## 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

Research articles contributed to this issue explore a large variety of topics and present many of the advances in the field of differential equations, dynamical systems and mathematical modeling, with emphasis on newly developed theory and techniques on analysis of nonlinear systems, as well as applications in natural science and engineering. These contributions not only present valuable new results, ideas and techniques in nonlinear systems, but also formulate a few open questions which may stimulate further study in this area. We would like to thank the authors for their excellent contributions, the referees for their tireless efforts in reviewing the manuscripts and making suggestions, and the chief editors of DCDS-S for making this issue possible. We hope that these works will help the readers and researchers to understand and make future progress in the field of nonlinear analysis and mathematical modeling.

This paper is concerned with traveling waves for temporally delayed, spatially discrete reaction-diffusion equations without quasi-monotonicity. We first establish the existence of non-critical traveling waves (waves with speeds *c*>*c*_{*}, where *c*_{*} is minimal speed). Then by using the weighted energy method with a suitably selected weight function, we prove that all noncritical traveling waves *Φ*(*x*+*ct*) (monotone or nonmonotone) are time-asymptotically stable, when the initial perturbations around the wavefronts in a certain weighted Sobolev space are small.

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In this paper, we are concerned with a time periodic and diffusivepredator-prey model with disease transmission in the prey. Firstwe consider a $ SI $ model when the predator species is absent. Byintroducing the basic reproduction number for the $ SI $ model, weshow the sufficient conditions for the persistence and extinctionof the disease. When the presence of the predator is taken intoaccount, a number of sufficient conditions for the co-existence ofthe prey and predator species, the global extinction of predatorspecies and the global extinction of both the prey and predatorspecies are given.

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