Construction, Dynamical Characteristics, and DSP Implementation of a Hyperbolic Tangent-Regulated Memcapacitor Neural Network

In recent years, despite the extensive deployment of several discrete mapping neuron models for their high efficiency, explicit expression and facile hardware implementation, most of these modes are shown deficient in simultaneously characterizing intricate firing patterns and strong nonlinear dynamical behaviors under a unified framework. This limitation is attributed to the absence of intrinsic synaptic memory mechanisms and the excessively simplified slow-variable structures in such models. To remedy the above-mentioned deficiencies, a novel discrete neural model that integrates memcapacitive memory mechanisms with the neural dynamics of chaotic mappings is proposed in this study. A hyperbolic tangent-modulated memcapacitor is constructed to describe synaptic nonlinear memory characteristics, discretized into an iterative computation-adaptable discrete model via the Euler forward difference method, embedded into a two-dimensional mapping neuron framework and used to replace the traditional recovery variable with its internal state quantity for achieving deep coupling between memory units and neural dynamics, thus forming a Hyperbolic Tangent-modulated Memcapacitive Neural Network (HTMNN). The model is analyzed on the basis of fixed-point stability theory, and its dynamical characteristics are systematically investigated via phase diagrams, bifurcation diagrams, Lyapunov exponent spectra, and spectral entropy analysis. It is demonstrated by the results that diverse dynamical states including periodic, chaotic, and superchaotic behaviors are exhibited by the HTMNN under parameter tuning. Multistability, coexisting attractors symmetric about the origin, diverse discharge patterns and flexible state transition dynamics are displayed by the model. Finally, the HTMNN is successfully implemented in hardware on the TMS320F28335 DSP platform, with its chaotic attractors reproduced and the engineering feasibility of the model validated accordingly.