Complex dynamics in a delay differential equation with two delays in tick growth with diapause

2020 ◽  
Vol 269 (12) ◽  
pp. 10937-10963 ◽  
Author(s):  
Hongying Shu ◽  
Wanxiao Xu ◽  
Xiang-Sheng Wang ◽  
Jianhong Wu
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Complex Dynamics ◽  
Two Delays ◽  
Delay Differential

scholarly journals Resonating delay equation

2022 ◽  
Author(s):  
Kenta Ohira
Keyword(s):  
Differential Equation ◽  
Power Spectrum ◽  
Delay Differential Equation ◽  
Complex Dynamics ◽  
Transient Dynamics ◽  
Large Delay ◽  
Oscillatory Dynamics ◽  
Resonant Behavior ◽  
New Type ◽  
Delay Differential

Abstract 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.

scholarly journals  Van der Pol Model in Two-Delay Differential Equation Representation

2021 ◽  
Author(s):  
M. A. Elfouly ◽  
M. A. Sohaly
Keyword(s):  
Differential Equation ◽  
Delay Differential Equation ◽  
Delay Model ◽  
Cubic Nonlinearity ◽  
Van Der Pol ◽  
Order Ordinary Differential Equation ◽  
Two Delays ◽  
Van Der Pol Model ◽  
Delay Differential ◽  
The Mathematical Model

Abstract The Van der Pol equation is the mathematical model of a second-order ordinary differential equation with cubic nonlinearity. In this paper, the differential equation of the Van der Pol model and RLC (resistor - inductor-capacitor) circuit are deduced from a delay differential equation. The Van der Pol delay model contains two delays, which opens the way for the re-use of its applications. Also, the model for Parkinson's disease modification is described as the Van der Pol model.

scholarly journals Smooth Stable Manifold for Delay Differential Equations with Arbitrary Growth Rate

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 105
Author(s):  
Lokesh Singh ◽  
Dhirendra Bahuguna
Keyword(s):  
Differential Equation ◽  
Growth Rate ◽  
Invariant Manifold ◽  
Delay Differential Equation ◽  
Delay Differential Equations ◽  
Stable Manifold ◽  
Exponential Dichotomy ◽  
Delay Differential ◽  
Stable Invariant ◽  
Nonuniform Exponential Dichotomy

In this article, we construct a C1 stable invariant manifold for the delay differential equation x′=Ax(t)+Lxt+f(t,xt) assuming the ρ-nonuniform exponential dichotomy for the corresponding solution operator. We also assume that the C1 perturbation, f(t,xt), and its derivative are sufficiently small and satisfy smoothness conditions. To obtain the invariant manifold, we follow the method developed by Lyapunov and Perron. We also show the dependence of invariant manifold on the perturbation f(t,xt).

Sign in / Sign up

Export Citation Format

Share Document