## 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
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

MBE

Symmetric evolutionary games, i.e., evolutionary games with symmetric fitness matrices, have important applications in population genetics, where they can be used to model for example the selection and evolution of the genotypes of a given population. In this paper, we review the theory for obtaining optimal and stable strategies for symmetric evolutionary games, and provide some new proofs and computational methods. In particular, we review the relationship between the symmetric evolutionary game and the generalized knapsack problem, and discuss the first and second order necessary and sufficient conditions that can be derived from this relationship for testing the optimality and stability of the strategies. Some of the conditions are given in different forms from those in previous work and can be verified more efficiently. We also derive more efficient computational methods for the evaluation of the conditions than conventional approaches. We demonstrate how these conditions can be applied to justifying the strategies and their stabilities for a special class of genetic selection games including some in the study of genetic disorders.

PROC

The authors study a type of nonlinear fractional boundary value problem with nonlocal boundary conditions. An associated Green's function is constructed. Then a criterion for the existence of at least one positive solution is obtained by using fixed point theory on cones.

PROC

In this paper, by using the dual least action principle, the authors investigate the existence of solutions to a multi-point boundary value problem for a second-order differential system with $p$-Laplacian.

PROC

Sufficient conditions are obtained for the existence of multiple solutions to the
discrete fourth order periodic boundary value problem
\begin{equation*}
\begin{array}{l}
\Delta^4 u(t-2)-\Delta(p(t-1)\Delta u(t-1))+q(t) u(t)=f(t,u(t)),\quad t\in [1,N]_{\mathbb{Z}},\\
\Delta^iu(-1)=\Delta^iu(N-1),\quad i=0, 1,2, 3.
\end{array}
\end{equation*}
Our analysis is mainly based on the variational method and critical point theory.
One example is included to illustrate the result.

DCDS-B

The reaction-diffusion system for an $SIR$ epidemic model with a free boundary is studied. This model describes a transmission of diseases. The existence, uniqueness and estimates of the global solution are discussed first. Then some sufficient conditions for the disease vanishing are given. With the help of investigating the long time behavior of solution to the initial and boundary value problem in half space, the long time behavior of the susceptible population $S$ is obtained for the disease vanishing case.

DCDS-B

In this paper, we consider a mathematical model for a prey-predator
dynamical system with diffusion and trophic interactions of three
levels. In this model, a general trophic function based on the ratio
between the prey and a linear function of the predator is used at
each level. At the two limits of this trophic function, one recovers
the classical prey-dependent and ratio-dependent predation models,
respectively. We offer a complete discussion of the dynamical
behavior of the model under the homogeneous Neumann boundary
condition (the same behavior is also seen in the absence of
diffusion). We also discuss existence, uniqueness, stability and
bifurcation of equilibrium behavior corresponding to positive steady
state solutions under the homogeneous Dirichlet boundary condition.
Finally, we give interpretations of some of these results in the
context of different predation models.

PROC

We study an elliptic system arising from a prey-predator model, where
cross diffusions are included to reflect the influences of density gradients of prey and
predator toward the fluxes of underlying populations. We establish existence and
non{existence of non{constant positive solutions, or the possible pattern of popula-
tion distribution.

JIMO

This paper develops a model to determine an optimal replenishment
policy with defective items and shortage backlogging under
conditions of permissible delay of payments. It is assumed that
100% of each lot are screened to separate good and defective items
which are classified as imperfect quality and scrap items.
Difference between unit selling price and unit purchase cost is also
included in our mathematical model and analysis. Under this
assumption, we model the retailer's inventory system as an expected
profit maximization problem to determine the retailer's optimal
inventory cycle time and optimal order quantity. Then, a theorem is
established to describe the optimal replenishment policy for the
retailer. Finally, numerical examples are given to illustrate the
theorem and obtain some managerial phenomena.

DCDS

Existence, uniqueness, and stability of
Heaviside function like solutions
of a Keller and Segel's minimal chemotaxis model
are established when a chemotaxis parameter is large enough.
Asymptotic expansions of the solution
in terms of the large chemotaxis parameter are also derived.

PROC

Using the variational method and critical point theory, the authors study the existence of infinitely many homoclinic solutions to the difference equation
\begin{equation*}
-\Delta \big(a(k)\phi_p(\Delta u(k-1))\big)+b(k)\phi_p(u(k))=\lambda f(k,u(k))),\quad k\in\mathbb{Z},
\end{equation*}
where $p>1$ is a real number, $\phi_p(t)=|t|^{p-2}t$ for $t\in\mathbb{R}$,
$\lambda>0$ is a parameter, $a, b:\mathbb{Z}\to (0,\infty)$, and
$f: \mathbb{Z}\times\mathbb{R}\to\mathbb{R}$ is continuous in the second variable.
Related results in the literature are extended.

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