We consider networks with a specific type of nodes that can have either a discrete or continuous set of states. It is shown that no matter how complex the network is, its dynamical response to arbitrary inputs is defined in a simple way by its response to a monotone input.  As illustrative applications, we propose and discuss a quasistatic mechanical model with objects interacting via friction forces, and a financial market model with avalanches and critical behavior induced by momentum trading strategies.
We show that for a certain class of dynamics at the nodes the response of a network of any topology to arbitrary inputs is defined in a simple way by its response to a monotone input. The nodes may have either a discrete or continuous set of states and there is no limit on the complexity of the network. The results provide both an efficient numerical method and the potential for accurate analytic approximation of the dynamics on such networks. As illustrative applications, we introduce a quasistatic mechanical model with objects interacting via frictional forces, and a financial market model with avalanches and critical behavior that are generated by momentum trading strategies.
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consider networks with a specific type of nodes that can have either a discrete or continuous set of states. It is shown that no matter how complex the network is, its dynamical response
show that for a certain class of dynamics at the nodes the response of a network of any topology
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The nodes may have either a discrete or continuous set of states and there is no limit on the complexity of the network. The results provide both an efficient numerical method and the potential for accurate analytic approximation of the dynamics on such networks.
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propose and discuss
introduce
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friction
frictional
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induced
that are generated