Theoretical and computational advances in nonlinear dynamical systems

Zhi Yuan Sun*, Panayotis G. Kevrekidis, Xin Yu, K. Nakkeeran

*Corresponding author for this work

Research output: Contribution to journalEditorialpeer-review

1 Citation (Scopus)

Abstract

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.
Original languageEnglish
Article number3925964
JournalAdvances in Mathematical Physics
Volume2017
DOIs
Publication statusPublished - 4 Jun 2017

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