## Journals

- Advances in Mathematics of Communications
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- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

DCDS-S

We analyze a competition model of two phytoplankton species for a
single nutrient with internal storage and light in a well mixed
aquatic environment. We apply the theory of monotone dynamical
system to determine the outcomes of competition: extinction of two
species, competitive exclusion, stable coexistence and bistability
of two species. We also present the graphical presentation to
classify the competition outcomes and to compare outcome of models with
and without internal storage.

DCDS-B

A discrete-delayed model of plasmid-bearing,
plasmid-free organisms competing for a single-limited nutrient in
a chemostat is established. Rigorous mathematical
analysis of the asymptotic behavior of this model is presented.
An interesting method to analyze the local stability of interior
equilibrium is developed. The argument is also applicable to a model of
plasmid-bearing, plasmid-free organisms competing for two
complementary nutrients in a chemostat.

keywords:
chemostat
,
plasmid-bearing
,
global attractivity.
,
plasmid-free
,
Delayed growth response
,
perturbation

CPAA

In this paper we construct a mathematical model of two microbial
populations competing for a single-limited nutrient with internal
storage in an unstirred chemostat. First we establish the existence
and uniqueness of steady-state solutions for the single population.
The conditions for the coexistence of steady states are determined.
Techniques include the maximum principle, theory of bifurcation and
degree theory in cones.

DCDS

This paper is concerned with the classical Nicholson-Bailey model [15] defined by $f_\lambda(x,y)=(y(1-e^{-x}), \lambda y
e^{-x})$. We show that for $\lambda=1$ a heteroclinic foliation exists and for $\lambda>1$ global strict oscillations take place.
The important phenomenon of delay of stability loss is established for a general
class of discrete dynamical systems, and it is applied to the study of nonexistence of periodic orbits for the Nicholson-Bailey model.

DCDS-B

It is known that some predator-prey system can possess a unique
limit cycle which is globally asymptotically stable. For a
prototypical predator-prey system, we show that the solution curve
of the limit cycle exhibits temporal patterns of a relaxation
oscillator, or a Heaviside function, when certain parameter is
small.

DCDS-B

The dynamics of a reaction-diffusion system for two species of microorganism in an unstirred chemostat with internal storage is studied. It is shown that the diffusion coefficient is a key parameter of determining the asymptotic dynamics, and there exists a threshold diffusion coefficient above which both species become extinct. On the other hand, for diffusion coefficient below the threshold, either one species or both species persist, and in the asymptotic limit, a steady state showing competition exclusion or coexistence is reached.

DCDS-B

Competition between species for resources is a fundamental ecological process,
which can be modeled by the mathematical models in the chemostat culture or in the water column. The chemostat-type models for resource competition have been extensively analyzed. However, the study on the competition for resources in the water column has been relatively neglected as a result of some technical difficulties.
We consider a resource competition model with two species in the water column. Firstly, the global existence
and $L^\infty$ boundedness of solutions to the model are established by inequality estimates. Secondly, the uniqueness of
positive steady state solutions and some dynamical behavior of the single population model are attained by degree theory and uniform
persistence theory. Finally, the structure of the coexistence solutions of the two-species system is investigated by
the global bifurcation theory.

DCDS-B

In this paper, we analyze the damped Duffing equation by means of
qualitative theory of planar systems. Under certain parametric
choices, the global structure in the Poincaré phase plane of an
equivalent two-dimensional autonomous system is plotted. Exact
solutions are obtained by using the Lie symmetry and the coordinate
transformation method, respectively. Applications of the second
approach to some nonlinear evolution equations such as the
two-dimensional dissipative Klein-Gordon equation are illustrated.

keywords:
equilibrium point
,
Duffing's equation
,
global structure
,
autonomous system
,
phase plane
,
Lie symmetry.

DCDS-B

Competitions between different interactions in strongly correlated electron systems often lead to exotic phases. Renormalization group is one of the powerful techniques to analyze the competing interactions without presumed bias. It was recently shown that the renormalization group transformations to the one-loop order in many correlated electron systems are described by potential flows. Here we prove several rigorous theorems in the presence of renormalization-group potential and find the complete classification for the potential flows. In addition, we show that the relevant interactions blow up at the maximal scaling exponent of unity, explaining the puzzling power-law Ansatz found in previous studies. The above findings are of great importance in building up the hierarchy for relevant couplings and the complete classification for correlated ground states in the presence of generic interactions.

DCDS-B

This volume is dedicated to the memory of Paul Waltman. Many of the authors of articles contained here were participants
at the NCTS International Conference on Nonlinear Dynamics with Applications to Biology held
May 28-30, 2014 at National Tsing-Hua University, Hsinchu, Taiwan. The purpose of the conference was to survey new developments
in nonlinear dynamics and its applications to biology and to honor the memory of Professor Paul Waltman for his influence on the development of Mathematical Biology and Dynamical Systems.
Attendees at the conference included Paul's sons Fred and Dennis, many of Paul's former doctoral and post-doctoral students, many others who,
although not students of Paul, nevertheless were recipients of Paul's valuable advice and council, and many colleagues from all over the world
who were influenced by Paul's mathematics and by his personality. We thank the NCTS for its financial support of the conference and Dr. J.S.W. Wong
for supporting the conference banquet.

For more information please click the “Full Text” above.

For more information please click the “Full Text” above.

keywords:

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