Several Classes Of Synchronization Control Of Fractional-order Memristor-based Chaotic Systems

Since scientists found that the synchronization of chaotic systems can be realized in the theoretical analysis and experimental simulation,chaotic synchronization has raised a research upsurge in the field of chaos and control.As a new type of nonlinear circuit elements,memristor has aroused great attention in the field of chaos because of its memory and nonlinear characteristics.With the presentation of the memristor model,memristor is used to replace the nonlinear circuit elements in traditional chaotic circuits,thus forming a new class of chaotic circuits,named as memristor-based chaotic circuits.With the development of fractional calculus theory,and the practical problems can be described more accurately by the fractional calculus,so we apply fractional calculus theory to memristive chaotic system,and research the synchronization control problem of this system.Due to the chaotic signals generated by fractional-order chaotic systems are more complex and changeable,the synchronization of fractional-order memristive chaotic systems has great practical application value in the field of secure communication.In this dissertation,we first derive a dynamical equation of the integer-order memristor-based chaotic system based on a memristive chaotic circuit.Then we deduce the fractional order equation based on the integer order dynamical equation,and the synchronization control problem of fractional-order memristor-based chaotic system has been researched in depth.Meanwhile,the number of chaotic systems involved in the chaotic synchronization scheme has been gradually increased in this dissertation.Based on the synchronization research of the two chaotic systems,we further study the combination-combination synchronization of the four chaotic systems and the compound-combination synchronization of the five chaotic systems.The main innovation points of this dissertation are summarized as follows:(1)Based on a class of novel integer-order memristive chaotic systems,the dynamical equations of fractional-order memristive chaotic systems are derived.The synchronization of fractional-order memristor-based chaotic system is of great importance for information security,however,there are few researches on the synchronization of fractional-order memristive chaotic system.Therefore,the synchronization control problem of this system is studied comprehensively in this dissertation.(2)Based on a synchronization model of one drive system and one response system,combination-combination synchronization model and compound-combination synchronization model are introduced.At the same time,combining the stability theory of fractional order system and the related lemmas,adjustable adaptive controllers are designed to analyse the synchronization,combination-combination synchronization and compound-combination synchronization of fractional-order memristive chaotic system,and the conditions that this system can achieve the synchronization under the three synchronization schemes are deduced respectively.(3)By changing the control parameters of the controller,the complete synchronization,anti-synchronization and projective synchronization of the fractional-order memristor-based chaotic system are all realized under the three synchronization schemes respectively.Finally,the simulation results show the validity of the controller and the correctness of the theoretical derivation.