Abstract
Fractional order systems have a wider range of applications. Hidden attractors are a peculiar phenomenon in nonlinear systems. In this paper, we construct a fractional‐order chaotic system with hidden attractors based on the Sprott C system. According to the Adomain decomposition method, we numerically simulate from several algorithms and study the dynamic characteristics of the system through bifurcation diagram, phase diagram, spectral entropy, and C0 complexity. The results of spectral entropy and C0 complexity simulations show that the system is highly complex. In order to apply such research results to engineering practice, for such fractional‐order chaotic systems with hidden attractors, we design a controller to synchronize according to the finite‐time stability theory. The simulation results show that the synchronization time is short and the robustness is stable. This paper lays the foundation for the study of fractional order systems with hidden attractors.
Highlights
Since Lorenz proposed the first chaotic system [1] in 1963, many chaotic systems [2,3,4,5,6] have been proposed successively
The self-excited attractor is mainly caused by the unstable equilibrium point, while the hidden attractor is mainly caused by the existence of infinite equilibrium points and disjoint with the unstable equilibrium point
The stable equilibrium point does not mean that the system is stable, which means that the previous judgment method cannot complete the judgment work
Summary
Since Lorenz proposed the first chaotic system [1] in 1963, many chaotic systems [2,3,4,5,6] have been proposed successively. The researches on hidden attractors are mostly of integer order and few of fractional order. With the in-depth research, people found the applicable range of the fractional order system is bigger than integer order more [12], especially secure communication. In 2003, Li Chunguang [13] realized the synchronization of fractional chaos system for the first time. Many synchronization methods [14, 15] of fractional-order chaotic systems have been proposed. We realize chaotic synchronization on the basis of fractional finite time stability theory. These properties have significant application value to the area of secure communication and image encryption
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