Open AccessAlgrithm for detecting homoclinic orbits of time-continuous dynamical system and its application
Author(s) -
Fumeng Yang,
Ming Hu,
Yao Shang-Ping
Publication year - 2013
Publication title -
wuli xuebao
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.