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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,...
| Clasificación: | Libro Electrónico |
|---|---|
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Amsterdam :
Elsevier,
2006.
|
| Colección: | Edited series on advances in nonlinear science and complexity ;
v. 1. |
| Temas: | |
| Acceso en línea: | Texto completo Texto completo |
Tabla de Contenidos:
- 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.