Dynamics analysis of Hindmarsh-Rose neuron model with a fractional-order magnetic flux memristor

In this paper, we investigate the dynamic behavior of a modified Hindmarsh-Rose (HR) neuron model incorporating a fractional-order magnetic flux-controlled memristor. By introducing the fractional-order derivative into the HR neuron system, the model exhibits rich and complex dynamics, including regular spiking and chaotic oscillations. The memristor is modeled based on a flux-controlled mechanism, capturing memory-dependent electrical characteristics and enhancing the bio-plausibility of the system. Through numerical simulations, bifurcation analysis, and phase space reconstruction, we reveal how the external stimulation parameter and memristor parameter affect the system’s excitability and stability. The results demonstrate that the combination of fractional calculus and memristive behavior provides a powerful framework for modeling and analyzing neural dynamics, with potential applications in neuromorphic computing, secure communication, and biological signal processing.