By introducing a sine function, a non-autonomous multi-wing chaotic system is proposed. The system has an infinite number of equilibrium points and produces symmetrical attractors. The complex dynamical behaviors of the system are demonstrated by phase portraits, Lyapunov exponents spectrum and bifurcation diagram. The effect of driving amplitudes and initial conditions on the resulting system dynamics is then thoroughly investigated. The resulting attractors will enter different oscillatory states or have topological changes. The rotational coexisting attractors depend on the initial conditions and external amplitudes. Besides, a variety of interesting symmetrical transient behaviors and initial-offset boosting behaviors are also found. The driving amplitudes of the system affect the number of attractor wings, a weak signal detection circuit is accordingly designed to estimate the amplitude of periodic weak signals at diverse frequencies. The circuit operates near the switching threshold between the four-wing and two-wing chaotic attractor. Finally, an experimental investigation of the proposed design is performed that demonstrates the theoretical and simulation results.
An autonomous memristive circuit is implemented by an active third-order generalized memristor. The mathematical model is established and the stability of the equilibrium point and divergence are analyzed. Lyapunov exponents and bifurcation analysis demonstrate the complex dynamical behaviors of the system. As an internal parameter of voltage controlled memristor is changed, the system changes from bursting chaos to general chaos, which includes chaotic bursting attractor and periodic bursting attractor. This system produces periodic bursting similar to the clusters discharge of biological neurons. Interestingly, the system differs from the single helical clusters discharge of neurons. The bifurcation mechanism of the periodic bursting behavior is explored by constructing equilibrium trajectories of the fast-scale subsystem to verify the Fold bifurcation and to establish the Hopf bifurcation sets. Finally, it is shown that a circuit experiment based on Multisim is consistent with the theoretical analysis and numerical simulations, which proves the feasibility of the real circuit.
This paper introduces a charge-controlled memristor based on the classical Chuas circuit. It also designs a novel four-dimensional chaotic system and investigates its complex dynamics, including phase portrait, Lyapunov exponent spectrum, bifurcation diagram, equilibrium point, dissipation and stability. The system appears as single-wing, double-wings chaotic attractors and the Lyapunov exponent spectrum of the system is symmetric with respect to the initial value. In addition, symmetric and asymmetric coexisting attractors are generated by changing the initial value and parameters. The findings indicate that the circuit system is equipped with excellent multi-stability. Finally, the circuit is implemented in Field Programmable Gate Array (FPGA) and analog circuits.
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