Characteristic Analysis Of Fractional-order Gene-Ralized Memristor And Its Application In Chaotic Circuits

As the fourth basic circuit element,the discovery of memristors has promoted the development and progress of the whole scientific field.In recent years,memristors have been widely used in resistive random access memory,neural networks,signal processing,chaos and control systems,and sample recognition.In this paper,a novel fractional-order model of a generalized memristor is established and applied to chaotic circuit based on fractional calculus theory.The dynamic behavior of fractional-order memristive chaotic circuits is analyzed in detail,and the equivalent circuit of fractional-order memristive chaotic circuit is realized.The main works are as follows:1.Three fractional-order models of generalized memristors are constructed based on fractional-order calculus theory.They are the fractional-order generalized memristor model consisting of a diode-bridge circuit cascaded a fractional-order RC filter,a fractional-order generalized memristor model consisting of a diode-bridge circuit cascaded a fractional-order RL filter and a fractional-order cubic nonlinear flux-controlled generalized memristor model.The volt-ampere characteristic curves of fractional-order generalized memristors are analyzed and has been proved that it has the characteristics of a memristor and can be called as a fractional-order generalized memristor.2.The proposed fractional-order generalized memristor is introduced into Chua's chaotic circuit to construct a fractional-order generalized memristor-based chaotic circuit.Its characteristics are analyzed by numerical simulation.The dynamic behavior of fractional-order memristive chaotic circuit is analyzed by means of phase diagram,stability of equilibrium points and bifurcation diagram,and the influence of order on memristive chaotic circuit is studied.3.The equivalent models of fractional capacitance and inductance are realized by equivalent circuit,and the specific parameters of fractional equivalent models are solved by Oustaloup filtering algorithm and undetermined coefficient method.The equivalent models are used to replace fractional order components,and the models of fractional order memristor and fractional order memristive chaotic circuit are constructed.The model is simulated and analyzed by circuit simulation software to verify the correctness of theoretical derivation and numerical simulationThe fractional-order generalized memristors proposed in this paper can better describe the actual characteristics of memristor and are easy to implement,so it has broad application prospects in the field of chaotic circuits.In addition,due to the introduction of new fractional-order parameters,fractional-order generalized memristor-based chaotic circuits have more abundant dynamic behavior,and have better applications in secure communications and other fields.