A New Chaotic System with Only Nonhyperbolic Equilibrium Points: Dynamics and Its Engineering Application

Abstract

In this work, we introduce a new non-Shilnikov chaotic system with an infinite number of nonhyperbolic equilibrium points. The proposed system does not have any linear term, and it is worth noting that the new system has one equilibrium point with triple zero eigenvalues at the origin. Also, the novel system has an infinite number of equilibrium points with double zero eigenvalues that are located on the z -axis. Numerical analysis of the system reveals many strong dynamics. The new system exhibits multistability and antimonotonicity. Multistability implies the coexistence of many periodic, limit cycle, and chaotic attractors under different initial values. Also, bifurcation analysis of the system shows interesting phenomena such as periodic window, period-doubling route to chaos, and inverse period-doubling bifurcations. Moreover, the complexity of the system is analyzed by computing spectral entropy. The spectral entropy distribution under different initial values is very scattered and shows that the new system has numerous multiple attractors. Finally, chaos-based encoding/decoding algorithms for secure data transmission are developed by designing a state chain diagram, which indicates the applicability of the new chaotic system.

WAM 3D Discrete Chaotic Map for Secure Communication Applications

“…Here are examples of suggested chaotic maps for addressing these issues: Pisarchik, A et al [3] proposed a hybrid communication system consisting of two identical oscillators of six orders, equally chosen between the transmitter and the receiver, each exhibiting synchronization to a huge number of chaotic attractors. Zolfaghari-Nejad, M et al [19] presented a new, non-Shilnikov chaotic system with a two zeros of eigenvalues positioned on the axis with a single equilibrium point and three eigenvalues at the origin. Simulation analysis of the system reveals applicability of the chaotic system in real applications.…”

“…The values of the parameters used are (a=1.52, b= 0.05 and c= 0.05) and initial values used for systems (X1=0.3 Y1=0.2, Z1=0.1, X2 = 0.2, Y2 = 0.1, and Z2 = 0.2). Chaotic systems were matched according to equations (18)(19)(20) as shown in Fig. 6.…”

Dynamics, periodic orbits of a novel four-dimensional hyperchaotic system with hidden attractors

“…However, this theorem has been overturned with the deepening of chaotic research. In recent years, it has been discovered that a class of systems can exhibit chaotic oscillations despite having only stable equilibrium points [16], no equilibrium point [17], or an infinite number of equilibrium points [18,19]. The attractors in such systems are referred to as hidden attractors.…”

Unstable periodic orbits analysis in the Qi system

“…[4][5][6] Chaos has become a hot research object in many disciplines and various types of attractors have been proposed. [7][8][9][10][11][12] In 2005, Qi et al discovered a new three-dimensional (3D) chaotic system with five equilibria, which is special. [13] The significant difference from the Lorenz system is that each equation of the Qi system contains nonlinear terms, and there are many studies on the Qi system.…”