Dynamics and Image Encryption Application of Fractional-Order Memristive Bridge-Type Crosstalk-Coupled HR-FN Neurons

While significant progress has been made in memristor-based synaptic crosstalk simulation research in recent years, existing models still exhibit theoretical limitations in characterizing synaptic crosstalk effects. To address this scientific problem, this study innovatively integrates the Hindmarsh-Rose (HR) neuron model and the FitzHugh-Nagumo (FN) neuron model to construct an 8-dimensional heterogeneous coupled neural network model based on fractional calculus, i.e., the Fractional-Order Memristive Bridge Crosstalk-Coupled Neural Network (FMBCCNN). By introducing a fractional-order memristive bridge coupling structure to overcome the theoretical constraints of traditional models, we investigate the impact of synaptic strength and crosstalk intensity on the firing activity of neural networks. The dynamic characteristics of the neural network are analyzed using methods such as time series, phase portraits, bifurcation diagrams, and Lyapunov exponents. Under varying parameter conditions, the system exhibits rich dynamical behaviors, including attractor coexistence, period-doubling bifurcation, and chaotic crisis. The influence of changes in the fractional order derivative is also simulated, providing a more generalized representation of neuronal firing phenomena. Finally, the sequences generated by this 8-dimensional chaotic system are integrated into an image encryption algorithm based on bit-plane decomposition and DNA sequence coding. Comprehensive security analyzes demonstrate that the combined sequence and algorithm exhibit favorable security performance and reliable encryption characteristics.