Multidirectional Multidouble-Scroll Hopfield Neural Network With Application to Image Encryption

Thanks to the biomimetic properties of synaptic plasticity, memristors are often utilized to mimic biological neuronal synapses. This article presents a new memristor synapse coupling (MSC) approach for producing multidirectional multidouble-scroll attractors. Through adopting flux-controlled hyperbolic memristor synapses to couple a Hopfield neural network, a novel multidirectional multidouble-scroll Hopfield neural network (MDMDSHNN) is constructed. Theoretical results and numerical calculations indicate that MDMDSHNN is capable of producing any desired amount of multidirectional multidouble-scroll attractors, including unidirectional (1-D), bidirectional (2-D), and three-directional (3-D) multidouble-scroll attractors. Furthermore, an infinite amount of initial offset-boosted coexisting multidouble-scroll chaotic attractors possessing identical shapes but different positions, i.e., homogeneous extreme multistability are also found via switching the memristor initial values. Furthermore, to validate the physical implementability and practicality of MDMDSHNN, the digital hardware platform is performed. Finally, to investigate MDMDSHNN in practical application, an image encryption scheme with superior security performance is given by employing the homogeneous multidouble-scroll chaotic sequences, further illustrating good superiority and effectiveness of the present MSC method.