As we all know, many biological and physical systems, such as neuronal systems and
disease systems, are featured by certain nonlinear and complex patterns in their elements
and networks. These phenomena carry significant biological and physical information
and regulate down-stream mechanism in many instances. This issue of Discrete and Continuous Dynamical Systems, Series S,
comprises a collection of recent works in the general area of nonlinear differential equations
and dynamical systems, and related applications in mathematical biology and
engineering. The common themes of this issue include theoretical analysis, mathematical models, computational and statistical
methods on dynamical systems and differential equations, as well as applications in fields of neurodynamics, biology, and engineering etc.
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.