Discrete Tri-Cycle Memristive Synapse Hopfield Neural Network: Dynamics and Implementations

In this paper, a discrete memristor model is first developed and then utilized to construct a tri-cycle memristive synapse Hopfield neural network, replacing traditional resistive synapses. The equilibrium point stability is analyzed to reveal the Neimark–Sacker bifurcation behaviors, clarifying the intricate dynamics of the proposed network. Dynamical characteristics, including periodic, quasi-periodic, chaotic, and hyperchaotic states, are systematically explored using phase diagrams, iterative series, Lyapunov exponent spectra, and bifurcation diagrams. Furthermore, symmetry-induced dynamical phenomena under symmetric initial conditions are observed, demonstrating the coexistence of stable points and chaotic attractors. Compared with traditional tri-cycle resistive synapse HNN models, the proposed TCMS-HNN significantly enhances dynamic complexity and computational efficiency. Finally, the DSP implementation is completed, realizing the digital circuit of the TCMS-HNN model. These results provide important theoretical insights for neuroscience research and complex dynamical systems, also highlight its substantial potential in neuromorphic computing and secure information encryption.