Title :
Bifurcation approach to analysis of chaotic dynamics in Hamiltonian and conservative systems
Author :
Magnitskii, N.A.
Author_Institution :
Inst. for Syst. Anal., Moscow, Russia
Abstract :
It is proved in the paper and illustrated with analytical and numerical examples that universal bifurcation Feigenbaum-Sharkovskii-Magnitskii mechanism of transition to dynamical chaos in all kinds of dissipative nonlinear systems of differential equations including ordinary and partial, autonomous and non-autonomous differential equations and differential equations with delay arguments takes place also in conservative and Hamiltonian systems.
Keywords :
bifurcation; chaos; nonlinear differential equations; partial differential equations; Hamiltonian system; analytical example; autonomous differential equation; bifurcation approach; chaotic dynamic analysis; conservative system; delay arguments; dissipative nonlinear systems; dynamical chaos; nonautonomous differential equation; numerical example; ordinary differential equation; partial differential equation; transition mechanism; universal bifurcation Feigenbaum-Sharkovskii-Magnitskii mechanism; Bifurcation; Chaos; Differential equations; Manifolds; Nonlinear dynamical systems; Trajectory;
Conference_Titel :
Nonlinear Science and Complexity (NSC), 2012 IEEE 4th International Conference on
Conference_Location :
Budapest
Print_ISBN :
978-1-4673-2702-2
Electronic_ISBN :
978-1-4673-2701-5
DOI :
10.1109/NSC.2012.6304730
