Algrithm for detecting homoclinic orbits of time-continuous dynamical system and its application | Zendy

Fangyan Yang | Zendy; Hu Ming | Zendy; Yao Shang-Ping | Zendy

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Algrithm for detecting homoclinic orbits of time-continuous dynamical system and its application

Author(s) -

Fangyan Yang,

Hu Ming,

Yao Shang-Ping

Publication year - 2013

Publication title -

acta physica sinica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.199

H-Index - 47

ISSN - 1000-3290

DOI - 10.7498/aps.62.100501

Subject(s) - homoclinic orbit , lorenz system , homoclinic bifurcation , computer science , dynamical systems theory , nonlinear system , trajectory , dynamical system (definition) , saddle point , key (lock) , bifurcation , point (geometry) , mathematics , saddle , control theory (sociology) , mathematical optimization , chaotic , physics , artificial intelligence , geometry , control (management) , quantum mechanics , computer security , astronomy

Detecting homoclinic orbits is a key problem in nonlinear dynamical systems, especially in the study of bifurcation and chaos. In this paper, we propose a new method to solve the problem with trajectory optimization. By defining a distance between a saddle point and its near trajectories, the problem becomes a common problem in unconstrained nonlinear optimization to minimize the distance. A subdivision algorithm is also proposed in this paper to improve the integrity of results. By applying the algorithm to the Lorenz system, the Shimizu-Morioka system and the hyperchaotic Lorenz system, we successfully find many homoclinic orbits with the corresponding parameters, which suggests that the method is effective.

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