Abstract
A memristive chaotic system which has no equilibrium points is constructed by introducing different nonlinear functions and a memristive device. A novel family of multi-scroll attractors and multi-pinched hysteresis loops which are only determined by the transient time length can be generated when the sinusoidal function with no restrict condition is provided. Differently, this method for generating multi-scroll attractors and multi-pinched hysteresis loops need not change the original nonlinear functions. In addition, a sort of adaptive sliding mode synchronization of proposed identical memristive systems with disturbances is given. From a theoretical perspective, the proposed approach needs no redesign of the nonlinear function and it can simplify the design complexity of the proposed system. From an application perspective, the proposed adaptive sliding mode synchronization approach of this multi-scroll and multi-pinched hysteresis loops memristive chaotic system is firstly given. The obtained results are in consistent with numerical simulation results.
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