## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- 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
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- Numerical Algebra, Control & Optimization
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

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-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

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:

DCDS-B

Predator-prey models with Hassell-Varley type functional response are appropriate for interactions where predators form groups and have applications in biological control. Here we present a systematic global qualitative analysis to a general predator-prey model with Hassell-Varley type functional response. We show that the predator free equilibrium is a global attractor only when the predator death rate is greater than its growth ability. The positive equilibrium exists if the above relation reverses. In cases of practical interest, we show that the local stability of the positive steady state implies its global stability with respect to positive solutions. For terrestrial predators that form a fixed number of tight groups, we show that the existence of an unstable positive equilibrium in the predator-prey model implies the existence of an unique nontrivial positive limit cycle.

DCDS-B

In this paper we study a mathematical model of two parallel food
chains in a chemostat. Each food chain consists of a prey species
$x$ and a predator species $y$. Two food chains are symmetric in the
sense that the prey species are identical and so are the specialized
predator species. We assume that both of the prey species in the
parallel food chains share the same nutrient $R$. In this paper we
show that as the input concentration $R^{(0)}$ of the nutrient
varies, there are several possible outcomes: (1) all species go
extinct; (2) only the two prey species survive;
(3) all species coexist at equilibrium; (4) all species coexist in
the form of oscillations. We analyze cases (1)-(3) rigorously; for
case (4) we do extensive numerical studies to present all possible
phenomena, which include limit cycles, heteroclinic cycles, and
chaos.

DCDS-B

In this paper, we analyze a system modeling the growth of single phytoplankton populations in a water column, where population
growth increases monotonically with the nutrient
quota stored within individuals. We establish a threshold result on
the global extinction and persistence of phytoplankton. Condition for persistence is shown to depend on the
principal eigenvalue of a boundary value problem, which is related to the physical transport
properties of the water column (i.e. the diffusivity and the sinking speed), nutrient uptake rate, and growth rate.

keywords:
threshold dynamics
,
spatial variations
,
internal storage
,
Steady states
,
a water column.

DCDS-B

Recent years have seen dramatic increase in the number and variety of new mathematical models describing biological processes. Many of these models are formulated in terms of systems of partial differential equations. Relevant biological questions give rise to interesting questions regarding properties of the solutions of these equations. The present volume includes eleven articles, each describing a set of problems and results in PDEs inspired by biology. Although in many instances the mathematical analysis may help to better understand the underlying biological processes, the emphasis here is on new mathematical ideas and new mathematical results. The goal is to demonstrate the broad spectrum of new PDE theories that are emerging on the border of two fields: biology and mathematics.

For more information please click the "Full Text" above.

For more information please click the "Full Text" above.

keywords:

## Year of publication

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