Chaos in Essentially Singular 3D Dynamical Systems with Two Quadratic Nonlinearities | Zendy

Vasiliy Ye. Belozyorov | Zendy

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Chaos in Essentially Singular 3D Dynamical Systems with Two Quadratic Nonlinearities

Author(s) -

Vasiliy Ye. Belozyorov

Publication year - 2016

Publication title -

journal of nonlinear dynamics

Language(s) - English

Resource type - Journals

eISSN - 2356-7503

pISSN - 2314-6893

DOI - 10.1155/2016/2410806

Subject(s) - attractor , lorenz system , class (philosophy) , generalization , mathematics , quadratic equation , limit cycle , chaotic , limit (mathematics) , dynamical systems theory , cascade , statistical physics , mathematical analysis , pure mathematics , control theory (sociology) , computer science , physics , control (management) , geometry , chemistry , chromatography , quantum mechanics , artificial intelligence

A new class of 3D autonomous quadratic systems, the dynamics of which demonstrate a chaotic behavior, is found. This class is a generalization of the well-known class of Lorenz-like systems. The existence conditions of limit cycles in systems of the mentioned class are found. In addition, it is shown that, with the change of the appropriate parameters of systems of the indicated class, chaotic attractors different from the Lorenz attractor can be generated (these attractors are the result of the cascade of limit cycles bifurcations). Examples are given

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