A Novel Multiscroll Memristive Hopfield Neural Network

Memristors are usually introduced into neuron models as neural synapses to investigate firing activities. In this paper, a novel generic memristor with smooth cosine memductance is proposed, and its dynamic characteristic concerning multistability, which is completely different from any known memristors, is analyzed and validated by numerical and PSIM simulations. The PSIM simulations intuitively reflect the memory properties of the constructed memristor emulator. To investigate the application of the proposed memristor, a multiscroll memristive Hopfield neural network is modeled by introducing the memristor into a tri-neuron Hopfield neural network as a synapse weight. Homogeneous single-scroll and double-scroll multistability phenomena are revealed by utilizing some analytical tools, such as bifurcation diagrams, local attraction basins, phase plane portraits, and so on. It is found that there is a multi-double-scroll attractor with growing scrolls for appropriate parameters. Furthermore, the average Hamiltonian energy, dependent on the homogeneous dynamics, is analyzed based on Helmholtz's theorem. It is discovered that the homogeneous dynamics is closely related to the energy transition, which may provide a new explanation for the occurrence of multistability in the human brain. Finally, several circuit experiments are carried out to confirm the dynamical behaviors, and it is found that the circuit can show similar dynamics as the numerical simulations.