Table of Contents
Journal of Nonlinear Dynamics
Volume 2016 (2016), Article ID 2410806, 12 pages
http://dx.doi.org/10.1155/2016/2410806
Research Article

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

Department of Applied Mathematics, Dnipropetrovsk National University, Gagarin Avenue 72, Dnipropetrovsk 49050, Ukraine

Received 23 March 2016; Revised 7 July 2016; Accepted 18 July 2016

Academic Editor: Zhao Lu

Copyright © 2016 Vasiliy Belozyorov. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.