Planar Homogeneous Coexisting Hyperchaos in Bi-Memristor Cyclic Hopfield Neural Network

Memristors with synaptic plasticity can act as changeable connection weights. To address the issue of no chaos in cyclic trineuron Hopfield neural network with resistive weights, a bimemristor cyclic Hopfield neural network (BM-CHNN) is presented by substituting two resistive weights with two memristive weights, and thus chaos and hyperchaos are demonstrated. BM-CHNN has a planar equilibrium set, and the stability distribution related to two memristor initial states is discussed by exploring three nonzero eigenvalues. Further, parameter-relied bifurcation and heterogeneous coexisting behaviors are disclosed, and planar homogeneous coexisting hyperchaotic (HC) attractors regulated by the memristor initial states are uncovered. The results manifest that BM-CHNN not only displays chaos and hyperchaos but also exhibits the planar homogeneous coexisting hyperchaos owning the elegant basins of attraction with fantastic manifold structures and fractal boundaries. Finally, a STM32-based hardware platform is fabricated and the heterogeneous and homogeneous coexisting attractors are captured experimentally to confirm the numerical results.