On Universality of Transition to Chaos Scenario in Nonlinear Systems of Ordinary Differential Equations of Shilnikov’s TypeReport as inadecuate




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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.

KEYWORDS

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

Cite this paper

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.





Author: Maria Zaitseva1,2

Source: http://www.scirp.org/



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