Neuromimetic Dynamic Networks with Hebbian Learning

Leveraging recent advances in neuroscience and control theory, this paper presents a neuromimetic network model with dynamic symmetric connections governed by Hebbian learning rules. Formal analysis grounded in graph theory and classical control establishes that this biologically plausible model exhibits boundedness, stability, and structural controllability given a generalized sym-cactus structure with multiple control nodes. We prove the necessity of this topology when there are distributed control inputs. Simulations using a 14-node generalized sym-cactus network with two input types validate the model's effectiveness in capturing key neural dynamics.