Amplitude Enhancements through rewiring of a non-autonomous delay system

Abstract

Complex systems, such as biological networks, often exhibit intricate rhythmic behaviors that emerge from simple, small-amplitude dynamics in individual components. This study explores how significant oscillatory signals can arise from a minimal system consisting of just two interacting units, each governed by a simple non-autonomous delay differential equation with a recently obtained exact analytical solution. Contrary to the common assumption that large-scale oscillations require numerous units, our model demonstrates that rewiring two units from self-feedback to cross-feedback can generate robust, finite-amplitude oscillations. With time delay, these interacting units produce strongly amplified oscillatory packets compared to self-feedback configurations. Our findings highlight the potential of this minimalistic mechanism for generating complex rhythmic outputs, with implications for oscillatory signal processing and various other applications.