Generating multi-scroll chaotic attractor in a three-dimensional memristive neuron model

Abstract

The tabu learning single neuron model with external stimulus is a significant model for describing the firing activities of neurons. The current generated by a magnetic-controlled memristor has the properties of electromagnetic induction current, which can be taken as special external interference in a complex physical environment. Can this neuron model still exhibit complex and diverse firing activities when memristive current is used instead of external stimulus? To solve this puzzle, this article proposes a novel three-dimensional (3-D) memristive tabu learning neuron (MTLN) model by substituting external stimulus with memristive current, which can generate a multi-scroll chaotic attractor (MSCA) whose scrolls grow with time. The MTLN model has a line equilibrium set with different stability types relied on the initial position of the memristor internal state. Using some numerical methods, complex dynamical behaviors and scroll-growing MSCAs are uncovered. Further, a simple scroll-control scheme is designed and its effectiveness is demonstrated numerically and theoretically. The results manifest that the scrolls of the generated MSCAs can grow with time and can be also controlled by bounding the memristor internal state. In addition, an FPGA hardware platform is exploited for the 3-D MTLN model and the scroll-growing and scroll-controlled MSCAs are yielded experimentally to confirm the numerical results.