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Bifurcation Theory and Methods of Dynamical Systems : Advanced Series In Dynamical Systems - Maoan Han

Bifurcation Theory and Methods of Dynamical Systems

Advanced Series In Dynamical Systems

Hardcover Published: 1998
ISBN: 9789810220945
Number Of Pages: 476

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Dynamical bifurcation theory is concerned with the changes that occur in the global structure of dynamical systems as parameters are varied. This text makes recent research in bifurcation theory of dynamical systems accessible to researchers interested in this subject. In particular, the relevant results obtained by Chinese mathematicians are introduced as well as some of the works of the authors which may not be widely known. The focus is on the analytic approach to the theory and methods of bifurcations. The book prepares graduate students for further study in this area, and it serves as a ready reference for researchers in nonlinear sciences and applied mathematics.

Basic Concepts and Factsp. 1
Hyperbolicity and Transversality. [Lambda]-Lemmap. 2
Structural Stability and Bifurcationp. 14
Codimension and Unfoldingsp. 27
Center Manifold Theoryp. 33
Bifurcation of 2-Dimensional Systemsp. 45
Generalized Hopf Bifurcationp. 45
Bifurcation of Multiple Limit Cyclesp. 55
Homoclinic and Heteroclinic Bifurcationsp. 62
Poincare Bifurcationp. 79
Bifurcation in Polynomial Lienard Systemsp. 91
Boundedness of Solutions and Existence of Limit Cyclesp. 93
Criteria for Deciding the Number of Limit Cyclesp. 110
Global Bifurcation of Cubic Lienard Systemsp. 132
Global Bifurcation in Some Applied Modelsp. 169
Periodic Perturbed Systems and Integral Manifoldsp. 185
Bifurcation of Periodic Solutionsp. 185
Method of Averaging and Integral Manifoldsp. 198
Periodic Perturbed Systems on a Planep. 206
Hopf Bifurcation of Invariant Torusp. 220
Poincare Bifurcation of Invariant Torusp. 232
Bifurcations of Higher Dimensional Systemsp. 253
Methods of Bifurcation Functions of Periodic Orbitsp. 253
Zero and Pure Imaginary Eigenvaluesp. 271
Two Pairs of Pure Imaginary Eigenvaluesp. 283
Global Bifurcations of Large Periodic Orbitsp. 298
Uniqueness and Stability of Bifurcated Periodic Orbitsp. 304
Chaotic Dynamics Bifurcated by Symmetric Homoclinic Loopsp. 319
Saddle-Focus Homoclinic Bifurcation. Chaosp. 329
Period-Doubling Bifurcation in Weak Sil'nikov Phenomenonp. 345
Melnikov Vector, Homoclinic and Heteroclinic Orbitsp. 357
Exponential Trichotomiesp. 359
Melnikov Vector in Higher Dimensionsp. 372
Orbits Heteroclinic to Invariant Manifoldsp. 390
Heteroclinic Orbits in Singular Perturbation Problemsp. 409
Heteroclinic to Nonhyperbolic Equilibriap. 426
Referencesp. 443
Indexp. 457
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9789810220945
ISBN-10: 9810220944
Series: Advanced Series In Dynamical Systems
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 476
Published: 1998
Publisher: World Scientific Publishing Co Pte Ltd
Country of Publication: SG
Dimensions (cm): 23.5 x 16.51  x 3.18
Weight (kg): 0.77

Earn 562 Qantas Points
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