Bifurcation Theory of Nonlinear Dynamics and Chaos. Periodic Skeletons and Rare Attractors

Proceedings of the 2nd International Symposium on Rare Attractors and Rare Phenomena in Nonlinear Dynamics 2011
Mihails Zakrževskis

The main features and components of a new so-called bifurcation theory of nonlinear dynamics and chaos and its applications, intended for direct global bifurcation analysis of nonlinear dynamical periodic systems is presented. The described part of bifurcation theory uses dynamical periodic systems, described by a model of ODE equations or a map-based model of discrete-time equations. Our approach is based on ideas of Poincaré, Andronov and other scientists’ results concerning structural stability and bifurcations of different dynamical nonlinear systems and their topological properties [1-22]. For illustration of the advantages of the new bifurcation theory we use in this paper several typical well-known nonlinear models: Duffing driven oscillator, trilinear soft impact driven model and pendulum driven oscillator. In each of them we have found important unknown regular or chaotic attractors and/or new bifurcation groups with rare attractors RA. Additional illustration of the bifurcation theory it is possible to find in the authors’ colleagues papers [55-61], published in this book.

Keywords
Bifurcation theory, periodic skeletons, rare attractors

Zakrževskis, M. Bifurcation Theory of Nonlinear Dynamics and Chaos. Periodic Skeletons and Rare Attractors. In: Proceedings of the 2nd International Symposium on Rare Attractors and Rare Phenomena in Nonlinear Dynamics, Latvia, Rīga - Jūrmala, 16-20 May, 2011. Rīga: Riga Technical University, 2011, pp.1-10. ISBN 978-9934-10-142-7.

Publication language
English (en)