Memristive-cyclic Hopfield neural network: spatial multi-scroll chaotic attractors and spatial initial-offset coexisting behaviors

Neural networks with changeable synaptic weights usually exhibit more complex and diverse dynamics than those with fixed synaptic weights. It was proved that the tri-neuron resistive-cyclic Hopfield neural network (RC-HNN) cannot show chaos. To this end, we first consider a RC-HNN with bipolar pulse current to generate double-scroll chaotic attractors. On this basis, we then construct a tri-neuron memristive-cyclic Hopfield neural network (MC-HNN) by replacing the resistive weights with memristive ones, and spatial multi-scroll chaotic behaviors and spatial initial-offset coexisting behaviors are revealed therein using phase portrait, Poincaré map and basin of attraction. The results manifest that by setting the parameters related to the internal states of three memristors, the MC-HNN can not only generate spatial multi-scroll chaotic attractors (MSCAs) with different scroll numbers, but also produce spatial initial-offset coexisting attractors (IOCAs) with different attractor numbers. Besides, an FPGA hardware platform is developed and the spatial MSCAs and spatial IOCAs are displayed experimentally to confirm the numerical simulations.