Numerical Analysis of a Novel 3D Chaotic System with Period-Subtracting Structures.

Zolfaghari-Nejad, Maryam; Hassanpoor, Hossein; Charmi, Mostafa

In this work, we present a novel three-dimensional chaotic system with only two cubic nonlinear terms. Dynamical behavior of the system reveals a period-subtracting bifurcation structure containing all m th-order (m = 1 , 2 , 3 , ...) periods that are found in the dynamical evolution of the novel system concerning different values of parameters. The new system could be evolved into different states such as point attractor, limit cycle, strange attractor and butterfly strange attractor by changing the parameters. Also, the system is multistable, which implies another feature of a chaotic system known as the coexistence of numerous spiral attractors with one limit cycle under different initial values. Furthermore, bifurcation analysis reveals interesting phenomena such as period-doubling route to chaos, antimonotonicity, periodic solutions, and quasi-periodic motion. In the meantime, the existence of periodic solutions is confirmed via constructed Poincaré return maps. In addition, by studying the influence of system parameters on complexity, it is confirmed that the chaotic system has high spectral entropy. Numerical analysis indicates that the system has a wide variety of strong dynamics. Finally, a message coding application of the proposed system is developed based on periodic solutions, which indicates the importance of studying periodic solutions in dynamical systems.

NUMERICAL analysis; BIFURCATION diagrams; LIMIT cycles; DYNAMICAL systems; ENTROPY

International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, 2021, Vol 31, Issue 11, p1

0218-1274

Academic Journal

10.1142/S0218127421501698