A chaotic system with an infinite number of equilibrium points located on a line and on a hyperbola and its fractional-order form

被引:56
作者
Kingni, Sifeu Takougang [1 ,4 ,5 ,6 ]
Viet-Thanh Pham [2 ]
Jafari, Sajad [3 ]
Woafo, Paul [4 ,5 ,6 ]
机构
[1] Univ Maroua, Inst Mines & Petr Ind, Dept Mech & Elect Engn, POB 46, Maroua, Cameroon
[2] Hanoi Univ Sci & Technol, Sch Elect & Telecommun, 01 Dai Co Viet, Hanoi, Vietnam
[3] Amirkabir Univ Technol, Dept Biomed Engn, 424 Hafez Ave, Tehran 158754413, Iran
[4] Univ Yaounde I, Fac Sci, Dept Phys, Lab Modelling & Simulat Engn Biomimet & Prototype, POB 812, Yaounde, Cameroon
[5] Univ Yaounde I, Fac Sci, Dept Phys, TWAS Res Unit, POB 812, Yaounde, Cameroon
[6] Vrije Univ Brussel, Appl Phys Res Grp APHY, Pl Laan 2, B-1050 Brussels, Belgium
关键词
Three-dimensional autonomous chaotic system; Line equilibrium; Hyperbolic equilibrium; Circuit implementation; Chaos synchronization; Fractional-order; PROJECTIVE SYNCHRONIZATION; AUTONOMOUS SYSTEM; HIDDEN OSCILLATIONS; ACTIVE CONTROL; ATTRACTOR; IMPLEMENTATION; SIMULATION; MECHANISM; FLOWS;
D O I
10.1016/j.chaos.2017.04.011
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
A three-dimensional autonomous chaotic system with an infinite number of equilibrium points located on a line and a hyperbola is proposed in this paper. To analyze the dynamical behaviors of the proposed system, mathematical tools such as Routh-Hurwitz criteria, Lyapunov exponents and bifurcation diagram are exploited. For a suitable choice of the parameters, the proposed system can generate periodic oscillations and chaotic attractors of different shapes such as bistable and monostable chaotic attractors. In addition, an electronic circuit is designed and implemented to verify the feasibility of the proposed system. A good qualitative agreement is shown between the numerical simulations and the Orcard-PSpice results. Moreover, the fractional-order form of the proposed system is studied using analog and numerical simulations. It is found that chaos, periodic oscillations and periodic spiking exist in this proposed system with order less than three. Then an electronic circuit is designed for the commensurate fractional order alpha=0.98, from which we can observe that a chaotic attractor exists in the fractional-order form of the proposed system. Finally, the problem of drive-response generalized projective synchronization of the fractional-order form of the chaotic proposed autonomous system is considered. (C) 2017 Elsevier Ltd. All rights reserved.
引用
收藏
页码:209 / 218
页数:10
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