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Mostafa Charmi

Maryam Zolfaghari-Nejad, Hossein Hassanpoor, Mostafa Charmi
Numerical analysis of a novel 3D chaotic system with period-subtracting structures
Abstract


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 mth-order (m=1, 2, 3, ...) periods that is found in the dynamical evolution of the novel system concerning di erent values of parameters. The new system could be evolved into di erent states such as point attractor, limit cycle, strange attractor, and butter y strange attractor by changing the parameters. Also, the system is multi-stable, which implies another feature of a chaotic system known as the coexistence of numerous spiral attractors with one limit cycle under di erent 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 con rmed via constructed Poincare return maps. In addition, by studying the in uence of system parameters on complexity, it is con rmed 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.

 

 

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