Journal
APPLIED MATHEMATICS AND COMPUTATION
Volume 229, Issue -, Pages 16-26Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2013.12.037
Keywords
Stretch-twist-fold flow; Chaos; Hopf bifurcation; Heteroclinic bifurcation; Lyapunov exponent
Categories
Funding
- National Natural Science Foundation of China [11271139]
- Science and Technology Planning Project of Guangdong Province, China [2012B061800088]
- Fundamental Research Funds for the Central Universities [2013ZM0115]
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Based on the stretch-twist-fold flow, a generalized stretch-twist-fold flow is introduced. By choosing an appropriate bifurcation parameter, Hopf bifurcations occur in this system when the bifurcation parameter exceeds a critical value. The formulae for determining the direction of the Hopf bifurcations and the stability of bifurcating periodic solutions are presented. In addition, the paper also investigates the bifurcations of the heteroclinic orbits for this system. The existence and its associated existing regions are given for two heteroclinic orbits, respectively. Finally, some numerical simulations for justifying the theoretical analysis are presented. (C) 2013 Elsevier Inc. All rights reserved.
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