Volume 1, Issue 1
Dynamics and Bifurcation Study on an Extended Lorenz System

J. Nonl. Mod. Anal., 1 (2019), pp. 107-128.

Published online: 2021-04

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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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@Article{JNMA-1-107, author = {Yu , PeiHan , Maoan and Bai , Yuzhen}, title = {Dynamics and Bifurcation Study on an Extended Lorenz System}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2021}, volume = {1}, number = {1}, pages = {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.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2019.107}, url = {http://global-sci.org/intro/article_detail/jnma/18871.html} }
TY - JOUR T1 - Dynamics and Bifurcation Study on an Extended Lorenz System AU - Yu , Pei AU - Han , Maoan AU - Bai , Yuzhen JO - Journal of Nonlinear Modeling and Analysis VL - 1 SP - 107 EP - 128 PY - 2021 DA - 2021/04 SN - 1 DO - http://doi.org/10.12150/jnma.2019.107 UR - https://global-sci.org/intro/article_detail/jnma/18871.html KW - Lorenz system, extended Lorenz system, Hopf bifurcation, limit cycle, normal form. AB -

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.

Pei Yu, Maoan Han & Yuzhen Bai. (1970). Dynamics and Bifurcation Study on an Extended Lorenz System. Journal of Nonlinear Modeling and Analysis. 1 (1). 107-128. doi:10.12150/jnma.2019.107
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