On the Asymptotic Stability, Uniform Stability, and Boundedness of Solutions to Nonlinear Volterra Integrodifferential Equations

2021 ◽  
Author(s):  
C. Tunç ◽  
S. A. Mohammed
Keyword(s):  
Asymptotic Stability ◽  
Integrodifferential Equations ◽  
Uniform Stability ◽  
Boundedness Of Solutions

scholarly journals On asymptotically stability, uniformly stability and boundedness of solutions of nonlinear Volterra integro-differential equations

2020 ◽  
Vol 72 (12) ◽  
pp. 1708-1720
Author(s):  
C. Tunç ◽  
S. A. Mohammed
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Uniform Stability ◽  
Lyapunov Functionals ◽  
Boundedness Of Solutions ◽  
Matlab Simulink ◽  
First Order

UDC 517.9 In this paper, two new Lyapunov functionals are defined. We apply these functionals to get sufficient conditions guaranteeing the asymptotic stability, uniform stability, and boundedness of solutions of certain nonlinear Volterra integro-differential equations of the first order. The results obtained are improvements and extensions of known results that can be found in literature. We also suggest examples to show the applicability of our results and for the sake of illustrations. Using MATLAB-Simulink, in particular cases we clearly show the behavior of orbits of Volterra integro-differential equations under consideration.

scholarly journals Stability of Volterra system with impulsive effect

1991 ◽  
Vol 4 (1) ◽  
pp. 83-93 ◽  
Author(s):  
M. Ramamohana Rao ◽  
S. Sivasundaram
Keyword(s):  
Asymptotic Stability ◽  
Sufficient Conditions ◽  
Integrodifferential Equations ◽  
Uniform Stability ◽  
Impulsive Effect ◽  
Property A ◽  
Uniform Asymptotic Stability ◽  
Volterra System ◽  
Piecewise Continuous ◽  
The Given

Sufficient conditions for uniform stability and uniform asymptotic stability of impulsive integrodifferential equations are investigated by constructing a suitable piecewise continuous Lyapunov-like functionals without the decresent property. A result which establishes no pulse phenomena in the given system is also discussed.

scholarly journals On the Uniform Stability of Impulsive Lotka-Volterra Type Systems with Supremums

2018 ◽  
Vol 4 (2) ◽  
Author(s):  
Ivanka Stamova ◽  
Gani Stamov
Keyword(s):  
Asymptotic Stability ◽  
Lyapunov Method ◽  
Sufficient Conditions ◽  
Type Systems ◽  
Uniform Stability ◽  
Volterra Model ◽  
Uniform Asymptotic Stability ◽  
Volterra Type

In this paper we propose an impulsive n- species Lotka-Volterra model with supremums. By using Lyapunov method we give sufficient conditions for uniform stability and uniform asymptotic stability of the positive states.

Asymptotic Stability for an Impulsive Model of Hematopoiesis with Time Delay

2012 ◽  
Vol 204-208 ◽  
pp. 4506-4512
Author(s):  
Rui Chen ◽  
Pei Jun Ju
Keyword(s):  
Time Delay ◽  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Function Method ◽  
Uniform Stability ◽  
Uniform Asymptotic Stability ◽  
Lyapunov Function Method ◽  
Impulsive Model

A model of hematopoiesis with time delay and impulses is studied. Based on the Lyapunov function method, uniform stability and uniform asymptotic stability of the equilibria is discussed.

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