Bidirectional Adaptive Synapse Hopfield Neural Network: Butterfly Attractor, Controllable Multi-Scrolls, and Circuit Realization

Investigating chaotic dynamics in artificial neural networks is essential for deciphering brain-like activity and advancing neuromorphic computing. While memristors are widely employed to emulate synaptic memory, conventional memristive networks lack a fundamental biological mechanism: the bidirectional regulation of synaptic strength by both pre- and post-synaptic neurons. To address this limitation, we propose a Bidirectional Adaptive Synapse Hopfield Neural Network (BAS-HNN) that dynamically models the adaptation of postsynaptic membrane receptors to synaptic stimuli. Dynamical analysis reveals that the BAS-HNN exhibits rich chaotic behaviors, distinct amplitude control effects, and complex butterfly attractors. To further harness its dynamical richness, we extend the model by integrating a multi-piecewise memristor as an autapse. This extended architecture generates controllable multi-scroll attractors and unveils initial-offset coexisting attractors and amplitude modulation of multi-scroll under varying parameter conditions. The theoretical models are rigorously analyzed, and their practical feasibility is conclusively validated through hardware circuit simulation. This work thus establishes a biologically plausible chaotic neural network framework, offering deep insights into brain dynamics and a powerful paradigm for neuromorphic engineering.