A chaotic system with an infinite number of equilibrium points located on a line and on a hyperbola and its fractional-order form. (June 2017)

• Record Type: Journal Article
• Authors: Kingni, Sifeu Takougang; Pham, Viet-Thanh; Jafari, Sajad; Woafo, Paul
• Is Part Of: Chaos, solitons and fractals. Volume 99(2017)
• Page Start: 209
• Page End: 218
• Publication Date: 2017-06
• Subjects: Three-dimensional autonomous chaotic system -- Line equilibrium -- Hyperbolic equilibrium -- Circuit implementation -- Chaos synchronization -- Fractional-order; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2017.04.011
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: 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 α = 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.