scholarly journals Stability of a Three-Species Cooperative System with Time Delays and Stochastic Perturbations

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Jinxing Zhao ◽  
Yuanfu Shao
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
System Dynamics ◽  
Numerical Simulations ◽  
Time Delays ◽  
Cooperative Systems ◽  
Asymptotical Stability ◽  
Cooperative System ◽  
Stochastic Perturbations ◽  
Stability In Probability

Considering the impacts of time delays and different kinds of stochastic perturbations, we propose two three-species delayed cooperative systems with stochastic perturbations in this paper. We establish the sufficient criteria of the asymptotical stability and stability in probability by constructing a neutral stochastic differential equation and some suitable functionals. The impacts of time delays and stochastic perturbations to the system dynamics are revealed by some numerical simulations at the end.

PERMANENCE FOR THE LOTKA–VOLTERRA COOPERATIVE SYSTEM WITH SEVERAL DELAYS

2009 ◽  
Vol 02 (03) ◽  
pp. 267-285 ◽  
Author(s):  
YUKIHIKO NAKATA
Keyword(s):  
Theoretical Analysis ◽  
Time Delays ◽  
Interspecific Interactions ◽  
Cooperative Systems ◽  
Numerical Results ◽  
Sufficient Condition ◽  
Cooperative System ◽  
Nonlinear Anal ◽  
Discrete Delays ◽  
Several Delays

In this paper, we establish a new sufficient condition of the permanence for the Lotka–Volterra cooperative systems with multiple discrete delays by extending the results in [Nakata and Muroya, Permanence for nonautonomous Lotka–Volterra cooperative systems with delays, Nonlinear Anal. RWA., in press]. Our condition holds even if the instantaneous feedback does not dominate over the total of the interspecific interactions and does not need the restriction on the size of time delays, different from the results in [Lu and Lu, Permanence for two-species Lotka–Volterra cooperative systems with delays, Math. Biosci. Eng.5 (2008) 477–484]. We offer an example for comparison with the previous results and numerical results supporting our theoretical analysis are given.

Asymptotic stability of fractional difference equations with bounded time delays

2020 ◽  
Vol 23 (2) ◽  
pp. 571-590
Author(s):  
Mei Wang ◽  
Baoguo Jia ◽  
Feifei Du ◽  
Xiang Liu
Keyword(s):  
Asymptotic Stability ◽  
Difference Equation ◽  
Difference Equations ◽  
Integral Inequality ◽  
Time Delays ◽  
Asymptotical Stability ◽  
Stability Conditions ◽  
Fractional Difference ◽  
Fractional Difference Equations ◽  
Fractional Difference Equation

AbstractIn this paper, an integral inequality and the fractional Halanay inequalities with bounded time delays in fractional difference are investigated. By these inequalities, the asymptotical stability conditions of Caputo and Riemann-Liouville fractional difference equation with bounded time delays are obtained. Several examples are presented to illustrate the results.

On Approximate Large Deviations for 1D Diffusion

2003 ◽  
Vol 10 (2) ◽  
pp. 381-399
Author(s):  
A. Yu. Veretennikov
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Large Deviations ◽  
Stochastic Differential Equation ◽  
Approximation Scheme ◽  
Sufficient Conditions ◽  
Rate Function ◽  
Euler Approximation ◽  
One Dimensional

Abstract We establish sufficient conditions under which the rate function for the Euler approximation scheme for a solution of a one-dimensional stochastic differential equation on the torus is close to that for an exact solution of this equation.

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