GLOBAL DYNAMIC BEHAVIORS OF A TWO-DIMENSIONAL INTEGRAL-DIFFERENTIAL ALMOST PERIODIC SYSTEM WITH INFINITE DELAYS AND DISCRETE DELAYS

2008 ◽  
Vol 01 (04) ◽  
pp. 487-502 ◽  
Author(s):  
XINZHU MENG ◽  
TONGQIAN ZHANG
Keyword(s):  
Periodic System ◽  
Sufficient Conditions ◽  
Computational Technique ◽  
Two Dimensional ◽  
Almost Periodic ◽  
Dynamic Behaviors ◽  
Global Dynamic ◽  
Infinite Delays ◽  
Discrete Delays ◽  
Dimensional Integral

A nonautomous two-dimensional integral-differential Lotka–Volterra almost periodic competitive system with infinite delays and discrete delays is considered. By use of the computational technique on functional differential equation, we obtain the sufficient conditions for the permanence and the global asymptotic stability of the system. By using almost periodic functional hull theory, we show that the almost periodic system has a unique strictly positive almost periodic solution which is globally asymptotically stable. Our results show that the global dynamic behaviors of the system is dependent of time delays.

THE STABILITY AND ALMOST PERIODIC SOLUTION FOR GENERALIZED LOGISTIC ALMOST PERIODIC SYSTEM WITH DELAYS

2011 ◽  
Vol 04 (03) ◽  
pp. 313-328 ◽  
Author(s):  
XIANGLAI ZHUO
Keyword(s):  
Periodic Solution ◽  
Periodic System ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Computational Techniques ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Globally Asymptotically Stable ◽  
Discrete Delays ◽  
The Stability

The stability and almost periodic solution for generalized logistic almost periodic system with infinite and discrete delays is considered. Some sufficient conditions for the boundedness of the system are obtained to guarantee that the system is globally asymptotically stable. We also show that the almost periodic system has a unique globally asymptotically stable strictly positive almost periodic solution by using the almost periodic functional Hull theory and new computational techniques. Furthermore, some recent results are improved, and an open question is answered.

scholarly journals Dynamic of a nonautonomous two-species impulsive competitive system with infinite delays

2019 ◽  
Vol 17 (1) ◽  
pp. 776-794 ◽  
Author(s):  
Mengxin He ◽  
Zhong Li ◽  
Fengde Chen
Keyword(s):  
Comparison Theorem ◽  
Mathematical Analysis ◽  
Global Attractivity ◽  
Infinite Delay ◽  
Applied Mathematics ◽  
Almost Periodic ◽  
Competitive System ◽  
Dynamic Behaviors ◽  
Impulsive Equation ◽  
Infinite Delays

Abstract In this paper, we consider a nonautonomous two-species impulsive competitive system with infinite delays. By the impulsive comparison theorem and some mathematical analysis, we investigate the permanence, extinction and global attractivity of the system, as well as the influence of impulse perturbation on the dynamic behaviors of this system. For the logistic type impulsive equation with infinite delay, our results improve those of Xuxin Yang, Weibing Wang and Jianhua Shen [Permanence of a logistic type impulsive equation with infinite delay, Applied Mathematics Letters, 24(2011), 420-427]. For the corresponding nonautonomous two-species impulsive competitive system without delays, we discuss its permanence, extinction and global attractivity, which weaken and complement the results of Zhijun Liu and Qinglong Wang [An almost periodic competitive system subject to impulsive perturbations, Applied Mathematics and Computation, 231(2014), 377-385].

scholarly journals ALMOST-PERIODIC SOLUTIONS FOR AN ECOLOGICAL MODEL WITH INFINITE DELAYS

2007 ◽  
Vol 50 (1) ◽  
pp. 229-249 ◽  
Author(s):  
Yonghui Xia ◽  
Jinde Cao
Keyword(s):  
Periodic Solution ◽  
Lyapunov Functional ◽  
Ecological Model ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Volterra Model ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Infinite Delays ◽  
Dominated Convergence

AbstractBy using Lebesgue’s dominated convergence theorem and constructing a suitable Lyapunov functional, we study the following almost-periodic Lotka–Volterra model with $M$ predators and $N$ prey of the integro-differential equations\begin{alignat*}{2} \dot{x}_i(t)\amp=x_i(t)\biggl[b_i(t)-a_{ii}(t)x_i(t)-\sum_{k=1,k\neq i}^{N}a_{ik}(t)\int_{-\infty}^tH_{ik}(t-\sigma)x_k(\sigma)\,\mathrm{d}\sigma\\ \amp\hskip45mm-\sum_{l=1}^{M}c_{il}(t)\int_{-\infty}^tK_{il}(t-\sigma)y_l(\sigma)\,\mathrm{d}\sigma\biggr],\amp\quad i\amp=1,2,\dots,N,\\ \dot{y}_j(t)\amp=y_j(t)\biggl[-r_j(t)-e_{jj}(t)y_j(t) +\sum_{k=1}^{N}d_{jk}(t)\int_{-\infty}^tP_{jk}(t-\sigma)x_k(\sigma)\,\mathrm{d}\sigma \\ \amp\hskip45mm-\sum_{l=1,l\neq j}^{M} e_{jl}(t)\int_{-\infty}^tQ_{jl}(t-\sigma)y_l(\sigma)\,\mathrm{d}\sigma\biggr],\amp\quad j\amp=1,2,\dots,M. \end{alignat*}Some sufficient conditions are obtained for the existence of a unique almost-periodic solution of this model. Several examples show that the obtained criteria are new, general and easily verifiable.

scholarly journals Dynamic Behaviors of a Competitive System with Beddington-DeAngelis Functional Response

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Shengbin Yu ◽  
Fengde Chen
Keyword(s):  
Periodic Solution ◽  
Numerical Simulations ◽  
Functional Response ◽  
Recent Literature ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic ◽  
Competitive System ◽  
Dynamic Behaviors ◽  
Partial Extinction

This article studies a competitive system with Beddington-DeAngelis functional response and establishes sufficient conditions on permanence, partial extinction, and the existence of a unique almost periodic solution for the system. The results supplement and generalize the main conclusions in recent literature. Numerical simulations have been presented to validate the analytical results.

State-of-the-Art of Modeling Surface Water Impoundments

1982 ◽  
Vol 14 (1-2) ◽  
pp. 241-261 ◽  
Author(s):  
P A Krenkel ◽  
R H French
Keyword(s):  
Water Quality ◽  
Surface Water ◽  
State Of The Art ◽  
Rate Coefficients ◽  
Two Dimensional ◽  
One Dimensional ◽  
Integral Energy ◽  
Range Of Values ◽  
Dimensional Integral ◽  
Water Impoundment

The state-of-the-art of surface water impoundment modeling is examined from the viewpoints of both hydrodynamics and water quality. In the area of hydrodynamics current one dimensional integral energy and two dimensional models are discussed. In the area of water quality, the formulations used for various parameters are presented with a range of values for the associated rate coefficients.

scholarly journals Solving two-dimensional integral equations

2011 ◽  
Vol 23 (1) ◽  
pp. 111-114 ◽  
Author(s):  
F. Bazrafshan ◽  
A.H. Mahbobi ◽  
A. Neyrameh ◽  
A. Sousaraie ◽  
M. Ebrahimi
Keyword(s):  
Integral Equations ◽  
Two Dimensional ◽  
Dimensional Integral

scholarly journals Stability Analysis of Impulsive Control Systems with Finite and Infinite Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Xuling Wang ◽  
Xiaodi Li ◽  
Gani Tr. Stamov
Keyword(s):  
Control Systems ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Stability Criteria ◽  
Numerical Examples ◽  
Infinite Delays ◽  
Impulsive Control Systems ◽  
Stable Matrix ◽  
Theoretical Results

This paper studies impulsive control systems with finite and infinite delays. Several stability criteria are established by employing the largest and smallest eigenvalue of matrix. Our sufficient conditions are less restrictive than the ones in the earlier literature. Moreover, it is shown that by using impulsive control, the delay systems can be stabilized even if it contains no stable matrix. Finally, some numerical examples are discussed to illustrate the theoretical results.

Sign in / Sign up

Export Citation Format

Share Document