Recent Advances in Applied Nonlinear Dynamics with Numerical Analysis

Fractional Dynamics, Network Dynamics, Classical Dynamics and Fractal Dynamics with Their Numerical Simulations

Nonlinear dynamics is still a hot and challenging topic. In this edited book, we focus on fractional dynamics, infinite dimensional dynamics defined by the partial differential equation, network dynamics, fractal dynamics, and their numerical analysis and simulation.

Fractional dynamics is a new topic in the research field of nonlinear dynamics which has attracted increasing interest due to its potential applications in the real world, such as modeling memory processes and materials. In this part, basic theory for fractional differential equations and numerical simulations for these equations will be introduced and discussed.

In the infinite dimensional dynamics part, we emphasize on numerical calculation and theoretical analysis, including constructing various numerical methods and computing the corresponding limit sets, etc.

In the last part, we show interest in network dynamics and fractal dynamics together with numerical simulations as well as their applications.

Contents:

• Gronwall Inequalities (Fanhai Zeng, Jianxiong Cao and Changpin Li)
• Existence and Uniqueness of the Solutions to the Fractional Differential Equations (Yutian Ma, Fengrong Zhang and Changpin Li)
• Finite Element Methods for Fractional Differential Equations (Changpin Li and Fanhai Zeng)
• Fractional Step Method for the Nonlinear Conservation Laws with Fractional Dissipation (Can Li and Weihua Deng)
• Error Analysis of Spectral Method for the Space and Time Fractional Fokker–Planck Equation (Tinggang Zhao and Haiyan Xuan)
• A Discontinuous Finite Element Method for a Type of Fractional Cauchy Problem (Yunying Zheng)
• Asymptotic Analysis of a Singularly Perturbed Parabolic Problem in a General Smooth Domain (Yu-Jiang Wu, Na Zhang and Lun-Ji Song)
• Incremental Unknowns Methods for the ADI and ADSI Schemes (Ai-Li Yang, Yu-Jiang Wu and Zhong-Hua Yang)
• Stability of a Collocated FV Scheme for the 3D Navier–Stokes Equations (Xu Li and Shu-qin Wang)
• Computing the Multiple Positive Solutions to p–Henon Equation on the Unit Square (Zhaoxiang Li and Zhonghua Yang)
• Multilevel WBIUs Methods for Reaction–Diffusion Equations (Yang Wang, Yu-Jiang Wu and Ai-Li Yang)
• Models and Dynamics of Deterministically Growing Networks (Weigang Sun, Jingyuan Zhang and Guanrong Chen)
• On Different Approaches to Synchronization of Spatiotemporal Chaos in Complex Networks (Yuan Chai and Li-Qun Chen)
• Chaotic Dynamical Systems on Fractals and Their Applications to Image Encryption (Ruisong Ye, Yuru Zou and Jian Lu)
• Planar Crystallographic Symmetric Tiling Patterns Generated From Invariant Maps (Ruisong Ye, Haiying Zhao and Yuanlin Ma)
• Complex Dynamics in a Simple Two-Dimensional Discrete System (Huiqing Huang and Ruisong Ye)
• Approximate Periodic Solutions of Damped Harmonic Oscillators with Delayed Feedback (Qian Guo)
• The Numerical Methods in Option Pricing Problem (Xiong Bo)
• Synchronization and Its Control Between Two Coupled Networks (Yongqing Wu and Minghai Lü)

Readership: Senior undergraduates, postgraduates and experts in nonlinear dynamics with numerical analysis.
Key Features:

• The topics in this edited book are very hot and highly impressive
• Issues and methods of such topics in this edited book have not been made available yet
• The present edited book is suitable for various levels of researchers, such as senior undergraduates, postgraduates, and experts