Torus and fixed point attractors of a new hyperchaotic 4D system

Abstract

In this article, a new 4D hyperchaotic system with torus attractors is developed and analyzed with integer and non-integer order operators. Various dynamical features of the new system are investigated and discussed. The equilibrium points with stability, Lyapunov spectra, Poincaré section, bifurcations, phase portraits, attractors projection, and inversion properties are studied. The phase inversion property concerning a single parameter, which is very rare for hyperchaotic dynamical systems, is observed in the proposed system. For integer order, the attractor projection shows that there exists a torus attractor, which is attracting all the nearby trajectories towards it. Moreover, the system is theoretically, numerically, and graphically examined from a fractional perspective. The fixed point notions are used to examine the existence of the solution of the proposed hyperchaotic system under the Caputo operator. The system is also studied numerically in fractional sense via a newly introduced numerical technique based on the Newton polynomials. We analyze that with a decrease in fractional order, the system shows a cone-type spiral behavior in which the amplitude of the oscillations decreases and the system tends towards E0. In addition, coexisting fixed point attractors are obtained through numerical simulations at a few fractional orders.