Abstract
The traditional method of solving fractional chaotic system has the problem of low precision and is computationally cumbersome. In this paper, different fractional-order calculus solutions, the Adams prediction–correction method, the Adomian decomposition method and the improved Adomian decomposition method, are applied to the numerical analysis of the fractional-order unified chaotic system. The result shows that different methods have higher precision, smaller computational complexity, and shorter running time, in which the improved Adomian decomposition method works best. Then, based on the fractional-order chaotic circuit design theory, the circuit diagram of fractional-order unified chaotic system is designed. The result shows that the circuit simulation diagram of fractional-order unified chaotic system is basically consistent with the phase space diagram obtained from the numerical solution of the system, which verifies the existence of the fractional-order unified chaotic system of 0.9-order. Finally, the active control method is used to control and synchronize in the fractional-order unified chaotic system, and the experiment result shows that the method can achieve synchronization in a shorter time and has a better control performance.
Highlights
Since the definition of the Lorenz system by Lorenz in 1963, the study of modern chaos theory has made rapid progress
In 2005, Qi et al [7] added a nonlinear term on the basis of Lorenz system and obtained a new chaotic system
Wu [13] proposed a new control method based on linear matrix inequality to solve the synchronizationofof two fractional-order chaotic
Summary
Since the definition of the Lorenz system by Lorenz in 1963, the study of modern chaos theory has made rapid progress. Wu [13] proposed a new control method based on linear matrix inequality to solve the synchronizationofof two fractional-order chaotic. Synchronization problem of uncertain fractional-order chaotic system with modeling errors and external [16] et derived obtained a four-dimensional fractional-order discrete power model. Fractional-order chaotic system solution methods for example calling function method have some Basedsuch on as these in this paper, different methods are used to solve the numerical problems, lowproblems, accuracy and computationally cumbersome. Solution of the fractional-order unified chaotic system, the to phase diagramsolution of the Based on these problems, in this paper, different methods and are used solvespace the numerical corresponding order unified is obtained. Control laws are obtained by the active control method, and the control and synchronization of the fractional-order unified chaotic system are completed
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