Author(s)

Maria Zaitseva^1,2

¹Scientific Research Institute of System Development, Russian Academy of Science, Moscow, Russia.
²Department of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia.

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.

Nonlinear Differential Equations, Dynamical Chaos, Singular Attractor, FSM-Theory

Zaitseva, M. (2016) On Universality of Transition to Chaos Scenario in Nonlinear Systems of Ordinary Differential Equations of Shilnikov’s Type. Journal of Applied Mathematics and Physics, 4, 871-880. doi: 10.4236/jamp.2016.45095.