Multi-scroll attractor and its broken coexisting attractors in cyclic memristive neural network

This paper proposes a simple-structured memristive neural network, which incorporates self-connections of memristor synapses alongside both unidirectional and bidirectional connections. Different from other multi-scroll chaotic systems, this network structure has a more concise three-neuron structure. This simple memristive neural network can generate a number of multi-scroll attractors in manageable quantities and shows the characteristics of the coexisting attractors and amplitude control. In particular, when the parameters are changed, the coexisting attractors break up around the center of gravity into two centrosymmetric chaotic attractors. Abundant dynamic behaviors are studied through phase portraits, bifurcation diagrams, Lyapunov exponents, and attraction basins. The feasibility of the system is demonstrated by building a circuit realization platform.