Scaling of attractors of a multiscroll memristive chaotic system and its generalized synchronization with sliding mode control. (English) Zbl 1464.34075
Summary: Memristor can greatly enhance the complexity of a chaotic system because of its nonlinear characteristics. In this paper, three different memristor models are introduced to the Yang system. The chaotic attractors with single scroll and double scrolls can be obtained by adjusting the action intensities of three memristors and all the attractors inherit the scaling property of attractors of the Yang system. By employing the complex polynomials transformation method in the chaotic system to expand the number of scrolls of the system, the ring-shaped multiscroll attractors are generated, and the number of scrolls can be changed by adjusting the powers of complex polynomials, which show that the memristive system has flexible scalability. Next, a synchronization method for the multiscroll chaotic system is proposed. The generalized synchronization controller and parameter adaptive law are designed by employing sliding mode control. The sufficient conditions for synchronization are given by Lyapunov stability theory. This method can be applied to the synchronization of multiscroll systems generated by means of changing the state variables of the original system by function transformation and then adding the transformation matrix to the system. Compared with the existing synchronization method, this method has a wider scope of application, and it can synchronize two multiscroll chaotic systems with greater difference. In addition, the conditions to be satisfied in this method are simpler. Finally, the method proposed above is applied to the synchronization between a chaotic system with a ring-shaped eight-scroll attractor and a grid-shaped \(4\times4\)-scroll attractor chaotic system with interference signals. The numerical simulation results verify the effectiveness of the method.
MSC:
| 34D06 | Synchronization of solutions to ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
| 34C28 | Complex behavior and chaotic systems of ordinary differential equations |
| 34D45 | Attractors of solutions to ordinary differential equations |
| 34H10 | Chaos control for problems involving ordinary differential equations |
| 94C60 | Circuits in qualitative investigation and simulation of models |
Keywords:
memristor; multiscroll chaotic system; scaling of attractors; sliding mode control; generalized synchronizationReferences:
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