Abstract
Investigation of the classical self-excited and hidden attractors in the modified Chua’s circuit is a hot and interesting topic. In this article, a novel Chua’s circuit system with an absolute item is investigated. According to the mathematical model, dynamic characteristics are analyzed, including symmetry, equilibrium stability analysis, Hopf bifurcation analysis, Lyapunov exponents, bifurcation diagram, and the basin of attraction. The hidden attractors are located theoretically. Then, the coexistence of the hidden limit cycle and self-excited chaotic attractors are observed numerically and experimentally. The numerical simulation results are consistent with the FPGA implementation results. It shows that the hidden attractor can be localized in the digital circuit.
Highlights
According to Jenkins [1] and Kuznetsov et al [2], there are two kinds of attractors, namely, the selfexcited attractors and the hidden attractors
When α 69, let z0 −1, y0 0.1 and x0 0.3, basins of attraction in the x0 − y0 plane, x0 − z0 plane, and y0 − z0 are shown in Figures 2D,E,F, respectively. It shows that the system has three coexisting states with different initial conditions
For the given parameters, the coexisting periodic circles or chaotic attractors are presented with initial conditions [x0, y0, z0] [0.01, 0, 0.01] and [x0, y0, z0] [−0.01, 0, −0.01]
Summary
According to Jenkins [1] and Kuznetsov et al [2], there are two kinds of attractors, namely, the selfexcited attractors and the hidden attractors. Investigation of the multiple coexisting hidden attractors in the nonlinear systems is a research hotspot [13,14,15,16]. It means that multiple coexisting attractors and hidden attractors are both found in the system with different initial conditions [17]. Analog circuit implementation of chaotic systems can generate real chaos, the initial conditions cannot be set, artificially and accurately.
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