An exact solution for a non-autonomous delay differential equation

Abstract

We derive an exact solution for a simple non-autonomous delay differential equation (DDE) over the entire real-time axis, representing it as a sum of Gaussian-shaped dynamics with distinct peak positions. This marks the first explicit solution for non-autonomous DDEs and is a rare example even among general DDEs. The constructed solution offers key physical insights and facilitates the analysis of system properties, such as the envelope profile of the dynamics.

arXiv comment16 pages, 8 figures, shorter version submitted for publication; ver.2. Fixed some technical errors; ver.3. Fixed some technical errors; ver.4 Fixed some technical erros, adding more references

References in corpus (5)

• 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
• Amplitude Enhancements through rewiring of a non-autonomous delay system