsb.2019007 +[Abstract](70) +[HTML](59) +[PDF](1112.39KB)
Abstract:

In this paper, we consider the environmental defensive expenditures model with delay proposed by Russu in [16] and obtain different results about stability of equilibria in the case of absence of delay. Moreover we provide a more detailed analysis of the stability for equilibria and Hopf bifurcation in the case with delay. Finally, we discuss possible modifications of the model in order to make it more accurate and realistic.

I. U. Bronshtein's conjecture for monotone nonautonomous dynamical systems
David Cheban
2019, 24(3) : 1095-1113 doi: 10.3934/dcdsb.2019008 +[Abstract](83) +[HTML](46) +[PDF](446.64KB)
Abstract:

In this paper we study the problem of Levitan/Bohr almost periodicity of solutions for dissipative differential equations (Bronshtein's conjecture for Bohr almost periodic case). We give a positive answer to this conjecture for monotone Levitan/Bohr almost periodic systems of differential/difference equations.

Inertial manifolds for the hyperbolic relaxation of semilinear parabolic equations
Vladimir V. Chepyzhov, Anna Kostianko and Sergey Zelik
2019, 24(3) : 1115-1142 doi: 10.3934/dcdsb.2019009 +[Abstract](81) +[HTML](52) +[PDF](517.13KB)
Abstract:

The paper gives a comprehensive study of Inertial Manifolds for hyperbolic relaxations of an abstract semilinear parabolic equation in a Hilbert space. A new scheme of constructing Inertial Manifolds for such type of problems is suggested and optimal spectral gap conditions which guarantee their existence are established. Moreover, the dependence of the constructed manifolds on the relaxation parameter in the case of the parabolic singular limit is also studied.

Bibliography: 38 titles.

A topological characterization of the $\omega$-limit sets of analytic vector fields on open subsets of the sphere
José Ginés Espín Buendía and Víctor Jiménez Lopéz
2019, 24(3) : 1143-1173 doi: 10.3934/dcdsb.2019010 +[Abstract](76) +[HTML](44) +[PDF](570.29KB)
Abstract:

In [15], V. Jiménez López and J. Llibre characterized, up to homeomorphism, the \begin{document}$ \omega $\end{document}-limit sets of analytic vector fields on the sphere and the projective plane. The authors also studied the same problem for open subsets of these surfaces.

Unfortunately, an essential lemma in their programme for general surfaces has a gap. Although the proof of this lemma can be amended in the case of the sphere, the plane, the projective plane and the projective plane minus one point (and therefore the characterizations for these surfaces in [15] are correct), the lemma is not generally true, see [6].

Consequently, the topological characterization for analytic vector fields on open subsets of the sphere and the projective plane is still pending. In this paper, we close this problem in the case of open subsets of the sphere.

Forward attraction of pullback attractors and synchronizing behavior of gradient-like systems with nonautonomous perturbations
Xuewei Ju, Desheng Li and Jinqiao Duan
2019, 24(3) : 1175-1197 doi: 10.3934/dcdsb.2019011 +[Abstract](127) +[HTML](49) +[PDF](489.66KB)
Abstract:

We consider the nonautonomous perturbation \begin{document}$ x_t+Ax = f(x)+\varepsilon h(t) $\end{document} of a gradient-like system \begin{document}$ x_t+Ax = f(x) $\end{document} in a Banach space \begin{document}$ X $\end{document}, where \begin{document}$ A $\end{document} is a sectorial operator with compact resolvent. Assume the non-perturbed system \begin{document}$ x_t+Ax = f(x) $\end{document} has an attractor \begin{document}$ {\mathscr A} $\end{document}. Then it can be shown that the perturbed one has a pullback attractor \begin{document}$ {\mathscr A} _\varepsilon $\end{document} near \begin{document}$ {\mathscr A} $\end{document}. If all the equilibria of the non-perturbed system in \begin{document}$ {\mathscr A} $\end{document} are hyperbolic, we also infer from [4,6] that \begin{document}$ {\mathscr A} _\varepsilon $\end{document} inherits the natural Morse structure of \begin{document}$ {\mathscr A} $\end{document}. In this present work, we introduce the notion of nonautonomous equilibria and give a more precise description on the Morse structure of \begin{document}$ {\mathscr A} _\varepsilon $\end{document} and the asymptotically synchronizing behavior of the perturbed system. Based on the above result we further prove that the sections of \begin{document}$ {\mathscr A} _\varepsilon $\end{document} depend on time symbol continuously in the sense of Hausdorff distance. Consequently, one concludes that \begin{document}$ {\mathscr A} _\varepsilon $\end{document} is a forward attractor of the perturbed nonautonomous system. It will also be shown that the perturbed system exhibits completely a global forward synchronizing behavior with the external force.

On relation between attractors for single and multivalued semiflows for a certain class of PDEs
Piotr Kalita, Grzegorz Łukaszewicz and Jakub Siemianowski
2019, 24(3) : 1199-1227 doi: 10.3934/dcdsb.2019012 +[Abstract](90) +[HTML](51) +[PDF](534.4KB)
Abstract:

Sometimes it is not possible to prove the uniqueness of the weak solutions for problems of mathematical physics, but it is possible to bootstrap their regularity to the regularity of strong solutions which are unique. In this paper we formulate an abstract setting for such class of problems and we provide the conditions under which the global attractors for both strong and weak solutions coincide and the fractal dimension of the common attractor is finite. We present two problems belonging to this class: planar Rayleigh–Bénard flow of thermomicropolar fluid and surface quasigeostrophic equation on torus.

Attractors of multivalued semi-flows generated by solutions of optimal control problems
Olexiy V. Kapustyan, Pavlo O. Kasyanov, José Valero and Mikhail Z. Zgurovsky
2019, 24(3) : 1229-1242 doi: 10.3934/dcdsb.2019013 +[Abstract](95) +[HTML](41) +[PDF](392.05KB)
Abstract:

In this paper we study the dynamical system generated by the solutions of optimal control problems. We obtain suitable conditions under which such systems generate multivalued semiprocesses. We prove the existence of uniform attractors for the multivalued semiprocess generated by the solutions of controlled reaction-diffusion equations and study its properties.

Quasi-optimal control with a general quadratic criterion in a special norm for systems described by parabolic-hyperbolic equations with non-local boundary conditions
Volodymyr O. Kapustyan, Ivan O. Pyshnograiev and Olena A. Kapustian
2019, 24(3) : 1243-1258 doi: 10.3934/dcdsb.2019014 +[Abstract](77) +[HTML](43) +[PDF](353.96KB)
Abstract:

In this work, we consider a dynamical system generated by a parabolic-hyperbolic equation with non-local boundary conditions. The optimal control problem for this system is studied using a notion of quasi-optimal solution. Existence and uniqueness of quasi-optimal control are proved.

Forward attracting sets of reaction-diffusion equations on variable domains
Peter E. Kloeden and Meihua Yang
2019, 24(3) : 1259-1271 doi: 10.3934/dcdsb.2019015 +[Abstract](103) +[HTML](55) +[PDF](365.28KB)
Abstract:

Reaction-diffusion equations on time-variable domains are instrinsically nonautonomous even if the coefficients in the equation do not depend explicitly on time. Thus the appropriate asymptotic concepts, such as attractors, are nonautonomous. Forward attracting sets based on omega-limit sets are considered in this paper. These are related to the Vishik uniform attractor but are not as restrictive since they depend only on the dynamics in the distant future. They are usually not invariant. Here it is shown that they are asymptotically positively invariant, in general, and, if the future dynamics is appropriately uniform, also asymptotically negatively invariant as well as upper semi continuous dependence in a parameter will be established. These results also apply to reaction-diffusion equations on a fixed domain.

On optimal control problem for an ill-posed strongly nonlinear elliptic equation with $p$-Laplace operator and $L^1$-type of nonlinearity
Peter I. Kogut and Olha P. Kupenko
2019, 24(3) : 1273-1295 doi: 10.3934/dcdsb.2019016 +[Abstract](85) +[HTML](34) +[PDF](557.11KB)
Abstract:

We study an optimal control problem for one class of non-linear elliptic equations with \begin{document}$p$\end{document}-Laplace operator and \begin{document}$L^1$\end{document}-nonlinearity. We deal with such case of nonlinearity when we cannot expect to have a solution of the state equation for any given control. After defining a suitable functional class in which we look for solutions, we reformulate the original problem and prove the existence of optimal pairs. In order to ensure the validity of such reformulation, we provide its substantiation using a special family of fictitious optimal control problems. The idea to involve the fictitious optimization problems was mainly inspired by the brilliant book of V.S. Mel'nik and V.I. Ivanenko "Variational Methods in Control Problems for the Systems with Distributed Parameters", Kyiv, 1998.

Existence of solutions for space-fractional parabolic hemivariational inequalities
Yongjian Liu, Zhenhai Liu and Ching-Feng Wen
2019, 24(3) : 1297-1307 doi: 10.3934/dcdsb.2019017 +[Abstract](123) +[HTML](39) +[PDF](380.94KB)
Abstract:

This paper is devoted to the existence of solutions for space-fractional parabolic hemivariational inequalities by means of the well-known surjectivity result for multivalued ($S_+$) type mappings.

Partial differential inclusions of transport type with state constraints
Thomas Lorenz
2019, 24(3) : 1309-1340 doi: 10.3934/dcdsb.2019018 +[Abstract](91) +[HTML](72) +[PDF](685.64KB)
Abstract:

The focus is on the existence of weak solutions to the quasilinear first-order partial differential inclusion

with values in \begin{document}$L^p({{\mathbb{R}}^{N}})$\end{document} for \begin{document}$p ∈ (1, ∞)$\end{document}. The solution is to satisfy state constraints in addition, i.e., all its values belong to a given set \begin{document}$\mathcal{V} \subset L^p({{\mathbb{R}}^{N}})$\end{document} of constraints. We specify sufficient conditions such that every function in \begin{document}$\mathcal{V}$\end{document} initializes at least one weak solution with all its values in \begin{document}$\mathcal{V}$\end{document}(so-called weak invariance a.k.a. viability of \begin{document}$\mathcal{V}$\end{document}). Due to the regularity assumptions about the set-valued coefficient mappings, these solutions prove to be renormalized (in the sense of Di Perna and Lions).

On the nonconserved Caginalp phase-field system based on the Maxwell-Cattaneo law with two temperatures and logarithmic potentials
Ahmad Makki, Alain Miranville and Georges Sadaka
2019, 24(3) : 1341-1365 doi: 10.3934/dcdsb.2019019 +[Abstract](86) +[HTML](40) +[PDF](756.26KB)
Abstract:

Our aim in this article is to study generalizations of the nonconserved Caginalp phase-field system based on the Maxwell-Cattaneo law with two temperatures for heat conduction and with logarithmic nonlinear terms. We obtain well-posedness results and study the asymptotic behavior of the system. In particular, we prove the existence of the global attractor. Furthermore, we give some numerical simulations, obtained with the $\mathtt{FreeFem++}$ software [24], comparing the nonconserved Caginalp phase-field model with regular and logarithmic nonlinear terms.

Asymptotic behavior of the stochastic Keller-Segel equations
Yadong Shang, Jianjun Paul Tian and Bixiang Wang
2019, 24(3) : 1367-1391 doi: 10.3934/dcdsb.2019020 +[Abstract](110) +[HTML](49) +[PDF](566.44KB)
Abstract:

This paper deals with the asymptotic behavior of the solutions of the non-autonomous one-dimensional stochastic Keller-Segel equations defined in a bounded interval with Neumann boundary conditions. We prove the existence and uniqueness of tempered pullback random attractors under certain conditions. We also establish the convergence of the solutions as well as the pullback random attractors of the stochastic equations as the intensity of noise approaches zero.

An optimal control problem for some nonlinear elliptic equations with unbounded coefficients
Gabriella Zecca
2019, 24(3) : 1393-1409 doi: 10.3934/dcdsb.2019021 +[Abstract](92) +[HTML](67) +[PDF](482.53KB)
Abstract:

We study an optimal control problem associated to a Dirichlet boundary value problem of the type

\begin{document}$ 1<p\leqslant 2, $\end{document} where \begin{document}$ \Omega $\end{document} is a bounded regular domain of \begin{document}$ \mathbb{R}^N $\end{document}, \begin{document}$ 0\in \Omega , $\end{document} \begin{document}$ \beta: \Omega \rightarrow {\mathbb R} $\end{document} is an unbounded function satisfying \begin{document}$ \beta(x)\geqslant\lambda_0>0 $\end{document} a.e., \begin{document}$ A $\end{document} is a suitably small constant, and \begin{document}$ g\in L^\infty( \Omega ; \mathbb{R}^N ) $\end{document}.

We consider the vector field \begin{document}$ \mathcal F $\end{document} as the control and the corresponding weak solution \begin{document}$ u $\end{document} to (BVP) as the state. Our aim is to find the optimal vector field \begin{document}$ \mathcal F\in L^p( \Omega ) $\end{document} so that the corresponding state \begin{document}$ u\in W^{1,p}_0( \Omega ) $\end{document} is close to the desired profile in \begin{document}$ L^p( \Omega ) $\end{document} while the norm of \begin{document}$ u $\end{document} in \begin{document}$ W^{1,p}( \Omega ) $\end{document} is not too large.

We prove that, for every \begin{document}$ p $\end{document} less than \begin{document}$ 2 $\end{document} and suitably close to \begin{document}$ 2 $\end{document}, (BVP) admits an unique weak solution and for such values of \begin{document}$ p $\end{document}, we prove the existence of optimal pairs.

Thermodynamical potentials of classical and quantum systems
Ruikuan Liu, Tian Ma, Shouhong Wang and Jiayan Yang
2018doi: 10.3934/dcdsb.2018214 +[Abstract](621) +[HTML](309) +[PDF](637.0KB)
On the path-independence of the Girsanov transformation for stochastic evolution equations with jumps in Hilbert spaces
Huijie Qiao and Jiang-Lun Wu
2018doi: 10.3934/dcdsb.2018215 +[Abstract](549) +[HTML](312) +[PDF](423.33KB)
Dynamic behavior and optimal scheduling for mixed vaccination strategy with temporary immunity
Siyu Liu, Xue Yang, Yingjie Bi and Yong Li
2018doi: 10.3934/dcdsb.2018216 +[Abstract](836) +[HTML](461) +[PDF](653.24KB)
Non-autonomous reaction-diffusion equations with variable exponents and large diffusion
Antonio Carlos Fernandes, Marcela Carvalho Gonçcalves and Jacson Simsen
2018doi: 10.3934/dcdsb.2018217 +[Abstract](656) +[HTML](379) +[PDF](3152.45KB)
Uniqueness and stability of traveling waves for a three-species competition system with nonlocal dispersal
Guo-Bao Zhang, Fang-Di Dong and Wan-Tong Li
2018doi: 10.3934/dcdsb.2018218 +[Abstract](705) +[HTML](363) +[PDF](472.18KB)
Fluctuations of mRNA distributions in multiple pathway activated transcription
Genghong Lin, Jianshe Yu, Zhan Zhou, Qiwen Sun and Feng Jiao
2018doi: 10.3934/dcdsb.2018219 +[Abstract](812) +[HTML](481) +[PDF](809.21KB)
Global existence and stability in a two-species chemotaxis system
Huanhuan Qiu and Shangjiang Guo
2018doi: 10.3934/dcdsb.2018220 +[Abstract](649) +[HTML](581) +[PDF](1061.01KB)
Novel spectral methods for Schrödinger equations with an inverse square potential on the whole space
Suna Ma, Huiyuan Li and Zhimin Zhang
2018doi: 10.3934/dcdsb.2018221 +[Abstract](666) +[HTML](421) +[PDF](7354.7KB)
Nonconstant periodic solutions with any fixed energy for singular Hamiltonian systems
Liang Ding, Rongrong Tian and Jinlong Wei
2018doi: 10.3934/dcdsb.2018222 +[Abstract](648) +[HTML](324) +[PDF](325.95KB)
A SIS reaction-diffusion model with a free boundary condition and nonhomogeneous coefficients
Yizhuo Wang and Shangjiang Guo
2018doi: 10.3934/dcdsb.2018223 +[Abstract](610) +[HTML](493) +[PDF](483.02KB)
Synchronization of first-order autonomous oscillators on Riemannian manifolds
Simone Fiori
2018doi: 10.3934/dcdsb.2018233 +[Abstract](447) +[HTML](291) +[PDF](2697.39KB)
Linear programming based optimality conditions and approximate solution of a deterministic infinite horizon discounted optimal control problem in discrete time
Vladimir Gaitsgory, Alex Parkinson and Ilya Shvartsman
2018doi: 10.3934/dcdsb.2018235 +[Abstract](458) +[HTML](289) +[PDF](512.69KB)
Limit cycles of discontinuous piecewise quadratic and cubic polynomial perturbations of a linear center
Jaume Llibre and Yilei Tang
2018doi: 10.3934/dcdsb.2018236 +[Abstract](474) +[HTML](373) +[PDF](418.99KB)
Spatial propagation for a parabolic system with multiple species competing for single resource
Zhiguo Wang, Hua Nie and Jianhua Wu
2018doi: 10.3934/dcdsb.2018237 +[Abstract](414) +[HTML](361) +[PDF](537.12KB)
Swarming in domains with boundaries: Approximation and regularization by nonlinear diffusion
Razvan C. Fetecau, Mitchell Kovacic and Ihsan Topaloglu
2018doi: 10.3934/dcdsb.2018238 +[Abstract](456) +[HTML](362) +[PDF](1341.85KB)
Spreading-vanishing dichotomy in information diffusion in online social networks with intervention
Jingli Ren, Dandan Zhu and Haiyan Wang
2018doi: 10.3934/dcdsb.2018240 +[Abstract](541) +[HTML](241) +[PDF](3790.08KB)
Periodic attractors of nonautonomous flat-topped tent systems
Luís Silva
2018doi: 10.3934/dcdsb.2018243 +[Abstract](397) +[HTML](280) +[PDF](315.98KB)
Evolutionarily stable dispersal strategies in a two-patch advective environment
Jing-Jing Xiang and Yihao Fang
2018doi: 10.3934/dcdsb.2018245 +[Abstract](421) +[HTML](304) +[PDF](444.2KB)
Asymptotic behavior for stochastic plate equations with rotational inertia and Kelvin-Voigt dissipative term on unbounded domains
Xiaobin Yao, Qiaozhen Ma and Tingting Liu
2018doi: 10.3934/dcdsb.2018247 +[Abstract](505) +[HTML](302) +[PDF](501.98KB)
Convergence rates of solutions for a two-species chemotaxis-Navier-Stokes sytstem with competitive kinetics
Hai-Yang Jin and Tian Xiang
2018doi: 10.3934/dcdsb.2018249 +[Abstract](484) +[HTML](315) +[PDF](526.21KB)
Smoothing dynamics of the non-autonomous stochastic Fitzhugh-Nagumo system on $\mathbb{R}^N$ driven by multiplicative noises
Wenqiang Zhao
2018doi: 10.3934/dcdsb.2018251 +[Abstract](500) +[HTML](361) +[PDF](461.94KB)
A randomized Milstein method for stochastic differential equations with non-differentiable drift coefficients
Raphael Kruse and Yue Wu
2018doi: 10.3934/dcdsb.2018253 +[Abstract](471) +[HTML](277) +[PDF](608.47KB)
Numerical methods for PDE models related to pricing and expected lifetime of an extraction project under uncertainty
María Suárez-Taboada and Carlos Vázquez
2018doi: 10.3934/dcdsb.2018254 +[Abstract](528) +[HTML](283) +[PDF](650.04KB)
Lyapunov type inequalities for Hammerstein integral equations and applications to population dynamics
Kunquan Lan and Wei Lin
2018doi: 10.3934/dcdsb.2018256 +[Abstract](369) +[HTML](280) +[PDF](502.25KB)
Global exponential attraction for multi-valued semidynamical systems with application to delay differential equations without uniqueness
Yejuan Wang and Lin Yang
2018doi: 10.3934/dcdsb.2018257 +[Abstract](357) +[HTML](232) +[PDF](490.61KB)
Confinement of a hot temperature patch in the modified SQG model
Roberto Garra
2018doi: 10.3934/dcdsb.2018258 +[Abstract](270) +[HTML](195) +[PDF](320.99KB)
Oscillations and asymptotic convergence for a delay differential equation modeling platelet production
Loïs Boullu, Mostafa Adimy, Fabien Crauste and Laurent Pujo-Menjouet
2018doi: 10.3934/dcdsb.2018259 +[Abstract](317) +[HTML](188) +[PDF](591.42KB)
Asymptotics of the Lebowitz-Rubinow-Rotenberg model of population development
Adam Gregosiewicz
2018doi: 10.3934/dcdsb.2018260 +[Abstract](349) +[HTML](186) +[PDF](641.03KB)
Symmetries of nonlinear vibrations in tetrahedral molecular configurations
Irina Berezovik, Carlos García-Azpeitia and Wieslaw Krawcewicz
2018doi: 10.3934/dcdsb.2018261 +[Abstract](369) +[HTML](212) +[PDF](274.11KB)
Unique continuation property for stochastic nonclassical diffusion equations and stochastic linearized Benjamin-Bona-Mahony equations
Peng Gao
2018doi: 10.3934/dcdsb.2018262 +[Abstract](302) +[HTML](188) +[PDF](354.81KB)
Global eradication for spatially structured populations by regional control
Sebastian Aniţa, Vincenzo Capasso and Ana-Maria Moşneagu
2018doi: 10.3934/dcdsb.2018263 +[Abstract](347) +[HTML](199) +[PDF](466.08KB)
Stability and bifurcation in an age-structured model with stocking rate and time delays
Shengqin Xu, Chuncheng Wang and Dejun Fan
2018doi: 10.3934/dcdsb.2018264 +[Abstract](532) +[HTML](240) +[PDF](471.73KB)
On the long-time behaviour of age and trait structured population dynamics
Tristan Roget
2018doi: 10.3934/dcdsb.2018265 +[Abstract](344) +[HTML](184) +[PDF](578.84KB)
Optimal control problems for the Gompertz model under the Norton-Simon hypothesis in chemotherapy
Luis A. Fernández and Cecilia Pola
2018doi: 10.3934/dcdsb.2018266 +[Abstract](448) +[HTML](210) +[PDF](616.77KB)
Global solution and decay rate for a reduced gravity two and a half layer model
Yongming Liu and Lei Yao
2018doi: 10.3934/dcdsb.2018267 +[Abstract](330) +[HTML](243) +[PDF](262.77KB)
Bifurcation scenarios in an ordinary differential equation with constant and distributed delay: A case study
Tomás Caraballo, Renato Colucci and Luca Guerrini
2018doi: 10.3934/dcdsb.2018268 +[Abstract](385) +[HTML](211) +[PDF](1025.84KB)
Stability of radial solutions of the Poisson-Nernst-Planck system in annular domains
Chia-Yu Hsieh
2018doi: 10.3934/dcdsb.2018269 +[Abstract](341) +[HTML](207) +[PDF](450.71KB)
Nondegenerate multistationarity in small reaction networks
Anne Shiu and Timo de Wolff
2018doi: 10.3934/dcdsb.2018270 +[Abstract](264) +[HTML](195) +[PDF](413.58KB)
Connected components of positive solutions for a Dirichlet problem involving the mean curvature operator in Minkowski space
Ruyun Ma and Man Xu
2018doi: 10.3934/dcdsb.2018271 +[Abstract](302) +[HTML](215) +[PDF](444.31KB)
Long time behavior of fractional impulsive stochastic differential equations with infinite delay
Jiaohui Xu and Tomás Caraballo
2018doi: 10.3934/dcdsb.2018272 +[Abstract](469) +[HTML](214) +[PDF](547.29KB)
H2-stability of some second order fully discrete schemes for the Navier-Stokes equations
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2018doi: 10.3934/dcdsb.2018273 +[Abstract](407) +[HTML](226) +[PDF](398.58KB)
Immunosuppressant treatment dynamics in renal transplant recipients: an iterative modeling approach
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Distribution profiles in gene transcription activated by the cross-talking pathway
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2018doi: 10.3934/dcdsb.2018275 +[Abstract](276) +[HTML](176) +[PDF](764.57KB)
Convergences of asymptotically autonomous pullback attractors towards semigroup attractors
Hongyong Cui
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Minimax joint spectral radius and stabilizability of discrete-time linear switching control systems
Victor Kozyakin
2018doi: 10.3934/dcdsb.2018277 +[Abstract](402) +[HTML](197) +[PDF](532.88KB)
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Jacson Simsen and Mariza Stefanello Simsen
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Global attractors for weak solutions of the three-dimensional Navier-Stokes equations with damping
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Modeling and analysis of random and stochastic input flows in the chemostat model
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Hierarchies and Hamiltonian structures of the Nonlinear Schrödinger family using geometric and spectral techniques
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Convex geometry of the carrying simplex for the May-Leonard map
Stephen Baigent
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A comparison of deterministic and stochastic predator-prey models with disease in the predator
Hongxiao Hu, Liguang Xu and Kai Wang
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A note on the convergence of the solution of the Novikov equation
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Dynamical behaviors of stochastic type K monotone Lotka-Volterra systems
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Global analysis of a stochastic TB model with vaccination and treatment
Tao Feng and Zhipeng Qiu
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Polynomial maps with hidden complex dynamics
Xu Zhang and Guanrong Chen
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Discontinuous phenomena in bioreactor system
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$ L^γ$-measure criteria for boundedness in a quasilinear parabolic-elliptic Keller-Segel system with supercritical sensitivity
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Comparison theorem and correlation for stochastic heat equations driven by Lévy space-time white noises
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Analysis and computation of some tumor growth models with nutrient: From cell density models to free boundary dynamics
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The maximum surplus before ruin in a jump-diffusion insurance risk process with dependence
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Inverse parameter-dependent Preisach operator in thermo-piezoelectricity modeling
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Uniqueness of traveling front solutions for the Lotka-Volterra system in the weak competition case
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Attractivity of saturated equilibria for Lotka-Volterra systems with infinite delays and feedback controls
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Bounds on the Hausdorff dimension of random attractors for infinite-dimensional random dynamical systems on fractals
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Interlocked multi-node positive and negative feedback loops facilitate oscillations
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Bifurcation solutions of Gross-Pitaevskii equations for spin-1 Bose-Einstein condensates
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Invariance principle in the singular perturbations limit
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Mild solutions to the time fractional Navier-Stokes delay differential inclusions
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The Vlasov-Navier-Stokes equations as a mean field limit
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A new proof of the competitive exclusion principle in the chemostat
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Uniqueness and traveling waves in a cell motility model
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Rate of attraction for a semilinear thermoelastic system with variable coefficients
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A new model of groundwater flow within an unconfined aquifer: Application of Caputo-Fabrizio fractional derivative
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A blow-up criterion for three-dimensional compressible magnetohydrodynamic equations with variable viscosity
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Pointwise wave behavior of the initial-boundary value problem for the nonlinear damped wave equation in $\mathbb{R}_{+}^{n} $
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Stochastic invariance for neutral functional differential equation with non-lipschitz coefficients
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On the global convergence of frequency synchronization for Kuramoto and Winfree oscillators
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Global existence and blowup on the energy space for the inhomogeneous fractional nonlinear Schrödinger equation
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Global existence and boundedness of solution of a parabolic-parabolic-ODE chemotaxis-haptotaxis model with (generalized) logistic source
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Weighted exponential stability of stochastic coupled systems on networks with delay driven by $ G $-Brownian motion
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Pullback attractors for bi-spatial continuous random dynamical systems and application to stochastic fractional power dissipative equation on an unbounded domain
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Complex dynamics in a discrete-time size-structured chemostat model with inhibitory kinetics
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Global boundedness in a quasilinear fully parabolic chemotaxis system with indirect signal production
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Existence of ground state solutions for the planar axially symmetric Schrödinger-Poisson system
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The diffusive model for Aedes aegypti mosquito on a periodically evolving domain
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Stochastic one layer shallow water equations with Lévy noise
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The Magneto–Hydrodynamic equations: Local theory and blow-up of solutions
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Construction of a contraction metric by meshless collocation
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The Mandelbrot-van Ness fractional Brownian motion is infinitely differentiable with respect to its Hurst parameter
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Analysis of multilevel Monte Carlo path simulation using the Milstein discretisation
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Multiobjective model predictive control for stabilizing cost criteria
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Some regularity results for a double time-delayed 2D-Navier-Stokes model
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