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This work aims to propose and design a class of networks of coupled linearand nonlinear oscillators, in which short bursts of exogenous excitation resultin sustained endogenous network activity that returns to a quiescent state onlyafter a characteristic time and along a different path than when originallyexcited. The desired hysteretic behavior is obtained through the coupling ofself-excited oscillations with purposely designed rate laws for slowly-varyingnodal parameters, governed only by local interactions in the network. Theproposed architecture and the sought dynamics take inspiration from complexbiological systems that combine endogenous energy sources with a paradigm fordistributed sensing and information processing. In this paper, the networkdesign problem considers arbitrary topologies and investigates the dependenceof the desired response on model parameters, as well as on the placement of asingle nonlinear node in an otherwise linear network. Perturbation analysis invarious asymptotic parameter limits is used to define the proposed internaldynamics. Parameter continuation techniques validate the asymptotic resultsnumerically and demonstrate their robustness over finite ranges of parametervalues. Both approaches suggest a nontrivial dependence of the optimaldistribution of nonlinearity on the network topology.

Design of active network filters as hysteretic sensors