TITLE:
On Universality of Transition to Chaos Scenario in Nonlinear Systems of Ordinary Differential Equations of Shilnikov’s Type
AUTHORS:
Maria Zaitseva
KEYWORDS:
Nonlinear Differential Equations, Dynamical Chaos, Singular Attractor, FSM-Theory
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.4 No.5,
May
23,
2016
ABSTRACT: Several nonlinear three-dimensional systems of ordinary differential equations are studied analytically and numerically in this paper in accordance with universal bifurcation theory of Feigenbaum-Sharkovskii-Magnitsky [1] [2]. All systems are autonomous and dissipative and display chaotic behaviour. The analysis confirms that transition to chaos in such systems is performed through cascades of bifurcations of regular attractors.