Study on a four-dimensional fractional-order system with dissipative and conservative properties

In this paper, based on an existing four-dimensional integer-order conservative system, the corresponding fractional-order system is proposed and solved by the Adomian decomposition method (ADM). In the process of analyzing the influence of parameters and initial values on the dynamic behaviors of system, we find various quasi-periodic and chaotic flows with different topological structures as well as hidden extreme multistability. In addition, we observe two types of transient transition behavior. It is worth noting that a new phenomenon is found, that is, the dynamic behaviors of system change from dissipative to conservative with the increase of order. Phase diagram, Lyapunov exponent spectrum, bifurcation diagram and spectral entropy (SE) complexity algorithm are used to analyze the above dynamic behaviors. Finally, the hardware implementation of system is realized on the DSP platform, and experimental results are consistent with numerical simulation results. The research results show that the fractional-order system has high complexity and better engineering application value.