Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 21, Issue 9, Pages 2559-2582Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127411029938
Keywords
Lu system; invariant algebraic surface; dynamics at infinity; global behavior; singularly degenerate heteroclinic cycle
Funding
- National Natural Science Foundation of China [11161051]
- Special Scientific Foundation of Yulin Normal University [2011YJZD12]
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Firstly, the dynamics of the Lu system having an invariant algebraic surface are analyzed. Secondly, by using the Poincare compactification in R-3, a global analysis of the system is presented, including the complete description of its dynamic behavior on the sphere at infinity. Lastly, combining analytical and numerical techniques, it is shown that for the parameter value b = 0, the system presents an infinite set of singularly degenerate heteroclinic cycles. The chaotic attractors for the Lu systemin the case of small b > 0 are found numerically, hence the singularly degenerate heteroclinic cycles.
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