Control And Dual Synchronization Of Fractional-order Chaotic Systems

In recent years, the topic of fractional-order chaos systems has attracted manyresearchers. In the real world, the shadow of fractional-order chaos systems appear inmany fields, because of the complexity of fractional-order chaos systems, the ability ofits security and resistance to decipher is stronger, have the extensive applicationprospects. These problems are considered, the first problem is when an integer ordersystem is chaotic, under what condition the corresponding fractional-order system isalso chaotic. The second is how to design a controller to realize the control andsynchronization of fractional-order chaotic systems. In this thesis, the problems ofcontrol and synchronization and dual synchronization of factional-order chaos systemsby using the methods of theoretical derivation and numerical simulation. The mainachievements contained in this article are as follows:Firstly, we analyze the chaos characteristics of a new fractional-order system, andthe Routh-Hurwitz criterion condition, a quadratic term YZ is added based on thefractional-order modified Autonomous Van der Pol-Duffing(MAVPD) chaos system tohelp us get a new fractional three-dimensional autonomous chaos system. We solve theunstable equilibrium points of the new chaos system, and analyze its unstableequilibrium points using the Routh-Hurwitz criterion condition, a stable condition thatthe new chaos system is stable in unstable equilibrium points is obtained, based onwhich we design a single-variable feedback controller, to control over the unstableequilibrium points. By numerical simulation, we verify the control result.Secondly, we studies the problem of self-synchronization and different structuresynchronization of the fractional-order chaos system. After analyzing the control offractional-order chaotic, by designing the activate control function, we gain the systemicsimultaneous condition and apply the Laplace transformation theory to achievesynchronization of chaotic. By numerical simulation, we verify the control result.Lastly, the problem of the dual synchronization of two different fractional-orderchaotic systems is investigated. On this basis, we propose a method of dualsynchronization of fractional-order chaotic systems. By stabilization theory, we design alinear controller to realize the dual synchronization of two different fractional-orderchaotic systems. The proposed method is applied for dual synchronization of Van der Pol-Willis systems and Van der Pol-Duffing systems. The numerical simulation showsthe accuracy of the theory.