## 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
- Electronic Research Announcements
- Conference Publications
- AIMS Mathematics

DCDS

Entropy sets are defined both topologically and for a
measure. The set of topological entropy sets is
the union of the sets of entropy sets for all invariant measures.
For a topological system $(X,T)$ and an invariant measure $\mu$ on
$(X,T)$, let $H(X,T)$ (resp. $H^\mu(X,T)$) be the closure of the
set of all entropy sets (resp. $\mu$- entropy sets) in the
hyperspace $2^X$. It is shown that if $h_{\text{top}}(T)>0$ (resp.
$h_\mu(T)>0$), the subsystem $(H(X,T),\hat{T})$ (resp.
$(H^\mu(X,T),\hat{T}))$ of $(2^X,\hat{T})$ has an
invariant measure with full support and infinite topological
entropy.

Weakly mixing sets and partial mixing of dynamical systems are introduced and characterized. It is proved that if $h_{\text{top}}(T)>0$ (resp. $h_\mu(T)>0$) the set of all weakly mixing entropy sets (resp. $\mu$-entropy sets) is a dense $G_\delta$ in $H(X,T)$ (resp. $H^\mu(X,T)$). A Devaney chaotic but not partly mixing system is constructed.

Concerning entropy capacities, it is shown that when $\mu$ is ergodic with $h_\mu(T)>0$, the set of all weakly mixing $\mu$-entropy sets $E$ such that the Bowen entropy $h(E)\ge h_\mu(T)$ is residual in $H^\mu(X,T)$. When in addition $(X,T)$ is uniquely ergodic the set of all weakly mixing entropy sets $E$ with $h(E)=h_{\text{top}}(T)$ is residual in $H(X,T)$.

Weakly mixing sets and partial mixing of dynamical systems are introduced and characterized. It is proved that if $h_{\text{top}}(T)>0$ (resp. $h_\mu(T)>0$) the set of all weakly mixing entropy sets (resp. $\mu$-entropy sets) is a dense $G_\delta$ in $H(X,T)$ (resp. $H^\mu(X,T)$). A Devaney chaotic but not partly mixing system is constructed.

Concerning entropy capacities, it is shown that when $\mu$ is ergodic with $h_\mu(T)>0$, the set of all weakly mixing $\mu$-entropy sets $E$ such that the Bowen entropy $h(E)\ge h_\mu(T)$ is residual in $H^\mu(X,T)$. When in addition $(X,T)$ is uniquely ergodic the set of all weakly mixing entropy sets $E$ with $h(E)=h_{\text{top}}(T)$ is residual in $H(X,T)$.

DCDS

The topological pressure is defined for
sub-additive potentials via separated sets and open covers
in general compact dynamical systems. A variational principle for
the topological pressure is set up without any additional
assumptions. The relations between different approaches in defining
the topological pressure are discussed. The result will have some potential applications in the multifractal analysis of iterated function systems with overlaps, the distribution of Lyapunov exponents and the dimension theory in dynamical systems.

DCDS-B

By constructing an invariant set in the
three dimensional space, we establish the existence of
traveling wave solutions to a reaction-diffusion-chemotaxis model describing biological processes such as the bacterial chemotactic movement in response to oxygen
and the initiation of angiogenesis. The minimal wave speed is
shown to exist and the role of each process of reaction, diffusion and chemotaxis in the wave propagation is investigated. Our results reveal three essential biological implications: (1) the cell growth increases the wave speed; (2) the chemotaxis must be strong enough to make a contribution to the increment of the wave speed; (3) the diffusion rate plays a role in increasing the wave speed only when the cell growth is present.

MBE

Recently an SIS epidemic reaction-diffusion model with Neumann (or no-flux) boundary condition has been proposed and studied by several authors to understand the dynamics of disease transmission in a spatially heterogeneous environment in which the individuals are subject to a random movement. Many important and interesting properties have been obtained: such as the role of diffusion coefficients in defining the reproductive number; the global stability of disease-free equilibrium; the existence and uniqueness of a positive endemic steady; global stability of endemic steady for some particular cases; and the asymptotical profiles of the endemic steady states as the diffusion coefficient for susceptible individuals is sufficiently small. In this research we will study two modified SIS diffusion models with the Dirichlet boundary condition that reflects a hostile environment in the boundary. The reproductive number is defined which plays an essential role in determining whether the disease will extinct or persist. We have showed that the disease will die out when the reproductive number is less than one and that the endemic equilibrium occurs when the reproductive number is exceeds one. Partial result on the global stability of the endemic equilibrium is also obtained.

DCDS-B

In this paper, we study the traveling wave
solutions of an SIS reaction-diffusion epidemic model. The
techniques of qualitative analysis has been developed which enable
us to show the existence of traveling wave solutions connecting the
disease-free equilibrium point and an endemic equilibrium point. In
addition, we also find the precise value of the minimum speed that
is significant to study the spreading speed of the population
towards to the endemic steady state.

BDIA

It is usually true that adding explanatory variables into a probability model increases association degree yet risks losing statistical reliability. In this article, we propose an approach to merge classes within the categorical explanatory variables before the addition so as to keep the statistical reliability while increase the predictive power step by step.

keywords:
Association
,
categorical data
,
category merging
,
statistical reliability
,
predictive power

BDIA

A bias-variance dilemma in categorical data mining and analysis is the fact that a prediction method can aim at either maximizing the overall point-hit accuracy without constraint or with the constraint of minimizing the distribution bias. However, one can hardly achieve both at the same time. A scheme to balance these two prediction objectives is proposed in this article. An experiment with a real data set is conducted to demonstrate some of the scheme's characteristics. Some basic properties of the scheme are also discussed.

MBE

For a reaction-diffusion model of microbial flow reactor with two
competing populations, we show the coexistence of weakly coupled traveling
wave solutions in the sense that one organism undergoes a population growth
while another organism remains in a very low population density in the first
half interval of the space line; the population densities then exchange the
position in the next half interval. This type of traveling wave can occur only
if the input nutrient slightly exceeds the maximum carrying capacity for these
two populations. This means, lacking an adequate nutrient, two competing
organisms will manage to survive in a more economical way.

CPAA

This paper is concerned with the existence of soliton solutions for a quasilinear Schrödinger equation in $R^N$
with critical exponent, which appears from modelling the self-channeling of a high-power ultrashort
laser in matter. By working with a perturbation approach which was initially proposed in [26],
we prove that the given problem has a positive ground state solution.

DCDS

Consider a reaction-diffusion model for a microbial flow reactor
with two competing species. Suppose that the amount of nutrient is
input in a constant velocity at one end of the flow reactor and is
washed out at the other end of the reactor. We study the dynamical
behavior of population growth of these two species. In particular we
are interested in the problem on the coexistence of traveling waves
that best describes the long time dynamical behavior. By developing
shooting method and continuation argument with the aid of an
appropriately Liapunov function, we obtain the sufficient conditions
for the coexistence of traveling waves as well as the minimum wave
speed.

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]