Design of active network filters as hysteretic sensors

TL;DR

This paper proposes a novel network of coupled oscillators that exhibits hysteretic behavior, inspired by biological systems, enabling sustained endogenous activity with specific response dynamics based on local interactions.

Contribution

It introduces a new class of networks with hysteretic dynamics using coupled linear and nonlinear oscillators, applicable to arbitrary topologies and with analysis of parameter effects.

Findings

Hysteretic behavior achieved through coupling and rate laws.

Dependence of response on network topology and node placement.

Robustness of dynamics confirmed via perturbation and continuation methods.

Abstract

This work aims to propose and design a class of networks of coupled linear and nonlinear oscillators, in which short bursts of exogenous excitation result in sustained endogenous network activity that returns to a quiescent state only after a characteristic time and along a different path than when originally excited. The desired hysteretic behavior is obtained through the coupling of self-excited oscillations with purposely designed rate laws for slowly-varying nodal parameters, governed only by local interactions in the network. The proposed architecture and the sought dynamics take inspiration from complex biological systems that combine endogenous energy sources with a paradigm for distributed sensing and information processing. In this paper, the network design problem considers arbitrary topologies and investigates the dependence of the desired response on model parameters, as well as on the placement of a single nonlinear node in an otherwise linear network. Perturbation analysis in various asymptotic parameter limits is used to define the proposed internal dynamics. Parameter continuation techniques validate the asymptotic results numerically and demonstrate their robustness over finite ranges of parameter values. Both approaches suggest a nontrivial dependence of the optimal distribution of nonlinearity on the network topology.