Journal
MATHEMATICS AND COMPUTERS IN SIMULATION
Volume 112, Issue -, Pages 40-55Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.matcom.2014.11.006
Keywords
Lorenz system; Hyperchaos; Curve of equilibria; Coexisting attractor; Singular degenerate heteroclinic cycles
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Funding
- National Natural Science Foundation of China [11271139]
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Little seems to be known about hyperchaotic systems with a curve of equilibria. Based on the classical Lorenz system, this paper proposes a new four-dimensional Lorenz-type hyperchaotic system which has a curve of equilibria. This new system can generate not only hyperchaotic attractors but also chaotic, quasi-periodic and periodic attractors, as well as singular degenerate heteroclinic cycles. Of particular interest is the observation that there are four types of coexisting attractors of this new hyperchaotic system: (i) chaotic attractor and quasi-periodic attractor, (ii) chaotic attractor and singular degenerate heteroclinic cycle, (iii) periodic attractor and singular degenerate heteroclinic cycle, and (iv) different periodic attractors. Furthermore, many singular degenerate heteroclinic cycles are found, which may lead to complex dynamics of hyperchaotic system with a curve of equilibria. (C) 2014 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
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