Dynamical analysis, multi-cavity control and DSP implementation of a novel memristive autapse neuron model emulating brain behaviors

Abstract

The construction and analysis of memristive neuron models is an important aspect of studying the working mechanisms of the brain and an approach to constituting chaotic systems. In the paper, a discrete local active memristor (DLAM) model is constructed with its properties analyzed. Later, the novel DLAM is applied to mimic autapse to constitute a memristive autapse neuron model. The activation function is replaced with a hyperbolic tangent function considering the threshold parameter to approach the biological properties of a neuron. Then, the equilibrium point about the neuron model is studied. Dynamical behaviors are investigated through the methods of phase diagram, iteration series, bifurcation diagram, Lyapunov Exponent spectrum (LEs), attractor basin, power spectrum and Spectral Entropy (SE) complexity. Abundant dynamical characteristics and neuron firing modes are presented as various parameters are varied, such as hyperchaos, chaos and period. The frequency distribution embodied in the power spectrum demonstrates that the electrical signals produced by the neuron model can emulate brain behaviors. Multi-cavity control of the attractor is completed with multistage step functions. In addition, this memristive autapse neuron model is implemented in DSP platform, proving the digital circuit feasibility of it. This autapse neuron model is essential for understanding and predicting brain behaviors. Meanwhile, the model with high complexity can provide chaotic sequences for image encryption or communication secrecy.