Structure and dynamics affect the controllability of complex systems: a Preliminary Study

Alexander Gates1,2 and Luis M. Rocha1,2,3

1Cognitive Science Program, Indiana University, Bloomington IN, USA
2School of Informatics and Computing, Indiana University, Bloomington IN, USA
3Instituto Gulbenkian de Ciencia, Portugal

Citation: A. Gates and L.M. Rocha [2014]. "Structure and dynamics affect the controllability of complex systems: a Preliminary Study". Artificial Life 14: Proceedings of the Fourteenth International Conference on the Synthesis and Simulation of Living Systems: 429-430, MIT Press.

The full text is available from the online proceedings at MIT Press. A pre-print is also available.


Complex systems are typically understood as large nonlinear multivariate systems. Their organization and behavior are commonly modeled by representations such as graphs and automata networks. Graphs, where nodes representing variables lack intrinsic dynamics, capture the structure or organization of complex systems. The simplest way to study multi-variate dynamics, is to allow network nodes to have states and update them with automata; for instance, Boolean networks (BN) are canonical models of complex systems and exhibit a wide range of dynamical behaviors.

The structure of networks has provided many insights into the organization of complex systems. The success of this approach is its ability to capture the organization of complex systems, and how it changes in time (network evolution) without explicit dynamical rules for node variables. As the field matures, however, there is a need to move from understanding to controlling complex systems. This is particularly true in systems biology and medicine, where increasingly accurate models of biochemical regulation have been produced. More than understanding the organization of biochemical regulation, we need to derive control strategies that allow us, for instance, to move a mutant cell to a wild-type state, or revert a mature cell to a pluripotent state. Towards these goals, a question of central importance remains: How well does network structure represent the multivariate dynamics of the underlying complex system, especially from the point of view of control?

Network controllability aims precisely to identify a minimal set of driver variables (a.k.a. driver nodes) from the structural network, which can fully control system dynamics—i.e. drive system dynamics to any state-space configuration. Structural controllability is an influential method to derive driver variables, using only structural properties of the system without any consideration of its dynamical details. It has been used to suggest, for instance, that biological systems are harder to control than social systems. However, applications of structural controllability have been heavily critiqued due to its stringent assumptions. Here we explore the relationship between network structure and controllability through the analysis of dynamical ensembles of BN.

Keywords:Control, dynamics, complex networks, Boolean networks, automata, structural control.

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Last Modified: July 15, 2015