A Memristive Synapse Control Method to Generate Diversified Multistructure Chaotic Attractors

Due to the synapse-like nonlinearity and memory characteristics, memristor is often used to construct memristive neural networks with complex dynamical behaviors. However, memristive neural networks with multistructure chaotic attractors have not been found yet. In this article, a novel method for designing multistructure chaotic attractors in memristive neural networks is proposed. By utilizing a multipiecewise memristive synapse control in a Hopfield neural network (HNN), various complex multistructure chaotic attractors can be produced. Theoretical analysis and numerical simulation demonstrate that multiple multistructure chaotic attractors with different topologies can be generated by conducting the memristive synapse-control in different synaptic coupling positions. Differing from traditional multiscroll attractors, the generated multistructure attractors contain multiple irregular shapes instead of simple scrolls. Meanwhile, the number of structures can be easily controlled with the memristor control parameters. Furthermore, we design a module-based analog memristive neural network circuit and the arbitrary number of multistructure attractors can be obtained by selecting corresponding control voltages. Finally, based on the memristive HNNs, a novel image encryption cryptosystem with a permutation-diffusion structure is designed and evaluated, exhibiting its excellent encryption performances, especially the extremely high key sensitivity.