Structure and Control of Biology-Inspired Networks

There is growing interest in developing the theoretical foundations of networked control systems. These efforts aim to illuminate how brain networks support sensory perception, motor control, memory, and other functions essential for survival. The present paper proposes a biologically inspired network model featuring dynamic connections regulated by Hebbian learning. Drawing on tools from graph theory and classical control, we show that our novel nonlinear model exhibits several biologically plausible features, including bounded evolution, stability, and resilience. It also demonstrates a form of structural stability, meaning that perturbations to the model parameters do not alter its essential properties. 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 remains resilient to disruptions that may occur in living organisms, such as those caused by disease or injury. A different model of the same type provides an example of a system that can perform data classification.