Offset-controlled plane dynamics in dual memristors-radiated discrete Hopfield neuron

Offset-controlled plane coexisting firing has been observed in continuous neural systems but has yet to be successfully reported in discrete neural maps. To address this challenge, this study first proposes a three-dimensional dual memristors-radiated discrete Hopfield neuron (3-D DMR-DHN) mapping framework, include two specific maps consisting of sine and cosine memristive electromagnetic radiations (MERs). The corresponding neuron circuit and the energy evaluation system are constructed, demonstrating the reliability of the map. The proposed maps feature plane invariant points related to the initial conditions (ICs) of two MERs, and the critical stability condition and its distribution are identified according to the presentation of characteristic roots. Subsequently, the MER intensities-dependent bifurcation mechanisms are elucidate through 2-D dynamical distributions, 1-D bifurcation diagrams, and phase portraits. Importantly, the topological invariance of the proposed maps is theoretically established, and the MER ICs-triggered extreme multistability are numerically simulated, leading to offset-controlled coexisting bifurcations and local basins of attraction with the similar profile and fractal boundary. With comprehensive performance indicators, the dynamical complexity and richness of the proposed maps are thoroughly evaluated. The findings indicate that the considered maps achieve exceptionally high-performance offset-controlled line/plane coexisting firing with the extreme multistability for the first time, and the MER ICs can flexibly and non-destructively control the offset of the coexisting phase point while preserving the dynamical performance. Additionally, a pseudo-random number generator and an MCU hardware circuit system are developed, and experimental results validated the physical realizability and application value of the proposed maps.