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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.
Highlights
In recent decades, particular attention has been paid to the chaos that arises in nonlinear dynamic systems. is is due to various potential applications of chaotic systems in science and engineering fields
We address chaos-based encoding and decoding algorithms for a secure data transmission scheme by designing a state chain (SC) diagram, which indicates the applicability of the new chaotic system
We will show the dynamical behaviors of system (1). e use of well-known tools such as bifurcation diagram, Lyapunov Exponents (LEs) spectrum, phase portrait, and spectral entropy (SE) complexity helps us to demonstrate the chaotic behavior of the proposed system. e largest Lyapunov exponents (LEs) is an important tool for detecting chaos
Summary
Received 25 August 2021; Revised 14 November 2021; Accepted 13 December 2021; Published 12 January 2022. We introduce a new non-Shilnikov chaotic system with an infinite number of nonhyperbolic equilibrium points. E 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. The novel system has an infinite number of equilibrium points with double zero eigenvalues that are located on the z-axis. Multistability implies the coexistence of many periodic, limit cycle, and chaotic attractors under different initial values. Bifurcation analysis of the system shows interesting phenomena such as periodic window, period-doubling route to chaos, and inverse period-doubling bifurcations. E spectral entropy distribution under different initial values is very scattered and shows that the new system has numerous multiple attractors. 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
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