Structure and Control of Biology-inspired Networks

TL;DR

This paper introduces a biologically inspired network model with dynamic, Hebbian-regulated connections, demonstrating stability, resilience, and structural stability, applicable to sensory systems and data classification.

Contribution

It presents a novel nonlinear network model based on generalized cactus graphs, combining graph theory and control to emulate brain network features with robustness to topology changes.

Findings

Model exhibits bounded evolution and stability.

Network resilience to topological perturbations.

Application to visual system and data classification.

Abstract

There is increasing interest in developing the theoretical foundations of networked control systems that illuminate how brain networks function so as to enable sensory perception, control of movement, memory and all the operations that are needed for animals to survive. The present paper proposes a biologically inspired network model featuring dynamic connections regulated by Hebbian learning. Drawing on the machinery of graph theory and classical control we show that our novel nonlinear model exhibits such biologically plausible features as bounded evolution, stability, resilience, and a kind of structural stability -- meaning that perturbations of the model parameters leave the essential properties of the model in tact. The proposed network model involves generalized cactus graphs with multiple control input nodes, and it is shown that the properties of the network are resilient to various changes in network topology provided these changes preserve the generalized cactus structure. A particular example described in what follows is an idealized network model of the visual system of a macaque monkey. The model displays resilience to network disruptions such as might occur in a living organism due to disease or injury. A different model of the same type provides an example of a system that can perform data classification.