Year: 2019
Author: Pei Yu, Maoan Han, Yuzhen Bai
Journal of Nonlinear Modeling and Analysis, Vol. 1 (2019), Iss. 1 : pp. 107–128
Abstract
In this paper, we study dynamics and bifurcation of limit cycles in a recently developed new chaotic system, called extended Lorenz system. A complete analysis is provided for the existence of limit cycles bifurcating from Hopf critical points. The system has three equilibrium solutions: a zero one at the origin and two non-zero ones at two symmetric points. It is shown that the system can either have one limit cycle around the origin, or three limit cycles enclosing each of the two symmetric equilibria, giving a total six limit cycles. It is not possible for the system to have limit cycles simultaneously bifurcating from all the three equilibria. Simulations are given to verify the analytical predictions.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2019.107
Journal of Nonlinear Modeling and Analysis, Vol. 1 (2019), Iss. 1 : pp. 107–128
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Lorenz system extended Lorenz system Hopf bifurcation limit cycle normal form.