Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

The Calculation Process of the Limit Cycle for Lorenz System

Version 1 : Received: 17 February 2021 / Approved: 18 February 2021 / Online: 18 February 2021 (13:47:19 CET)

How to cite: Dong, H.; Zhong, B. The Calculation Process of the Limit Cycle for Lorenz System. Preprints 2021, 2021020419 (doi: 10.20944/preprints202102.0419.v1). Dong, H.; Zhong, B. The Calculation Process of the Limit Cycle for Lorenz System. Preprints 2021, 2021020419 (doi: 10.20944/preprints202102.0419.v1).

Abstract

This work focuses on the bifurcation behavior before chaos phenomenon happens. Traditional numerical method is unable to solve the unstable limit cycle of nonlinear system. One algorithm is introduced to solve the unstable one, which is based one of the continuation method is called DEPAR approach. Combined with analytic and numerical method, the two stable and symmetrical equilibrium solutions exist through Fork bifurcation and the unstable and symmetrical limit cycles exist through Hopf bifurcation of Lorenz system. With the continuation algorithm, the bifurcation behavior and its phase diagram is solved. The results demonstrate the unstable periodical solution is around the equilibrium solution, besides the trajectory into the unstable area cannot escape but only converge to the equilibrium solution.

Keywords

Lorenz equation; Hopf bifurcation; Unstable limit cycle; Calculation process; Continuation method

Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

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