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作者 Li, Changpin
書名 Recent Advances in Applied Nonlinear Dynamics with Numerical Analysis : Fractional Dynamics, Network Dynamics, Classical Dynamics and Fractal Dynamics with Their Numerical Simulations
出版項 Singapore : World Scientific Publishing Co Pte Ltd, 2013
©2013
國際標準書號 9789814436465 (electronic bk.)
9789814436458
book jacket
說明 1 online resource (414 pages)
text txt rdacontent
computer c rdamedia
online resource cr rdacarrier
系列 Recent Advances In Computational Chemistry ; v.15
Recent Advances In Computational Chemistry
附註 Intro -- Contents -- Foreword -- Preface -- 1. Gronwall inequalities Fanhai Zeng, Jianxiong Cao and Changpin Li -- 1.1 Introduction -- 1.2 The continuous Gronwall inequalities -- 1.3 The discrete Gronwall inequalities -- 1.4 The weakly singular Gronwall inequalities -- 1.5 Conclusion -- Bibliography -- 2. Existence and uniqueness of the solutions to the fractional differential equations Yutian Ma, Fengrong Zhang and Changpin Li -- 2.1 Introduction -- 2.2 Preliminaries and notations -- 2.3 Existence and uniqueness of initial value problems for fractional differential equations -- 2.3.1 Initial value problems with Riemann-Liouville derivative -- 2.3.2 Initial value problems with Caputo derivative -- 2.3.3 The positive solution to fractional differential equation -- 2.4 Existence and uniqueness of the boundary value problems -- 2.4.1 Boundary value problems with Riemann-Liouville derivative -- 2.4.2 Boundary value problems with Caputo derivative -- 2.4.3 Fractional differential equations with impulsive boundary conditions -- 2.5 Existence and uniqueness of the fractional differential equations with time-delay -- 2.6 Conclusions -- Bibliography -- 3. Finite element methods for fractional differential equations Changpin Li and Fanhai Zeng -- 3.1 Introduction -- 3.2 Preliminaries and notations -- 3.3 Finite element methods for fractional differential equations -- 3.4 Conclusion -- Bibliography -- 4. Fractional step method for the nonlinear conservation laws with fractional dissipation Can Li and Weihua Deng -- 4.1 Introduction -- 4.2 Fractional step algorithm -- 4.2.1 Discretization of the fractional calculus -- 4.2.2 Discretization of the conservation law -- 4.3 Numerical results -- 4.4 Concluding remarks -- Bibliography -- 5. Error analysis of spectral method for the space and time fractional Fokker-Planck equation Tinggang Zhao and Haiyan Xuan
5.1 Introduction -- 5.2 Preliminaries -- 5.3 Spectral method -- 5.4 Stability and convergence -- 5.4.1 Semi-discrete of space spectral method -- 5.4.2 The time discretization of Caputo derivative -- 5.5 Fully discretization and its error analysis -- 5.6 Conclusion remarks -- Bibliography -- 6. A discontinuous finite element method for a type of fractional Cauchy problem Yunying Zheng -- 6.1 Introduction -- 6.2 Fractional derivative space -- 6.3 The discontinuous Galerkin finite element approximation -- 6.4 Error estimation -- 6.5 Numerical examples -- 6.6 Conclusion -- Bibliography -- 7. Asymptotic analysis of a singularly perturbed parabolic problem in a general smooth domain Yu-Jiang Wu, Na Zhang and Lun-Ji Song -- 7.1 Introduction -- 7.2 The curvilinear coordinates -- 7.3 Asymptotic expansion -- 7.3.1 Global expansion -- 7.3.2 Boundary corrector -- 7.3.3 Estimates of the solutions of boundary layer equations -- 7.4 Error estimate -- 7.5 An example -- Bibliography -- 8. Incremental unknowns methods for the ADI and ADSI schemes Ai-Li Yang, Yu-Jiang Wu and Zhong-Hua Yang -- 8.1 Introduction -- 8.2 Two dimensional heat equation and the AD scheme -- 8.3 ADIUSI scheme and stability -- 8.3.1 ADIUSI scheme -- 8.3.2 Stability study of the ADIUSI scheme -- 8.3.2.1 The minimum of P( p) is obtained in (-1, 1) -- 8.3.2.2 The condition P(1) > 0 -- 8.3.2.3 The condition P(-1) > 0 -- 8.4 Numerical results -- Bibliography -- 9. Stability of a colocated FV scheme for the 3D Navier-Stokes equations Xu Li and Shu-qin Wang -- 9.1 Introduction -- 9.2 Full discretization: finite volume scheme in space and projection method in time -- 9.3 The main result: stability of the scheme -- 9.3.1 Notations -- 9.3.2 Discrete weak formulation -- 9.3.3 Stability result -- 9.4 Technical lemmas -- 9.4.1 The Poincare inequality and an inverse inequality -- 9.4.2 Standard lemma
9.4.3 Specific lemmas for the Navier-Stokes equations -- 9.5 Apriori Estimate -- 9.6 Proof of stability -- Acknowledgement -- Bibliography -- 10. Computing the multiple positive solutions to p-Henon equation on the unit square Zhaoxiang Li and Zhonghua Yang -- 10.1 Introduction -- 10.2 Computation of D4 symmetric positive solutions -- 10.3 Computation of the symmetry-breaking bifurcation point -- 10.4 Branch switching to symmetric solutions -- 10.5 Numerical results -- Bibliography -- 11. Multilevel WBIUs methods for reaction-diffusion equations Yang Wang, Yu-Jiang Wu and Ai-Li Yang -- 11.1 Introduction -- 11.2 Multilevel WBIUs method -- 11.3 Approximate schemes and their equivalent forms -- 11.3.1 Approximate schemes -- 11.3.2 The equivalent forms of approximate schemes -- 11.4 Stability analysis -- 11.4.1 Lemmas for new vector norms -- 11.4.2 Stability analysis -- 11.5 Numerical results -- Bibliography -- 12. Models and dynamics of deterministically growing networks Weigang Sun, Jingyuan Zhang and Guanrong Chen -- 12.1 Introduction -- 12.2 A generation algorithm -- 12.3 Structural properties -- 12.3.1 Degree distribution -- 12.3.2 Clustering coefficient -- 12.3.3 Average path length -- 12.3.4 Degree correlations -- 12.4 Random walks on Koch networks -- 12.4.1 Evolutionary rule for first passage time -- 12.4.2 Explicit expression for average return time -- 12.4.3 Average sending time from a hub node to another node -- 12.5 An exact solution for mean first passage time -- 12.5.1 First passage time at the first step -- 12.5.2 Evolution scaling for the first passage time -- 12.5.3 Analytic formula for mean first passage time -- 12.6 Conclusions -- Bibliography -- 13. On different approaches to synchronization of spatiotemporal chaos in complex networks Yuan Chai and Li-Qun Chen -- 13.1 Introduction -- 13.2 Design of the synchronization controller
13.3 Numerical results -- 13.4 Active sliding mode controller design -- 13.5 Numerical results -- 13.6 Master stability functions -- 13.7 Numerical results -- 13.8 Conclusion -- Bibliography -- 14. Chaotic dynamical systems on fractals and their applications to image encryption Ruisong Ye, Yuru Zou and Jian Lu -- 14.1 Introduction -- 14.2 Chaotic dynamical systems on fractals -- 14.2.1 Iterated function systems -- 14.2.2 Chaotic dynamical systems on fractals -- 14.3 A special shift dynamical system associated with IFS -- 14.4 The image encryption scheme based on the shift dynamical system associated with IFS -- 14.4.1 Permutation process -- 14.4.2 Diffusion process -- 14.4.3 Security analysis -- 14.4.3.1 Key space analysis -- 14.4.3.2 Statistical analysis -- 14.4.3.3 Differential attack -- 14.4.3.4 Resistance to known-plaintext and chosen-plaintext attacks -- 14.5 Conclusions -- Bibliography -- 15. Planar crystallographic symmetric tiling patterns generated from invariant maps Ruisong Ye, Haiying Zhao and Yuanlin Ma -- 15.1 Introduction -- 15.2 Planar crystallographic groups -- 15.2.1 Groups p2, pm, pmm -- 15.2.2 Groups pg, pmg, pgg, cm, cmm -- 15.2.3 Groups p4, p4g, p4m -- 15.2.4 Groups p3, p3m1, p31m -- 15.2.5 Groups p6, p6m -- 15.3 Rendering method for planar crystallographic symmetric tiling patterns -- 15.3.1 Description of colormaps -- 15.3.2 Description of orbit trap methods -- 15.3.3 Description of the rendering scheme -- 15.4 Conclusions -- Bibliography -- 16. Complex dynamics in a simple two-dimensional discrete system Huiqing Huang and Ruisong Ye -- 16.1 Introduction -- 16.2 Fixed points and bifurcations -- 16.2.1 The existence of fixed points -- 16.2.2 The stability of fixed points and bifurcations -- 16.3 Existence of Marotto-Li-Chen chaos -- 16.4 Numerical simulation results -- Bibliography
17. Approximate periodic solutions of damped harmonic oscillators with delayed feedback Qian Guo -- 17.1 Introduction -- 17.2 Hopf bifurcation analysis -- 17.3 Lyapunov-Schmidt reduction approach for periodic solutions -- 17.3.1 Preliminary: reformulation and projection operators -- 17.3.2 Quadratic Taylor polynomial approximation -- 17.3.3 Bifurcation equations -- 17.3.4 Accuracy of approximation -- 17.4 Multiple scales analysis for periodic solutions -- 17.5 Simulation of period-doubling cascade -- Bibliography -- 18. The numerical methods in option pricing problem Xiong Bo -- 18.1 Introduction -- 18.2 Black-Scholes option pricing theory assumptions -- 18.3 Binomial tree methods -- 18.4 Finite difference method -- Bibliography -- 19. Synchronization and its control between two coupled networks Yongqing Wu and Minghai Lu -- 19.1 Introduction -- 19.2 Anti-synchronization between two coupled networks with nonlinear signal's connection and the inter-network actions -- 19.2.1 Two coupled networks with nonlinear signals -- 19.2.2 Two coupled networks with reciprocity -- 19.2.3 Numerical examples -- 19.3 Pinning anti-synchronization between two general complex dynamical networks -- 19.3.1 Pinning anti-synchronization criterion -- 19.3.2 Numerical simulations -- 19.4 Generalized synchronization between two networks -- 19.4.1 Generalized synchronization criterion -- 19.4.2 Numerical examples -- 19.5 Conclusion -- Bibliography -- Index
Key Features:The topics in this edited book are very hot and highly impressiveIssues and methods of such topics in this edited book have not been made available yetThe present edited book is suitable for various levels of researchers, such as senior undergraduates, postgraduates, and experts
Description based on publisher supplied metadata and other sources
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2020. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
鏈接 Print version: Li, Changpin Recent Advances in Applied Nonlinear Dynamics with Numerical Analysis : Fractional Dynamics, Network Dynamics, Classical Dynamics and Fractal Dynamics with Their Numerical Simulations Singapore : World Scientific Publishing Co Pte Ltd,c2013 9789814436458
主題 Dynamics -- Mathematics.;Nonlinear theories -- Mathematics
Electronic books
Alt Author Wu, Yujiang
Ye, Ruisong
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