Abstract
In this paper, a class of fractional-order symmetric hyperchaotic systems is studied based on the Adomian decomposition method. Starting from the definition of Adomian, the nonlinear term of a fractional-order five-dimensional chaotic system is decomposed. At the same time, the dynamic behavior of a fractional-order hyperchaotic system is analyzed by using bifurcation diagrams, Lyapunov exponent spectrum, complexity and attractor phase diagrams. The simulation results show that with the decrease of fractional order q, the complexity of the hyperchaotic system increases. Finally, based on the fractional-order circuit design principle, a circuit diagram of the system is designed, and the circuit is simulated by Multisim. The results are consistent with the numerical simulation results, which show that the system can be realized, which provides a foundation for the engineering applications of fractional-order hyperchaotic systems.
Highlights
Integer-order and fractional-order calculus have the same long history, both of which have been around for 300 years
Under Caputo’s definition, numerical solutions are all to find an approximate solution to fractional calculus by simulation, such as the frequency domain method (FDM) [15], Adam–Bashforth–Moulton algorithm (ABM) [16–18], and Adomian decomposition method (ADM) [19–22]
ADM has become a popular algorithm in fractional-order numerical solutions because it has many advantages, such as dealing with linear and nonlinear problems with high precision in the time domain, fast calculation speed, less consumption of computer resources, and a low order of chaos [22–26]
Summary
Integer-order and fractional-order calculus have the same long history, both of which have been around for 300 years. ADM has become a popular algorithm in fractional-order numerical solutions because it has many advantages, such as dealing with linear and nonlinear problems with high precision in the time domain, fast calculation speed, less consumption of computer resources, and a low order of chaos [22–26]. [7] used an ADM algorithm to analyze the complexity and dynamic behavior of a fractional-order chaotic system with line equilibrium, and ref. We focus on the numerical solution and dynamics of a fractional-order hyperchaotic system with three positive Lyapunov exponents based on the ADM algorithm.
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