nonlinear oscillations dynamical systems and bifurcations of vector fields pdf

Nonlinear oscillations dynamical systems and bifurcations of vector fields pdf

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AM 0220: Nonlinear Dynamical Systems - Theory and Applications

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Nonlinear Oscillations Dynamical Systems, and Bifurcations of Vector Fields

The elementary chapters are suitable for an introductory graduate course for mathematicians and physicists.

AM 0220: Nonlinear Dynamical Systems - Theory and Applications

Necessary and sufficient conditions on the existence and stability of the fixed points of this system are established. By applying the center manifold theorem and bifurcation theory, we show that the system has the fold bifurcation, flip bifurcation, and Neimark-Sacker bifurcation under certain conditions. Numerical simulations are presented to not only show the consistence between examples and our theoretical analysis, but also exhibit complexity and interesting dynamical behaviors, including period, , , , , , and orbits, quasi-periodic orbits, chaotic behaviors which appear and disappear suddenly, coexisting chaotic attractors. Chen , The function cascade synchronization scheme for discrete-time hyperchaotic systems, Commun Nonlinear Sci Numer Simulat , 14 , Google Scholar. Gonchenko and S. D , , 43—57, arXiv:

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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Authors; (view affiliations). John Guckenheimer; Philip Holmes.


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Nonlinear Oscillations Dynamical Systems, and Bifurcations of Vector Fields

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Nonlinear Oscillations Dynamical Systems, and Bifurcations of Vector Fields

Lectures: Mittwoch -- , P Tutorial: every second Donnerstags -- , A The following topics will be covered in the course:.

Necessary and sufficient conditions on the existence and stability of the fixed points of this system are established. By applying the center manifold theorem and bifurcation theory, we show that the system has the fold bifurcation, flip bifurcation, and Neimark-Sacker bifurcation under certain conditions. Numerical simulations are presented to not only show the consistence between examples and our theoretical analysis, but also exhibit complexity and interesting dynamical behaviors, including period, , , , , , and orbits, quasi-periodic orbits, chaotic behaviors which appear and disappear suddenly, coexisting chaotic attractors.

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Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

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