  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.
