Journal
PRAMANA-JOURNAL OF PHYSICS
Volume 88, Issue 4, Pages -Publisher
INDIAN ACAD SCIENCES
DOI: 10.1007/s12043-017-1363-6
Keywords
Hyperchaos; hidden attractors; reduced order; projective synchronization; Lyapunov stability theorem
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Funding
- National Natural Science Foundation of China [11561069]
- Guangxi Natural Science Foundation of China [2016GXNSFBA380170]
- Scientific Research Foundation of the Higher Education Institutions of Guangxi Province of China [KY2016YB364]
- Key Projects of Yulin Normal University [2014YJZD01]
- Open Foundation for Guangxi Colleges and Universities Key Lab of Complex System Optimization and Big Data Processing [2016CSOBDP0202]
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By introducing an additional state feedback into classic Rikitake system, a new hyperchaotic system without equilibrium is derived. The proposed system is investigated through numerical simulations and analyses including time phase portraits, Lyapunov exponents, and Poincare maps. Based on adaptive control and Lyapunov stability theory, we design a reduced-order projective synchronization scheme for synchronizing the hyperchaotic Rikitake system coexisting without equilibria and the original classic Rikitake system coexisting with two nonhyperbolic equilibria. Finally, numerical simulations are given to illustrate the effectiveness of the proposed synchronization scheme.
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