Dynamic Analysis And Finite Time Synchronization Of A Novel Fractional Order Chaotic Circuit

Chaos theory is a research hotspot in nonlinear field.Chaos circuit modeling and implementation is the basis of its application in engineering practice.As an extension of integer order chaotic circuits,fractional order chaotic circuits have more complex dynamic behaviors and are closer to reality,with broader application prospects.This article designs a new type of four-dimensional integer order chaotic circuit and extends it to fractional order.It conducts research on dynamic behavior analysis,circuit simulation,circuit implementation,and synchronization control.The specific content is as follows:Firstly,a novel four-dimensional integer order chaotic circuit was proposed,and its stability was analyzed by calculating the equilibrium point.Its complex dynamic behavior under different parameters was analyzed through state variable time series diagrams,bifurcation diagrams,Lyapunov exponents,and other means,clarifying that the circuit has periodic and chaotic states.Subsequently,numerical and circuit simulations were conducted on this system,and a circuit model was built on an FPGA experimental platform to implement this new integer order chaotic circuit.The results of numerical simulation,circuit simulation,and circuit experiments were consistent,verifying the correctness of the theoretical analysis.Secondly,based on the fractional order calculus theory,this new integer order chaotic system is extended to the fractional order,and the parameter values of each component in the fractional order equivalent unit are obtained through the time-domain and frequency-domain method.The fractional order chaotic circuit is constructed using the fractional order equivalent unit and the circuit simulation analysis is carried out,which verifies that the fractional order chaotic circuit has complex dynamic behavior.The system is solved based on Adomian decomposition method,and the dynamic behavior of this fractional order chaotic system is realized on FPGA.The results are consistent with the numerical simulation,which proves the realizability of this fractional order chaotic system.Finally,the synchronization control problem of this fractional order chaotic circuit was studied based on finite time synchronization theory.A fractional order synchronization controller was designed using finite time synchronization theory,and it was observed that the error curve quickly approached zero after adding the synchronization controller,verifying the correctness and feasibility of the finite time synchronization theory.On this basis,circuit experiments were conducted and results consistent with numerical simulations were obtained,further proving the effectiveness of the synchronization scheme.A synchronization model was provided for this fractional order chaotic circuit,laying the foundation for its practical application.