Dual memristors-radiated discrete Hopfield neuron with complexity enhancement

Designing a low-dimensional bionic memristive neuron map with complexity enhancement characteristics is of great significance for improving the dynamic performance and application value of neurons or networks. It is a challenging work and remains underreported to date. To this end, this paper first discloses the simplest one-dimensional (1-D) Hopfield neuron map, and proposes a 3-D dual memristive electromagnetic radiations-enhanced discrete Hopfield neuron (DMER-HN) map by using discrete memristors to imitate multiple radiation sources. It has infinitely many fixed points at a plane, and the stability boundary and distribution are studied according to the unique non-one characteristic root. Subsequently, the parameters-related firing domain and the extreme multistability firing controlled by initial conditions are further elucidated by numerical simulations. Significantly, strange hyperchaotic attractors and firing sequences are comprehensively evaluated and compared using various dynamical performance indicators. The results demonstrate that the proposed map exhibits complexity enhancement, characterized by its capability to generate extreme multistability and robust hyperchaotic firings. The developed microcontroller-based digital circuit platform robustly verifies the numerical findings. Finally, the complexity enhancement of the DMER-HN map has been effectively applied and faithfully validated in the pseudo-random number generator and image encryption tasks.