edited by Yisong Yang (Polytechnic Institute of New York University, USA) , Xinchu Fu (Shanghai University, China) , & Jinqiao Duan (Illinois Institute of Technology, USA)

Mathematical sciences have been playing an increasingly important role in modern society. They are in high demand for investigating complex problems in physical science, environmental and geophysical sciences, materials science, life science and chemical sciences.

This is a review volume on some timely and interesting topics in applied mathematical sciences. It surveys new developments and presents some future research directions in these topics. The chapters are written by experts in these fields, with a wide audience in mind and hence will be accessible to graduate students, junior researchers and other professionals who are interested in the subjects. The contributions of Professor Youzhong Guo, a leading expert in these areas, will be celebrated. His life and academic achievements are highlighted in the Preface and Postscript of the book. The underlying theme that binds the various chapters seamlessly is a set of dedicated ideas and techniques from partial differential equations and dynamical systems.

• Bifurcation Analysis of the Swift–Hohenberg Equation
• Canonical Sample Spaces for Random Dynamical Systems
• Lattice Boltzmann Simulation of Nonlinear Schrödinger Equation
• Perspectives in Nonlinear Dynamics
• Subharmonic Bifurcation and Chaos for MEMs Models
• Exponential Stability of Nonlocal Time-Delayed Burgers Equation
• Mathematical Modeling in Traffic Flow Research
• Spreading Dynamics on Complex Networks
• Chaotic Dynamics for the Two-Component Bose–Einstein Condensate System
• Harmonic Representation of Topological Classes
• Nonlinear Analysis of Problems in Cold Plasma Physics
• Yang–Mills Instantons and Gravitation