Coexisting and multiple scroll attractors in a Hopfield neural network with a controlled memristor

A method of generating multi-double scroll attractors is proposed based on the memristor Hopfield neural network (HNN) under pulse control. First, the original hyperbolic-type memristor is added to the neural network mathematical model, and the influence of this memristor on the dynamic behavior of the new HNN is analyzed. The numerical results show that after adding the memristor, the abundant dynamic behaviors such as chaos coexistence, period coexistence and chaos period coexistence can be observed when the initial value of the system is changed. Then the logic pulse is added to the external memristor. It is found that the equilibrium point of the HNN can multiply and generate multi-double scroll attractors after the pulse stimulation. When the number of logical pulses is changed, the number of multi-double scroll attractors will also change, so that the pulse can control the generation of multi-double scroll attractors. Finally, the HNN circuit under pulsed stimulation was realized by circuit simulation, and the results verified the correctness of the numerical results.