A Novel Autonomous 5-D Hyperjerk RC Circuit with Hyperbolic Sine Function

Abstract

A novel autonomous 5-D hyperjerk RC circuit with hyperbolic sine function is proposed in this paper. Compared to some existing 5-D systems like the 5-D Sprott B system, the 5-D Lorentz, and the Lorentz-like systems, the new system is the simplest 5-D system with complex dynamics reported to date. Its simplicity mainly relies on its nonlinear part which is synthetized using only two semiconductor diodes. The system displays only one equilibrium point and can exhibit both periodic and chaotic dynamical behavior. The complex dynamics of the system is investigated by means of bifurcation analysis. In particular, the striking phenomenon of multistability is revealed showing up to seven coexisting attractors in phase space depending solely on the system's initial state. To the best of author's knowledge, this rich dynamics has not yet been revealed in any 5-D dynamical system in general or particularly in any hyperjerk system. Pspice circuit simulations are performed to verify theoretical/numerical analysis.

A Multidimensional Hyperjerk Oscillator: Dynamics Analysis, Analogue and Embedded Systems Implementation, and Its Application as a Cryptosystem

“…Figure 2 provides four views of the 5-D Hyperjerk chaotic attractor where the stable equilibrium point is shown as a red dot. that a point attractor coexists with a strange attractor [27,28]. This is further clarified later in the next section.…”

“…As the real parts of the correlated eigen values are always negatively valued; the equilibrium is stable for the entire region of system parameters. For instance, if we set b = 3; a 0 = 1.5; a 1 = 3; a 2 = 2; a 3 = 1; a 4 = 1; l 1 = 1; l 2 = 2.6 then its eigen values can be calculated as: λ 1 = − 0.1194 + 2.5677i; λ 2 = − 0.1194 − 2.5677i; λ 3 = − 0.8425 + 0.0000i λ 4 = − 0.2094 + 0.7036i; λ 5 = − 0.2094 − 0.7036i (3) It is a general conclusion that since the equilibrium point is always stable, it can be predicted that a point attractor coexists with a strange attractor [27,28]. This is further clarified later in the next section.…”

Complex Dynamics of the Chua’s Circuit System with Adjustable Symmetry and Nonlinearity: Multistability and Simple Circuit Realization

“…Symmetry always plays an important role in physical system. This property is found in a variety of system including nonlinear and chaotic systems [30][31][32][33][34][35][36][37][38][39][40]. Symmetric chaotic systems provide the possibility to observe coexisting attractors.…”

A new hyperjerk dynamical system with hyperchaotic attractor and two saddle-focus rest points exhibiting Hopf bifurcations, its hyperchaos synchronisation and circuit implementation

“…Recently, good interest has been devoted to the finding of both jerk and hyperjerk systems in the chaos literature (Vaidyanathan et al, 2018a;Vaidyanathan, 2017;Vaidyanathan, 2016El-Nabulsi, 2018;Prousalis et al, 2018;Ahmad and Srisuchinwong, 2018;Tsafack and Kengne, 2018;Daltzis et al, 2018;Vaidyanathan et al, 2018b;Wang et al, 2017). Vaidyanathan et al (2018a) reported a new chaotic jerk system with two quadratic nonlinearities and discussed its applications to electronic circuit implementation and image encryption.…”

“…Ahmad and Srisuchinwong (2018) reported a 4-D hyperjerk system with hyperchaos and having no rest point. Tsafack and Kengne (2018) reported a 5-D hyperjerk system with circuit design. Daltzis et al (2018) reported a 4-D hyperjerk system with hyperchaos and built a real circuit design for the hyperjerk system.…”