Theoretical and Computational Advances in Nonlinear Dynamical Systems

The theory of dynamical systems is a paradigm for studying various scientific phenomena, ranging from complex atomic lattices to planetary motion, from water waves to weather systems, from chemical reaction to biological behaviors, and many more. Relevant applications have widely arisen in multidisciplinary fields including mathematics, physics, chemistry, biology, and even economics and sociology. Due to the rapid development of theoretical and computational techniques in recent years, the role of nonlinearity in dynamical systems has attracted increasing interest and has been intensely investigated. Typical research areas include spatial and temporal evolution of nonlinear systems, pattern formation and their interactions, localized solutions and stability analysis, and many others. At the same time, the mathematical tools, for both of the symbolic and numerical aspects, have been developed in dealing with the nonlinear dynamical systems qualitatively and quantitatively. On the other hand, complexity of the nonlinear dynamical systems can be further portrayed when chaotic and stochastic behaviors are revealed. Interplay between nonlinearity and randomness is also a highlight topic which can be simulated and studied by modern computational resources. Focusing on the nonlinearity of dynamical systems, this special issue has receivedmore than 30 submissions, 12 papers of which have been accepted after strict review process.These papers cover works from theoretical analysis to applications in chaotic systems, fluid dynamics, solid mechanics, and stochastic and economical systems. Mathematical methods to analyze and obtain exact solutions for types of nonlinear dynamical systems have been included in our issue as well. A brief summarywill be presented in the following sections.We expect these articles, including their substantial bibliographic resources, to be of great interest to the scholars in the relevant scientific and engineering communities.