A fractional-order ship power system with extreme multistability

• Published in: Nonlinear dynamics Vol. 106; no. 1; pp. 1027 - 1040
• Main Authors: Zhang, Haoyu, Sun, Kehui, He, Shaobo
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01-09-2021; Springer Nature B.V
• Subjects: Automotive Engineering; Bifurcations; Chaos theory; Classical Mechanics; Control; Decomposition; Digital electronics; Dynamical Systems; Engineering; Extreme values; Liapunov exponents; Mathematical analysis; Mechanical Engineering; Original Paper; Phase diagrams; Trigonometric functions; Vibration; Chaos; Ship power system; Extreme multistability; Multi-scroll chaotic attractor; Fractional calculus
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-021-06875-5

In this paper, by introducing Caputo fractional-order definition into a ship power system with two parallel generators, a fractional-order ship power system with extreme multistability is constructed. The decomposition of trigonometric function product terms is optimized based on the Adomian decomposition method (ADM). Dynamics of the fractional-order ship power system is analyzed by phase diagrams, bifurcation diagrams, Lyapunov exponents (LEs) and SE complexity. The results show that it has rich dynamical characteristics, including variable phase space trajectory, coexisting attractors and typical bifurcations. Moreover, some interesting phenomena are observed, such as angular instability, multi-scroll chaotic attractor and the attractor offset based on the initial values. The influencing factors of multi-scroll number are explored and extreme multistability of the system is proved. Finally, the numerical simulation and theoretical analysis are verified by digital circuit realization. The research results lay the foundation for the application of the fractional-order ship power system.