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| Dynamics and bifurcation study on an extended Lorenz system |
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| KeyWord:Lorenz system extended Lorenz system Hopf bifurcation limit cycle normal form |
| Author Name | Affiliation | | Pei Yu | Department of Applied Mathematics, Western University,
London, Ontario N6A 5B7, Canada | | Maoan Han | Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang
321004, China
Department of Mathematics, Shanghai Normal University, Shanghai 200234,
China | | Yuzhen Bai | School of Mathematical Sciences, Qufu Normal University, Qufu, shandong
273165, China |
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| 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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