RECENT ADVANCES IN APPLIED NONLINEAR DYNAMICS WITH NUMERICAL ANALYSIS:FRACTIONAL DYNAMICS, NETWORK DYNAMICS, CLASSICAL DYNAMICS AND FRACTAL DYNAMICS WITH THEIR NUMERICAL SIMULATIONS

图书简介

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. 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

Gronwall Inequalities; Existence and Uniqueness of Solutions to Fractional Differential Equations; Finite Element Methods for Fractional Partial Differential Equations; Fractional Step Methods for the Nonlinear Conservation Laws with Fractional Dissipation; Error Analysis of Spectral Method for the Space and Time Fractional Fokker–Planck Equation; The Discontinuous Galerkin Solutions for the Time Fractional Nonlinear Cauchy Problem; Numerical Solutions of the Time Fractional Nonlinear Diffusion Equation in R2; Asymptotic Analysis of a Singularly Perturbed Parabolic Problem in a General Smooth Domain; Incremental Unknowns Methods for the Alternating Directional Implicit and Semi-implicit Schemes; Stability of a Collocated Finite Volume Scheme for the Three-dimensional Navier–Stokes Equations; Computing Multiple Solutions to the p–Henon Equation; Multilevel Wavelet-like Block Incremental Unknowns Methods for a Class of Reaction–Diffusion Equations; Models and Applications of Deterministically Growing Networks; On Different Approaches to Synchronization of Spatiotemporal Chaos in Complex Networks: A Case Study; Chaotic Dynamical Systems on Fractals and Their Application to Image Encryption; Approximate Periodic Solutions of a Damped Harmonic Oscillator with Delayed Feedback; The Numerical Methods in Option Pricing Problem; Colorful Images with Group Symmetry From Dynamics; Synchronization and its Control Between Two Coupled Networks.

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