Dynamics of Hindmarsh–Rose neuron with locally active memristor and its analog circuit simulation

When neurons are exposed to external electromagnetic radiation, the movement of charged ions can be influenced by the electromagnetic field, resulting in an induced current. At present, research on the bifurcation and firing patterns of neurons under the combined effects of multiple parameters is still insufficient, which cannot meet the needs of multiple stimuli acting on the nervous system simultaneously in real-world scenarios. In this paper, we propose a novel locally active memristor with bistable characteristics, which is introduced into a two-dimensional Hindmarsh–Rose neuron system to simulate induced current, constructing a neuron system under magnetic induction. We conducted detailed numerical analysis and experimental studies, varying parameters such as memristor parameter, external stimulation current, and electromagnetic induction intensity, to identify the unique and rich dynamical behaviors of the neuronal system in different regions. We discovered the distribution patterns of periodic firing in different regions, including interesting and rare regions with self-similar structures, such as shrimp-shaped regions and mosaic-shaped periodic firing regions, as well as firing activity clusters with composite cascade structures, which have not been reported in the previous studies on memristor neurons. The model proposed in this paper can exhibit firing activity in multiple modes, laying the foundation for further research on the effects of electromagnetic radiation on neuronal activity. Finally, to validate the accuracy of the numerical simulations, we designed an analog equivalent circuit for the neural system to verify the physical feasibility of the system circuit experiments. Graphical abstract