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 dynamical oscillations. This phenomenon arises in this context when an appropriate amount of delay is present in the feedback line. Our findings highlight the potential of this minimalistic mechanism to generate high-amplitude dynamical oscillations from much smaller amplitude units, drawing a physical analogy to rewiring feedback lines.