Functional Control of Network Dynamical Systems: An Information Theoretic Approach

Abstract In neurological networks, the emergence of various causal interactions and information flows among nodes is governed by the structural connectivity in conjunction with the node dynamics. The information flow describes the direction and the magnitude of an excitatory neuron’s influence to the neighbouring neurons. However, the intricate relationship between network dynamics and information flows is not well understood. Here, we address this challenge by first identifying a generic mechanism that defines the evolution of various information routing patterns in response to modifications in the underlying network dynamics. Moreover, with emerging techniques in brain stimulation, designing optimal stimulation directed towards a target region with an acceptable magnitude remains an ongoing and significant challenge. In this work, we also introduce techniques for computing optimal inputs that follow a desired stimulation routing path towards the target brain region. This optimization problem can be efficiently resolved using non-linear programming tools and permits the simultaneous assignment of multiple desired patterns at different instances. We establish the algebraic and graph-theoretic conditions necessary to ensure the feasibility and stability of information routing patterns (IRPs). We illustrate the routing mechanisms and control methods for attaining desired patterns in biological oscillatory dynamics. Author Summary A complex network is described by collection of subsystems or nodes, often exchanging information among themselves via fixed interconnection pattern or structure of the network. This combination of nodes, interconnection structure and the information exchange enables the overall network system to function. These information exchange patterns change over time and switch patterns whenever a node or set of nodes are subject to external perturbations or stimulations. In many cases one would want to drive the system to desired information patterns, resulting in desired network system behaviour, by appropriately designing the perturbating signals. We present mathematical framework to design perturbation signals that drive the system to the desired behaviour. We demonstrate the applicability of our framework in the context of brain stimulation and in modifying causal interactions in gene regulatory networks.