A novel memristor Hopfield neural network with homogeneous coexisting multi-scroll attractors

Abstract Compared to conventional single-scroll or double-scroll attractors, multi-scroll chaotic attractors possess wide potential for application due to their adjustability and complex topology. However, neural network models for generating multiple scrolls are often implemented using memristors with piecewise nonlinear functions. To further explore multi-scroll attractors with different working mechanisms,a unique memristor containing a group of hyperbolic tangent functions is designed and then applied in a three-dimensional Hopfield neural network (HNN). The proposed memristive Hopfield neural network (MHNN) has multi-scroll chaotic attractors, where the number and parity of the scrolls be changed by adjusting the control parameters of the memristor. The complex dynamical behaviors of MHNN are studied by utilizing diverse numerical modeling approaches like bifurcation diagrams, Lyapunov exponents and phase plot. In addition, the proposed MHNN also has a complicated offset boosting coexisting behavior. By selecting suitable parameters, multiple coexisting chaotic attractors could be obtained. Homogeneous coexisting multi-scroll attractors can be shifted in multiple directions including unidirectional, planar and spatial ones. Moreover, theoretically speaking, there could be an infinite number of coexisting attractors. Finally, experimental results are validated through numerical simulations and circuit experiments to confirm the feasibility of the proposed MHNN model.