BECS: Pattern-Steering in Nonlinear Dynamical Networks

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We investigate computational methods for moving the activity of a complex dynamical network from one state to another. Complicated nonlinear networks appear to be multistable and multirhythmic, a mix of chaotic and periodic stable attractors, together with other metastable transients that may be effectively stable for the time interval of an engineering application. Computational methods will be developed for steering between basins of attractors, and tested in three different experimental platforms: primary neuronal cell cultures from vertebrates and invertebrates, hippocampal slices from rodents, and defect activity in convection rolls in nematic liquid crystals. Better understanding of these test cases could be a first step to new approaches to neural engineering, machine learning, and optimization of energy transfer and production. The experimental examples have in common a lack of known equations of motion, which severely limits the use of classical control theory and motivates development of our new techniques.The hallmark of complex systems behavior in engineering devices is the appearance of dynamical patterns that vary in time and space. In this exploratory study, we will expose the main problems and bottlenecks that need to be overcome to enable low-power steering between different spatiotemporal patterns in engineered networks, and to begin to develop efficient computational methods to accomplish this switching quickly and automatically. The project includes theoretical, computational, and experimental components. Methods will be developed and tested experimentally in systems that have nonlinear, complex network characteristics, such as primary neuronal cell cultures, hippocampal slices from rodents, and nematic liquid crystals.