Abstract
Memristor possesses synapse-like properties that can mimic excitation and inhibition between neurons. This article introduces the Sigmoid functions to the memristor and constructs a new memristive Hopfield neural network (HNN). Its most distinctive feature is the simple topology, which contains only unidirectional connections in neurons. The equilibrium points analysis reveals the mechanism of its multiscroll attractors generation. Homogeneous and heterogeneous coexisting attractors are observed with the variation of the network parameters. Note that the state equation of memristor can affect the number of coexisting attractors. A hardware implementation is designed for it, and the multiscroll attractors are captured in the oscilloscope. Finally, it is also applied to developing an image encryption algorithm with excellent performance.
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