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Recent advances in crosstalk simulation using integer-order memristive synapses have shown considerable progress. However, most existing models still employ a single-memristor structure, which constrains synaptic weight modulation and makes it difficult to represent both excitatory and inhibitory synaptic connections in a unified manner. These models also often fail to capture the memory effects and nonlocal dynamic properties inherent in biological neurons. To address these issues, this study introduces a fractional-order memristive bridge synapse model for crosstalk coupling. By combining Hindmarsh–Rose (HR) and FitzHugh–Nagumo (FN) neurons, we construct an 8D heterogeneous coupled neural network based on fractional calculus—designated as the Fractional-Order Memristive Bridge Crosstalk-Coupled Neural Network (FMBCCNN). A major innovation is the incorporation of a fractional-order memristive bridge structure that mimics synaptic connections in a bridge configuration. This design provides both historical memory characteristics and bidirectional synaptic weight regulation, overcoming limitations of traditional coupling forms.
Using dynamical analysis tools such as phase portraits, bifurcation diagrams, and Lyapunov exponents, we systematically investigate how synaptic and crosstalk strengths influence system behavior under conventional fractional-order conditions. The results reveal diverse dynamical behaviors, including attractor coexistence, forward and reverse period-doubling bifurcations, and chaotic crises. Further analysis under the more generalized condition of non-uniform fractional orders shows that, compared with the conventional case, the system maintains continuous periodic motion over broader parameter ranges and exhibits clear parameter hysteresis. Although local dynamic patterns remain similar, the corresponding parameter intervals are substantially widened. In addition, the system displays more concentrated and marked alternation between periodic and chaotic behaviors. We also simulate the effect of varying the fractional-order derivative, offering a more general mathematical characterization of neuronal firing activity.
Finally, the chaotic sequences generated by the system are applied to an image encryption algorithm incorporating bit-plane decomposition and DNA encoding. Security analysis confirms that the encrypted images have pixel correlation coefficients below 0.01 in horizontal, vertical, and diagonal directions, information entropy greater than 7.999, and a key space of 22080. These results verify the excellent encryption performance and reliability of the proposed scheme and the generated sequences.-
Keywords:
- Memristive bridge /
- synaptic crosstalk /
- fractional-order heterogeneous neural network /
- nonlinear dynamics
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