Analysis of three types of initial offset-boosting behavior for a new fractional-order dynamical system

Abstract

• A new four dimensional fractional-order dynamical system with no equilibrium points is proposed and the corresponding numerical solution based on the Adomian decomposition method is given. • The system exhibits three initial offset boosting behaviors that are conservative, quasi-conservative, and dissipative, respectively. • The system was implemented by the digital signal processor (DSP) platform. In this study, a new fractional-order chaotic system is proposed based on the Adomian decomposition method (ADM). The system is proved to have no equilibrium point, so the system has hidden nonlinear characteristics. Furthermore, the initial-offset boosting behavior can be observed from this system. When the system parameters are fixed and the initial value changes, the evolution of the conservative, quasi-conservative, and dissipative phase trajectory boosts are analyzed in detail by numerical simulations, such as phase diagrams, mean values of the state variables, bifurcation diagrams, and dynamical distribution maps. These dynamic behaviors also indicate that the system has striking hidden multistability. Although some chaotic systems with initial-offset boosting behavior has been previously reported, it should be noted that this non-equilibrium fractional-order chaotic system with three types of offset-boosted control of initial value is the first to build and study. Finally, a circuit implementation on a digital signal processor (DSP) demonstrates the validity of the numerical analysis and the physical implementability of the system.