Initial Boosting Phenomenon And Sliding Mode Control Of A Fractional-Order Hyperchaotic System Based On Dual Memristors

Memristor is known as the four basic components in electronic circuit,which reveals the relationship between the amount of charge and magnetic flux in the circuit.On the one hand,the emergence of memristor fills the lack of traditional circuit theory.On the other hand,it provides a new research direction for plenty of fields.When the current through the memristor changes,the resistance of the memristor will change accordingly,which makes the memristor have great potential in practical application.An important application carrier of memristor is memristive chaotic circuit.The circuit design based on memristor and memristive chaotic circuit has become a hot research direction.Especially,with the development of fractional calculus in physics and engineering,more and more researchers pay attention to fractional-order memristive chaotic system.In this thesis,the fractional-order hyperchaotic system based on dual memristors is studied.Firstly,the fractional-order hyperchaotic system is proposed and the memristor initial boosting phenomenon of the system is discussed.Moreover,the sliding mode control strategy is used to control the chaos of the fractional-order hyperchaotic system.The specific work of this thesis is as follows(1)Dual memristors are used to replace the coupling resistors in the original circuit,the capacitor is replaced by the fractional-order capacitor.Thus,the circuit model of fractional-order memristor hyperchaotic system is established,and the equilibrium point and stability of the system are analyzed.(2)The fractional-order hyperchaotic system has two zero eigenvalues and three nonzero eigenvalues.Therefore,the equilibrium plane can be separated into two diverse,which demonstrates the appearance of bi-stability.The simulation results illustrate that the initial states have a significant impact on the dynamic behaviors,which can be mirrored by the phase portraits,the bifurcation diagrams,the power spectrum and the time-domain waveform.Especially,the memristor initial boosting phenomenon is investigated and the numerical simulation results under different initial value controllers are given.Finally,a hardware circuit based on PSPICE software is fabricated.(3)Based on the fractional-order memristive hyperchaotic system,the sliding mode control strategy is utilized to control the system.Furthermore,the asymptotic stability of the system is analyzed theoretically,and the conditions that should be followed in the design of fractional-order sliding mode controller are obtained.Then,the sliding mode control scheme is designed to make the system in a stable state,so as to eliminate chaos.