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Existence and stability of periodic solutions are studied for a system of delay differential equations with two delays, with periodic coefficients. It models the evolution of hematopoietic stem cells and mature neutrophil cells in chronic myelogenous leukemia under a periodic treatment that acts only on mature cells. Existence of a guiding function leads to the proof of the existence of a strictly positive periodic solution by a theorem of Krasnoselskii....

Periodicity and stability in neutral nonlinear differential equations with functional delay.

Dib, Youssef M., Maroun, Mariette R., Raffoul, Youssef N. (2005)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Periodicity and stability in neutral nonlinear dynamic equations with functional delay on a time scale.

Kaufmann, Eric R., Raffoul, Youssef N. (2007)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Periodicity in a ratio-dependent predator-prey system with stage structure for predator.

Chen, Fengde (2005)

Journal of Applied Mathematics

Permanence and global exponential stability of Nicholson-type delay systems

Zhonghuai Wu, Jianying Shao, Mingquan Yang, Wei Gao (2011)

Annales Polonici Mathematici

We present several results on permanence and global exponential stability of Nicholson-type delay systems, which correct and generalize some recent results of Berezansky, Idels and Troib [Nonlinear Anal. Real World Appl. 12 (2011), 436-445].

Permanence and positive periodic solutions of a discrete delay competitive system.

Qin, Wenjie, Liu, Zhijun (2010)

Discrete Dynamics in Nature and Society

Permanence and stability of an age-structured prey-predator system with delays.

Cai, Liming, Li, Xuezhi, Song, Xinyu, Yu, Jingyuan (2007)

Discrete Dynamics in Nature and Society

Permanence in logistic and Lotka-Volterra systems with dispersal and time delays.

Cui, Jingan, Guo, Mingna (2005)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Persistence and bifurcation analysis on a predator–prey system of holling type

Debasis Mukherjee (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We present a Gause type predator–prey model incorporating delay due to response of prey population growth to density and gestation. The functional response of predator is assumed to be of Holling type II. In absence of prey, predator has a density dependent death rate. Sufficient criterion for uniform persistence is derived. Conditions are found out for which system undergoes a Hopf–bifurcation.

Persistence and bifurcation analysis on a predator–prey system of holling type

Debasis Mukherjee (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Persistence and stability for a generalized Leslie-Gower model with stage structure and dispersal.

Huo, Hai-Feng, Ma, Zhan-Ping, Liu, Chun-Ying (2009)

Abstract and Applied Analysis

Positive solutions of $p$ -type retarded functional linear differential equations

Svoboda, Zdeněk (2007)

Proceedings of Equadiff 11

Preservation of exponential stability for equations with several delays

Leonid Berezansky, Elena Braverman (2011)

Mathematica Bohemica

We consider preservation of exponential stability for the scalar nonoscillatory linear equation with several delays $\dot{x} (t) + \sum_{k = 1}^{m} a_{k} (t) x (h_{k} (t)) = 0, a_{k} (t) \geq 0$ under the addition of new terms and a delay perturbation. We assume that the original equation has a positive fundamental function; our method is based on Bohl-Perron type theorems. Explicit stability conditions are obtained.

Pseudo almost-periodic solution of shunting inhibitory cellular neural networks with delay.

Wu, Haihui (2011)

Journal of Applied Mathematics

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