From Network Structure to Dynamics and Back Again: Relating Dynamical Stability and Connection Topology in Biological Complex Systems

Abstract

The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from statistical physics and non-linear dynamics. In this paper, we look at a few examples of biological networks to see how similar questions can come up in very different contexts. We review some of our recent work that looks at how network structure (e.g., its connection topology) can dictate the nature of its dynamics, and conversely, how dynamical considerations constrain the network structure. We also see how networks occurring in nature can evolve to modular configurations as a result of simultaneously trying to satisfy multiple structural and dynamical constraints. The resulting optimal networks possess hubs and have heterogeneous degree distribution similar to those seen in biological systems.

Modeling the online social transmission through the theory of complex adaptive systems and neural network models based on the brain dynamics

“…Examples of similar structure and dynamics abound among various types of complex networks. For instance, the intracellular communication through a signaling system based on enzymatic reactions is analogous to the exchange of information packets among the Internet servers, and to ecological networks of interdependent species connected through trophic links [147]. The universality in the structure and dynamics of complex networks makes the transfer of modeling principles from one field to another a compelling and fascinating approach.…”