Diffusively Coupled Networks: Synchronization, De-Synchronization, and Structure

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ObjectiveThis project will develop novel design and analysis techniques for spatially distributed networks that exhibit a diffusive coupling structure, common in biomolecular networks and multi-agent systems. The first step in this development will be to unravel structural properties of agent dynamics and their interconnection that yield prescribed spatial behaviors, such as synchronization or pattern formation. The second step will be to enhance the desirable properties via architectural decisions. The techniques to be developed will serve biomolecular networks and multi-agent systems, as well as other applications that possess similar structuresIntellectual MeritPart One of the proposal sets forth a new technique to determine which conditions guarantee synchronous behavior in diffusively coupled networks. In addition to networks of discrete agents, this technique is applicable to continuous reaction-diffusion models where synchrony means spatial homogeneity. A key research task will be to develop new system gain concepts that quantify the amount of inhomogeneity caused by the amount of spatial model variation, and to apply the results to oscillator networks and biomolecular signaling cascades. Part Two aims to induce desirable forms of de-synchronization to generate spatial patterns, which is one of the outstanding problems in synthetic biology. It proposes to employ systemtheoretic concepts to design new gene networks that are amenable to synthetic implementation and that exhibit diffusion-driven instability in prescribed spatial modes, thus leading to gene expression patterns dominated by these modes. One such topology is identified and detailed in the proposal. Part Three posits a connection between diffusion-driven instability and nonminimum-phase agent dynamics, and demonstrates that a form of this instability can occur in multi-agent systems. It then proposes to investigate the limits of achievable synchronization performance imposed by nonminimum-phase agents, and to mitigate the resulting design tradeoffs with a re-allocation of node and link weights to be performed via convex optimization.Broader Impact The PI will continue incorporating research material into graduate courses. In addition, he will introduce selected topics from this project into two undergraduate courses. The PI leads recruitment and mentoring of underrepresented graduate students in his department, and will make every effort to recruit a female or minority graduate student researcher for the proposed project.