Journal
PRAMANA-JOURNAL OF PHYSICS
Volume 86, Issue 4, Pages 801-807Publisher
INDIAN ACAD SCIENCES
DOI: 10.1007/s12043-015-1118-1
Keywords
Four-wing; non-equilibrium; hidden attractor; Poincare maps; circuit implementation
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Funding
- National Natural Science Foundation of China [61274020]
- Open Fund Project of Key Laboratory in Hunan University [13K015]
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In this paper, we construct a novel, 4D smooth autonomous system. Compared to the existing chaotic systems, the most attractive point is that this system does not display any equilibria, but can still exhibit four-wing chaotic attractors. The proposed system is investigated through numerical simulations and analyses including time phase portraits, Lyapunov exponents, bifurcation diagram, and Poincar maps. There is little difference between this chaotic system without equilibria and other chaotic systems with equilibria shown by phase portraits and Lyapunov exponents. But the bifurcation diagram shows that the chaotic systems without equilibria do not have characteristics such as pitchfork bifurcation, Hopf bifurcation etc. which are common to the normal chaotic systems. The Poincare maps show that this system is a four-wing chaotic system with more complicated dynamics. Moreover, the physical existence of the four-wing chaotic attractor without equilibria is verified by an electronic circuit.
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