scholarly journals Discretization of Asymptotically Stable Stationary Solutions of Delay Differential Equations with a Random Stationary Delay

2006 ◽  
Vol 18 (4) ◽  
pp. 863-880 ◽  
Author(s):  
Tomás Caraballo ◽  
Peter E. Kloeden ◽  
José Real
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Stationary Solutions ◽  
Asymptotically Stable ◽  
Delay Differential ◽  
Stationary Delay ◽  
Stable Stationary Solutions

scholarly journals Periodic Solutions of a System of Delay Differential Equations for a Small Delay

2002 ◽  
Vol 7 (2) ◽  
pp. 295
Author(s):  
Adu A.M. Wasike ◽  
Wandera Ogana
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Periodic Solutions ◽  
Delay Differential Equations ◽  
Original System ◽  
System Of Equations ◽  
Asymptotically Stable ◽  
Stable Periodic Solution ◽  
Stable Periodic ◽  
Delay Differential

We prove the existence of an asymptotically stable periodic solution of a system of delay differential equations with a small time delay t > 0. To achieve this, we transform the system of equations into a system of perturbed ordinary differential equations and then use perturbation results to show the existence of an asymptotically stable periodic solution. This approach is contingent on the fact that the system of equations with t = 0 has a stable limit cycle. We also provide a comparative study of the solutions of the original system and the perturbed system.  This comparison lays the ground for proving the existence of periodic solutions of the original system by Schauder's fixed point theorem.   

scholarly journals Periodicity, Stability, and Boundedness of Solutions to Certain Second Order Delay Differential Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
A. T. Ademola ◽  
B. S. Ogundare ◽  
M. O. Ogundiran ◽  
O. A. Adesina
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Lyapunov Functional ◽  
Second Order ◽  
Asymptotically Stable ◽  
Boundedness Of Solutions ◽  
Deviating Arguments ◽  
Nonlinear Delay Differential Equations ◽  
Delay Differential ◽  
Nonlinear Delay

The behaviour of solutions to certain second order nonlinear delay differential equations with variable deviating arguments is discussed. The main procedure lies in the properties of a complete Lyapunov functional which is used to obtain suitable criteria to guarantee existence of unique solutions that are periodic, uniformly asymptotically stable, and uniformly ultimately bounded. Obtained results are new and also complement related ones that have appeared in the literature. Moreover, examples are given to illustrate the feasibility and correctness of the main results.

scholarly journals Stability of scalar nonlinear fractional differential equations with linearly dominated delay

2020 ◽  
Vol 23 (1) ◽  
pp. 250-267 ◽  
Author(s):  
Hoang The Tuan ◽  
Stefan Siegmund
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Equilibrium Points ◽  
Asymptotic Behavior Of Solutions ◽  
Asymptotically Stable ◽  
Fractional Delay ◽  
Fractional Differential ◽  
Delay Differential ◽  
Fractional Delay Differential Equations

AbstractIn this paper, we study the asymptotic behavior of solutions to a scalar fractional delay differential equations around the equilibrium points. More precise, we provide conditions on the coefficients under which a linear fractional delay equation is asymptotically stable and show that the asymptotic stability of the trivial solution is preserved under a small nonlinear Lipschitz perturbation of the fractional delay differential equation.

scholarly journals Asymptotic Properties of Solutions to Delay Differential Equations Describing Plankton—Fish Interaction

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3064
Author(s):  
Maria A. Skvortsova
Keyword(s):  
Differential Equations ◽  
Equilibrium Point ◽  
Delay Differential Equations ◽  
Asymptotic Properties ◽  
Asymptotic Behavior Of Solutions ◽  
Asymptotically Stable ◽  
System Of Differential Equations ◽  
Estimates Of Solutions ◽  
Two Delays ◽  
Delay Differential

We consider a system of differential equations with two delays describing plankton–fish interaction. We analyze the case when the equilibrium point of this system corresponding to the presence of only phytoplankton and the absence of zooplankton and fish is asymptotically stable. In this case, the asymptotic behavior of solutions to the system is studied. We establish estimates of solutions characterizing the stabilization rate at infinity to the considered equilibrium point. The results are obtained using Lyapunov–Krasovskii functionals.

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