Abstract
This paper proposed a novel fractional-order memristor-based chaotic circuit. A memristive diode bridge cascaded with a fractional-order RL filter constitutes the generalized fractional-order memristor. The mathematical model of the proposed fractional-order chaotic circuit is established by extending the nonlinear capacitor and inductor in the memristive chaotic circuit to the fractional order. Detailed theoretical analysis and numerical simulations are carried out on the dynamic behavior of the proposed circuit by investigating the stability of equilibrium points and the influence of circuit parameters on bifurcations. The results show that the order of the fractional-order circuit has a great influence on the dynamical behavior of the system. The system may exhibit complicated nonlinear dynamic behavior such as bifurcation and chaos with the change of the order. The equivalent circuits of the fractional-order inductor and capacitor are also given in the paper, and the parameters of the equivalent circuits are solved by an undetermined coefficient method. Circuit simulations of the equivalent fractional-order memristive chaotic circuit are carried out in order to validate the correctness of numerical simulations and the practicability of using the integer-order equivalent circuit to substitute the fractional-order element.
Highlights
Since memristor was first postulated by Leon O
Memristor has been widely used in many fields such as resistive random access memory (RRAM) [4, 5], neural networks [6,7,8], signal processing [9], chaotic and control systems [10], and sample recognition [7, 11]
Because the proposed fractional-order memristive Chua’s circuit has four dynamic elements, there are four corresponding state variables, which are the voltages across the fractional-order capacitors Cλ1 and Cλ2v1 and v2, the current flowing through the fractional-order inductor Lλi3
Summary
Since memristor was first postulated by Leon O. It is proved that an elementary electronic circuit consisting of a full-wave rectifier and a second-order RLC filter has memory properties [13] Removing the resistor, another diode bridge circuit cascaded with a second-order filter containing an inductor and a capacitor can constitute a generalized memristor [14]. In paper [30], a fractional-order memristor model was applied to the Chua’s oscillator for the first time, which constructed a fractional-order memristor-based chaotic circuit.
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