scholarly journals Attractivity analysis on a neoclassical growth system incorporating patch structure and multiple pairs of time-varying delays

2021 ◽  
pp. 1-17
Author(s):  
Qian Cao
Keyword(s):  
Positive Equilibrium ◽  
Global Dynamics ◽  
Time Varying ◽  
Boundedness Of Solutions ◽  
Patch Structure ◽  
All Solutions ◽  
Growth System ◽  
Positive Equilibrium Point ◽  
Delay Dependent ◽  
Neoclassical Growth

In this paper, we focus on the global dynamics of a neoclassical growth system incorporating patch structure and multiple pairs of time-varying delays. Firstly, we prove the global existence, positiveness and boundedness of solutions for the addressed system. Secondly, by employing some novel differential inequality analyses and the fluctuation lemma, both delay-independent and delay-dependent criteria are established to ensure that all solutions are convergent to the unique positive equilibrium point, which supplement and improve some existing results. Finally, some numerical examples are afforded to illustrate the effectiveness and feasibility of the theoretical findings.

scholarly journals Delay-dependent attractivity on a tick population dynamics model incorporating two distinctive time-varying delays

2021 ◽  
Vol 477 (2251) ◽  
pp. 20210302
Author(s):  
Chuangxia Huang ◽  
Jian Zhang ◽  
Jinde Cao
Keyword(s):  
Population Dynamics ◽  
Global Attractivity ◽  
Positive Equilibrium ◽  
Tick Population ◽  
Time Varying ◽  
Dynamics Model ◽  
Population Dynamics Model ◽  
All Solutions ◽  
Positive Equilibrium Point ◽  
Delay Dependent

In this paper, we aim to investigate the influence of delay on the global attractivity of a tick population dynamics model incorporating two distinctive time-varying delays. By exploiting some differential inequality techniques and with the aid of the fluctuation lemma, we first prove the persistence and positiveness for all solutions of the addressed equation. Consequently, a delay-dependent criterion is derived to assure the global attractivity of the positive equilibrium point. And lastly, some numerical simulations are presented to verify that the obtained results improve and complement some existing ones.

scholarly journals Global Attractivity for Lasota–Wazewska-Type System with Patch Structure and Multiple Time-Varying Delays

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Zhiwen Long ◽  
Yanxiang Tan
Keyword(s):  
Global Attractivity ◽  
Type System ◽  
Small Time ◽  
Positive Equilibrium ◽  
Multiple Time ◽  
Time Varying ◽  
Patch Structure ◽  
Small Time Delay ◽  
Inequality Techniques ◽  
Theoretical Results

This paper aims to study the asymptotic behavior of Lasota–Wazewska-type system with patch structure and multiple time-varying delays. Based on the fluctuation lemma and some differential inequality techniques, we prove that the positive equilibrium is a global attractor of the addressed system with small time delay. Finally, we provide an example to illustrate the feasibility of the theoretical results.

Domain-decomposition method for the global dynamics of delay differential equations with unimodal feedback

2007 ◽  
Vol 463 (2086) ◽  
pp. 2655-2669 ◽  
Author(s):  
Gergely Röst ◽  
Jianhong Wu
Keyword(s):  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Sufficient Conditions ◽  
Heteroclinic Orbits ◽  
Positive Equilibrium ◽  
Global Dynamics ◽  
Nicholson’S Blowflies Equation ◽  
All Solutions ◽  
Trivial Equilibrium ◽  
Delay Differential

The dynamics generated by the delay differential equation with unimodal feedback is studied. The existence of the global attractor is shown and bounds of the attractor are given. We find attractive invariant intervals and give sufficient conditions that guarantee that all solutions enter the domain where f ′ is negative with respect to a positive equilibrium, so the results for delayed monotone feedback can be applied to describe the asymptotic behaviour of solutions. In particular, the existence of heteroclinic orbits from the trivial equilibrium to a periodic orbit oscillating around the positive equilibrium is established. Numerical examples using Nicholson's blowflies equation and the Mackey–Glass equation are provided to illustrate the main results.

Dynamics of a prey predator disease model with Holling type functional response and stochastic perturbation

2020 ◽  
pp. 471-488
Author(s):  
M. N. Srinivas ◽  
G. Basava Kumar ◽  
V. Madhusudanan
Keyword(s):  
Equilibrium Point ◽  
Disease Model ◽  
Stochastic Perturbation ◽  
Positive Equilibrium ◽  
Type Ii ◽  
Asymptotically Stable ◽  
Unique Positive Solution ◽  
Stochastic Nature ◽  
Research Article ◽  
Positive Equilibrium Point

The present research article constitutes Holling type II and IV diseased prey predator ecosystem and classified into two categories namely susceptible and infected predators.We show that the system has a unique positive solution. The deterministic and stochastic nature of the dynamics of the system is investigated. We check the existence of all possible steady states with local stability. By using Routh-Hurwitz criterion we showed that the positive equilibrium point $E_{7}$ is locally asymptotically stable if $x^{*} > \sqrt{m_{1}}$ .Moreover condition of the global stability of positive equilibrium point $E_{7}$ are also entrenched with help of Lyupunov theorem. Some Numerical simulations are carried out to illustrate our analytical findings.

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