Global attractivity of asymptotically almost periodic Nicholson’s blowflies models with a nonlinear density-dependent mortality term

2018 ◽  
Vol 11 (06) ◽  
pp. 1850079 ◽  
Author(s):  
Yi Tang ◽  
Shenglan Xie
Keyword(s):  
Differential Inequality ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Almost Periodic Function ◽  
Almost Periodic ◽  
Density Dependent ◽  
Density Dependent Mortality ◽  
Inequality Techniques ◽  
Asymptotically Almost Periodic ◽  
Dependent Mortality

This paper focuses on the study of a class of asymptotically almost periodic Nicholson’s blowflies models with a nonlinear density-dependent mortality term. By virtue of differential inequality techniques, a set of easily verifiable sufficient conditions are established to show that every solution of the considered model is asymptotically almost periodic, and it also converges to a same almost periodic function as [Formula: see text], which improves and supplements some previously known researches. Moreover, a numerical example is given to test the feasibility and effectiveness of the obtained results.

scholarly journals New results on global asymptotic stability for a nonlinear density-dependent mortality Nicholson’s blowflies model with multiple pairs of time-varying delays

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Qian Cao ◽  
Guoqiu Wang ◽  
Hong Zhang ◽  
Shuhua Gong
Keyword(s):  
Asymptotic Stability ◽  
Global Asymptotic Stability ◽  
Differential Inequality ◽  
Time Varying ◽  
Density Dependent ◽  
Nicholson’S Blowflies Model ◽  
Density Dependent Mortality ◽  
Inequality Techniques ◽  
Independent Criterion ◽  
Dependent Mortality

AbstractThis paper is concerned with a class of Nicholson’s blowflies model involving nonlinear density-dependent mortality terms and multiple pairs of time-varying delays. By using differential inequality techniques and the fluctuation lemma, we establish a delay-independent criterion on the global asymptotic stability of the addressed model, which improves and complements some existing ones. The effectiveness of the obtained result is illustrated by some numerical simulations.

scholarly journals Global Exponential Stability of Almost Periodic Solutions for SICNNs with Continuously Distributed Leakage Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Hong Zhang ◽  
Mingquan Yang
Keyword(s):  
Exponential Stability ◽  
Periodic Solutions ◽  
Differential Inequality ◽  
Sufficient Conditions ◽  
Functional Method ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Leakage Delays ◽  
Lyapunov Functional Method ◽  
Inequality Techniques

Shunting inhibitory cellular neural networks (SICNNs) are considered with the introduction of continuously distributed delays in the leakage (or forgetting) terms. By using the Lyapunov functional method and differential inequality techniques, some sufficient conditions for the existence and exponential stability of almost periodic solutions are established. Our results complement with some recent ones.

scholarly journals Existence and Global Exponential Stability of Almost Periodic Solutions for SICNNs with Nonlinear Behaved Functions and Mixed Delays

2010 ◽  
Vol 2010 ◽  
pp. 1-20 ◽  
Author(s):  
Xinsong Yang ◽  
Jinde Cao ◽  
Chuangxia Huang ◽  
Yao Long
Keyword(s):  
Exponential Stability ◽  
Periodic Solutions ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Sufficient Conditions ◽  
Mixed Delays ◽  
Time Varying ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Inequality Techniques

By using the Leray-Schauder fixed point theorem and differential inequality techniques, several new sufficient conditions are obtained for the existence and global exponential stability of almost periodic solutions for shunting inhibitory cellular neural networks with discrete and distributed delays. The model in this paper possesses two characters: nonlinear behaved functions and all coefficients are time varying. Hence, our model is general and applicable to many known models. Moreover, our main results are also general and can be easily deduced to many simple cases, including some existing results. An example and its simulation are employed to illustrate our feasible results.

scholarly journals GLOBAL EXPONENTIAL STABILITY OF ALMOST PERIODIC SOLUTIONS FOR NICHOLSON’S BLOWFLIES SYSTEM WITH NONLINEAR DENSITY-DEPENDENT MORTALITY TERMS AND PATCH STRUCTURE

2017 ◽  
Vol 22 (4) ◽  
pp. 484-502 ◽  
Author(s):  
Pengyan Liu ◽  
Liang Zhang ◽  
Shitao Liu ◽  
Lifei Zheng
Keyword(s):  
Periodic Solution ◽  
Global Exponential Stability ◽  
Almost Periodic Solution ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Patch Structure ◽  
Density Dependent ◽  
Density Dependent Mortality ◽  
Positive Almost Periodic Solution ◽  
Dependent Mortality

This paper considers a generalized Nicholson’s blowflies system with nonlinear density-dependent mortality terms and patch structure. Under appropriate conditions, we establish some criteria to ensure that the solutions of this system exist and converge globally exponentially to a positive almost periodic solution. The results complement another case of nonlinear density-dependent mortality terms in Chen and Wang [5].

scholarly journals Time lags and density dependence in age dependent two species competition

1982 ◽  
Vol 25 (2) ◽  
pp. 271-291 ◽  
Author(s):  
K. Gopalsamy
Keyword(s):  
Density Dependence ◽  
Linear Stability ◽  
Sufficient Conditions ◽  
Time Lags ◽  
Species Competition ◽  
Density Dependent ◽  
Density Dependent Mortality ◽  
Age Dependent ◽  
Time Lagged ◽  
Dependent Mortality

Sufficient conditions are obtained for the existence and linear stability of time independent age distributions in two species competition with age and time lagged density dependent mortality and fertility functions.

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