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This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence analysis tools based on nonlinear contraction theory and virtual dynamical systems. This synergy between structural properties (symmetries) and convergence properties (contraction) is illustrated in the contexts of network motifs arising e.g. in genetic networks, of invariance to environmental symmetries, and of imposing different patterns of synchrony in a network.

In this project we developed an input-output approach to predict and engineer collective behavior in networks. This approach overcomes the complexity of the large-scale, nonlinear dynamical model by dividing the analysis and design tasks into two layers: At the network layer, we represent the nodes with appropriate input-output properties as abstractions of their detailed models and exploit these properties in conjunction with the interconnection structure to ascertain desirable behaviors. At the network layer, we represent the nodes with appropriate input-output properties as abstractions of their detailed models and exploit these properties in conjunction with the interconnection structure to ascertain desirable behaviors. At the node layer, we study the individual dynamical models to verify or assign the input-output properties without relying on knowledge of global network properties.

In this project we developed an input-output approach to predict and engineer collective behavior in networks. This approach overcomes the complexity of the large-scale, nonlinear dynamical model by dividing the analysis and design tasks into two layers: At the network layer, we represent the nodes with appropriate input-output properties as abstractions of their detailed models and exploit these properties in conjunction with the interconnection structure to ascertain desirable behaviors. At the network layer, we represent the nodes with appropriate input-output properties as abstractions of their detailed models and exploit these properties in conjunction with the interconnection structure to ascertain desirable behaviors. At the node layer, we study the individual dynamical models to verify or assign the input-output properties without relying on knowledge of global network properties.

In this project we developed an input-output approach to predict and engineer collective behavior in networks. This approach overcomes the complexity of the large-scale, nonlinear dynamical model by dividing the analysis and design tasks into two layers: At the network layer, we represent the nodes with appropriate input-output properties as abstractions of their detailed models and exploit these properties in conjunction with the interconnection structure to ascertain desirable behaviors. At the network layer, we represent the nodes with appropriate input-output properties as abstractions of their detailed models and exploit these properties in conjunction with the interconnection structure to ascertain desirable behaviors. At the node layer, we study the individual dynamical models to verify or assign the input-output properties without relying on knowledge of global network properties.

In this project we developed an input-output approach to predict and engineer collective behavior in networks. This approach overcomes the complexity of the large-scale, nonlinear dynamical model by dividing the analysis and design tasks into two layers: At the network layer, we represent the nodes with appropriate input-output properties as abstractions of their detailed models and exploit these properties in conjunction with the interconnection structure to ascertain desirable behaviors. At the network layer, we represent the nodes with appropriate input-output properties as abstractions of their detailed models and exploit these properties in conjunction with the interconnection structure to ascertain desirable behaviors. At the node layer, we study the individual dynamical models to verify or assign the input-output properties without relying on knowledge of global network properties.