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Centered around dynamics, DCDSB 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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TOP 10 Most Read Articles in DCDSB, May 2015
1 
Positive feedback control of RayleighBénard convection
Volume 3, Number 4, Pages: 619  642, 2003
B. A. Wagner,
Andrea L. Bertozzi
and L. E. Howle
Abstract
Full Text
Related Articles
We consider the problem of active feedback control of RayleighBénard convection via shadowgraphic measurement.
Our theoretical studies show, that when the feedback control is
positive, i.e. is
tuned to advance the onset of convection, there is a critical
threshold beyond which the system becomes linearly illposed
so that shortscale disturbances are greatly amplified.
Experimental observation suggests that finite size effects become
important and we develop a theory to explain these contributions.
As an efficient modelling tool for studying the dynamics of such a
controlled pattern forming system, we use a Galerkin approximation
to derive a dimension reduced model.

2 
Modelling the dynamics of endemic malaria in growing populations
Volume 4, Number 4, Pages: 1173  1202, 2004
G.A. Ngwa
Abstract
Full Text
Related Articles
A mathematical model for endemic malaria involving variable human
and mosquito populations is analysed. A threshold parameter $R_0$ exists
and the disease can persist if and only if $R_0$ exceeds $1$. $R_0$ is seen to be a generalisation
of the basic reproduction ratio associated with the RossMacdonald
model for malaria transmission. The disease free equilibrium always exist and
is globally stable when $R_0$ is below $1$. A perturbation analysis is used to approximate
the endemic equilibrium in the important case where the disease
related death rate is nonzero, small but significant. A diffusion approximation
is used to approximate the quasistationary distribution of the associated stochastic
model. Numerical simulations show that when $R_0$ is distinctly greater
than $1$, the endemic deterministic equilibrium is globally stable. Furthermore,
in quasistationarity, the stochastic process undergoes oscillations about
a mean population whose size can be approximated by the stable endemic
deterministic equilibrium.

3 
Approximation of attractors of nonautonomous dynamical systems
Volume 5, Number 2, Pages: 215  238, 2005
Bernd Aulbach,
Martin Rasmussen
and Stefan Siegmund
Abstract
Full Text
Related Articles
This paper is devoted to the numerical approximation of attractors. For general nonautonomous dynamical systems we first introduce a new
type of attractor which includes some classes of noncompact attractors such as
unbounded unstable manifolds. We then adapt two cell mapping algorithms
to the nonautonomous setting and use the computer program GAIO for the
analysis of an explicit example, a twodimensional system of nonautonomous
difference equations. Finally we present numerical data which indicate a bifurcation of nonautonomous attractors in the Duffingvan der Pol oscillator.

4 
A spectral formulation of the Nekhoroshev theorem and its relevance for numerical and experimental data analysis
Volume 1, Number 1, Pages: 1  28, 2001
Massimiliano Guzzo
and Giancarlo Benettin
Abstract
Full Text
Related Articles
In this paper we provide an analytical characterization of the Fourier spectrum of
the solutions of quasiintegrable Hamiltonian systems, which completes the Nekhoroshev theorem
and looks particularly suitable to describe resonant motions. We also discuss the application of
the result to the analysis of numerical and experimental data. The comparison of the rigorous
theoretical estimates with numerical results shows a quite good agreement. It turns out that an
observation of the spectrum for a relatively short time scale (of order $1/\sqrt{\varepsilon}$, where $\varepsilon$ is a natural
perturbative parameter) can provide information on the behavior of the system for the much larger
Nekhoroshev times.

5 
On the box method for a nonlocal parabolic variational inequality
Volume 1, Number 1, Pages: 71  88, 2001
Walter Allegretto,
Yanping Lin
and Shuqing Ma
Abstract
Full Text
Related Articles
In this paper we study a box scheme (or finite volume element method) for a
nonlocal nonlinear parabolic variational inequality arising in the study
of thermistor problems. Under some assumptions on
the data and regularity of the solution, optimal error estimates in the
$H^1$norm are attained.

6 
Sufficient conditions for stability of linear differential equations with distributed delay
Volume 1, Number 2, Pages: 233  256, 2001
Samuel Bernard,
Jacques Bélair
and Michael C Mackey
Abstract
Full Text
Related Articles
We develop conditions for the stability of the constant (steady
state) solutions oflinear delay differential equations with distributed delay
when only information about the moments of the density of delays is available.
We use Laplace transforms to investigate the properties of different distributions
of delay. We give a method to parametrically determine the boundary
of the region of stability, and sufficient conditions for stability based on the
expectation of the distribution of the delay. We also obtain a result based
on the skewness of the distribution. These results are illustrated on a recent
model of peripheral neutrophil regulatory system which include a distribution
of delays. The goal of this paper is to give a simple criterion for the stability
when little is known about the distribution of the delay.

7 
Bifurcations of an SIRS epidemic model with nonlinear
incidence rate
Volume 15, Number 1, Pages: 93  112, 2010
Zhixing Hu,
Ping Bi,
Wanbiao Ma
and Shigui Ruan
Abstract
References
Full Text
Related Articles
The main purpose of this paper is to explore the dynamics of an
epidemic model with a general nonlinear incidence
$\beta SI^p/(1+\alpha I^q)$. The existence and stability
of multiple endemic equilibria of the epidemic model are analyzed.
Local bifurcation theory is applied to explore the rich dynamical
behavior of the model. Normal forms of the model are derived for
different types of bifurcations, including Hopf and BogdanovTakens
bifurcations. Concretely speaking, the first Lyapunov coefficient is
computed to determine various types of Hopf bifurcations. Next,
with the help of the BogdanovTakens normal form, a family of
homoclinic orbits is arising when a Hopf and a saddlenode
bifurcation merge. Finally, some numerical results and simulations
are presented to illustrate these theoretical results.

8 
Solitary waves in nonlinear dispersive systems
Volume 2, Number 3, Pages: 313  378, 2002
Jerry Bona
and Hongqiu Chen
Abstract
Full Text
Related Articles
Evolution equations that feature both nonlinear and dispersive effects
often possess solitarywave solutions. Exact theory for such waves has been developed
and applied to single equations of Kortewegde Vries type, Schrödingertype and
regularized longwavetype for example. Much less common has been the analysis of
solitarywave solutions for systems of equations. The present paper is concerned with
solitary travellingwave solutions to systems of equations arising in fluid mechanics
and other areas of science and engineering. The aim is to show that appropriate
modification of the methods coming to the fore for single equations may be effectively
applied to systems as well. This contention is demonstrated explicitly for the Gear
Grimshaw system modeling the interaction of internal waves and for the Boussinesq
systems that arise in describing the twoway propagation of longcrested surface
water waves.

9 
Stable transport of information near essentially unstable localized structures
Volume 4, Number 2, Pages: 349  390, 2004
Thierry Gallay,
Guido Schneider
and Hannes Uecker
Abstract
Full Text
Related Articles
When the steady states at infinity become unstable through a
pattern forming bifurcation, a travelling wave may bifurcate
into a modulated front which is timeperiodic in a moving
frame. This scenario has been studied by B. Sandstede and A. Scheel
for a class of reactiondiffusion systems on the real line.
Under general assumptions, they showed that the modulated
fronts exist and are spectrally stable near the bifurcation
point. Here we consider a model problem for which
we can prove the nonlinear stability of these solutions with
respect to small localized perturbations.
This result does not follow from the spectral stability, because
the linearized operator around the modulated front has essential
spectrum up to the imaginary axis. The analysis is illustrated by
numerical simulations.

10 
Population dynamics of sea bass and young sea bass
Volume 4, Number 3, Pages: 833  840, 2004
Masahiro Yamaguchi,
Yasuhiro Takeuchi
and Wanbiao Ma
Abstract
Full Text
Related Articles
This paper considers population dynamics of sea bass and young sea
bass which are modeled by stagestructured delaydifferential
equations. It is shown that time delay can stabilize the dynamics.
That is, as time delay increases, system becomes periodic and stable
even if system without time delay is chaotic.

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