Bifurcation and chaos in complex systems /

Presents the achievements on bifurcation studies of nonlinear dynamical systems. This book deals with the fundamental theoretical issues of bifurcation analysis in smooth and non-smooth dynamical systems. The cell mapping methods are presented for global bifurcations in stochastic and deterministic,...

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Bibliographic Details
Call Number:Libro Electrónico
Other Authors: Sun, Jian-Qiao, Luo, Albert C. J.
Format: Electronic eBook
Language:Inglés
Published: Amsterdam : Elsevier, 2006.
Series:Edited series on advances in nonlinear science and complexity ; v. 1.
Subjects:
Bifurcation theory.
Chaotic behavior in systems.
Nonlinear systems.
Th�eorie de la bifurcation.
Chaos.
Syst�emes non lin�eaires.
MATHEMATICS > Differential Equations > General.
Bifurcation theory
Chaotic behavior in systems
Nonlinear systems
Online Access:Texto completo
Texto completo
Table of Contents:
  • Cover Dedication Preface Contents Bifurcation, Limit Cycle and Chaos of Nonlinear Dynamical Systems
  • Introduction
  • Bifurcation of limit cycles
  • Lifting 2-D model with delayed feedback control
  • Internet congestion model
  • Hilbert's 16th problem
  • Bifurcation control and chaos synchronization
  • Global ultimate boundedness of chaotic systems
  • Hopf bifurcation control
  • Tracking and chaos synchronization
  • Competitive modes
  • Definition of CM
  • Application of CM: estimating chaotic parameter regimes
  • Application of CM: constructing new chaotic systems
  • Conclusions
  • Acknowledgement
  • References Grazing Flows in Discontinuous Dynamic Systems
  • Introduction
  • Domain accessibility
  • Discontinuous dynamic systems
  • Oriented boundary and singular sets
  • Local singularity and grazing flows
  • Piecewise linear systems
  • Friction-induced oscillators
  • Conclusions
  • Appendix
  • References Global Bifurcations of Complex Nonlinear Dynamical Systems with Cell Mapping Methods
  • Introduction
  • Cell mapping methods
  • Simple cell mapping
  • Generalized cell mapping
  • Crises in deterministic systems
  • A chaotic boundary crisis
  • Chaotic boundary and interior crises
  • Wada fractal boundary and indeterminate crisis
  • Double crises
  • Bifurcations of nonlinear systems with small random disturbances
  • Logistic map with random coefficients
  • A two-dimensional random map
  • Duffing oscillator with small random excitations
  • Noisy crisis in a twin-well Duffing system
  • Fuzzy bifurcations
  • Fuzzy generalized cell mapping
  • Bifurcation of one-dimensional fuzzy systems
  • Bifurcation of fuzzy nonlinear oscillators
  • Conjectures
  • Effect of bifurcation on semiactive optimal controls
  • Optimal control problem
  • Saddle-node bifurcation
  • Supercritical Pitchfork bifurcation
  • Subcritical Hopf bifurcation
  • References Bifurcation Analysis of Nonlinear Dynamic Systems with Time-Periodic Coefficients
  • Introduction
  • Formulation of the problem
  • Local stability and conditions for bifurcations: Floqu�et theory
  • Lyapunov-Floqu�et transformation
  • Nonlinear analysis
  • Time-periodic center manifold reduction
  • Time-dependent normal form theory
  • Versal deformation of the normal form
  • Solution in the original (physical) variables
  • The codimension one bifurcations
  • Flip bifurcation
  • Transcritical and symmetry breaking bifurcations
  • Cyclic fold bifurcation
  • Secondary Hopf bifurcation
  • Applications
  • A system with an exact solution: an example of the flip bifurcation
  • A system with a small parameter: a comparison with averaging method
  • A simple pendulum with periodic base excitation: an example of the symmetry breaking bifurcation
  • An example of the secondary Hopf bifurcation: a double inverted pendulum with a periodic follower load
  • Summary and conclusions
  • References Modal Interactionsmodal interactions in Asymmetric Vibrations of Circular Platescircular plates
  • Introduction
  • Governing equations
  • Solution
  • Steady-state responses and numerical examples
  • The plate without elastic foundation (K = 0): the case of no internal resonance
  • The plate on elastic foundation (K> 0): the case of internal resonance (omegaNM 3?CD, where N = 3C)
  • The plate on elastic foundation (K> 0): the case of internal resonance (?NM 3?CD, where N = C)
  • Appendix A
  • Appendix B
  • Case 1:?32 3?11 and??11
  • Case 2:?32 3?11 and??32
  • Appendix C
  • References List of Contributors Author Index Subject Index Last Page.

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