arXiv subjects

Kenta Ohira

Publications and source records attributed to Kenta Ohira.

7 recordsLinked to original sources

arXiv2025

Amplitude Enhancements through rewiring of a non-autonomous delay system

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.

nlin.AO↗

arXiv2024

An exact solution for a non-autonomous delay differential equation

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.

math.DS↗

arXiv2024

Transient Reviving Dynamics with an Exact Solution for Delay Differential Equations

We present a new approach to examine transient dynamics in a class of non-autonomous delay differential equations. Exact solutions for these equations are obtained using the Lambert W function alongside an appropriately chosen initial function. These solutions provide a reliable approximation for transient dynamics when the initial functions are not markedly distinct. We explore a non-autonomous equation that exhibits a distinctive phenomenon of reviving dynamics as an illustrative example. The derived exact solutions effectively encapsulate the qualitative characteristics of this reviving dynamics over various delay values.

nlin.AO↗

arXiv2024

Solving a Delay Differential Equation through Fourier Transform

In this study, we introduce and explore a delay differential equation that lends itself to explicit solutions in the Fourier-transformed space. Through the careful alignment of the initial function, we can construct a highly accurate solution to the equation. These findings open new avenues for understanding delay systems, demonstrating the efficacy of Fourier transform techniques in capturing transient oscillatory dynamics.

nlin.AO↗

arXiv2023

Delay, resonance and the Lambert W function

We discuss a new type of delay differential equation that exhibits resonating transient oscillations. The power spectrum peak of the dynamical trajectory reaches its maximum height when the delay is suitably tuned. Furthermore, our analysis of the resonant conditions for this equation has revealed a new connection between the solutions of the transcendental trigonometric equation and the Lambert W function. These results offer fresh insights into the nonlinear dynamics induced by delayed feedback.

nlin.AO↗

arXiv2023

Delayed Dynamics with Transient Resonating Oscillations

Recently, we have studied a delay differential equation which has a coefficient that is a linear function of time. The equation has shown the oscillatory transient dynamics appear and disappear as the delay is increased between zero to asymptotically large delay. We here propose and study another equation that shows similar transient oscillations. It has an extra exponential gaussian factor on the delayed feedback term. It is shown that this equation is analytically tractable with the use of the Lambert $W$ function. This equation is also studied numerically to confirm some of the properties inferred from the analytical solution. We also have found that the amplitude of transient oscillation changes and goes through a maximum as we increase the value of the delay. In this sense, the proposed equation is one of the simplest dynamical equations that brings out a resonant behavior without any external oscillating inputs.

nlin.AO↗

arXiv2022

Resonating Delay Equation

We propose here a delay differential equation that exhibits a new type of resonating oscillatory dynamics. The oscillatory transient dynamics appear and disappear as the delay is increased between zero to asymptotically large delay. The optimal height of the power spectrum of the dynamical trajectory is observed with the suitably tuned delay. This resonant behavior contrasts itself against the general behaviors where an increase of delay parameter leads to the persistence of oscillations or more complex dynamics.

nlin.AO↗