Amplitude Enhancements through rewiring of a non-autonomous delay system
arXiv:2411.01965 · doi:10.1063/5.0252300
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.
arXiv comment10pages, 7figures, Submitted for a publication; ver 2: extensively rewritten with new figures and more references;
References in corpus (6)
- 20 years of developments in optical frequency comb technology and applications
- Resonance between Noise and Delay
- Stabilisation of dynamics of oscillatory systems by non-autonomous perturbation
- Route to hyperbolic hyperchaos in a nonautonomous time-delay system
- Delayed Dynamics with Transient Resonating Oscillations
- Solving a Delay Differential Equation through Fourier Transform