scholarly journals Partial Extinction, Permanence, and Global Attractivity in Nonautonomousn-Species Gilpin-Ayala Competitive Systems with Impulses

2012 ◽  
Vol 2012 ◽  
pp. 1-19
Author(s):  
Juan Hou ◽  
Hanhui Liu
Keyword(s):  
Global Attractivity ◽  
Impulsive Effects ◽  
Qualitative Properties ◽  
Competitive Systems ◽  
Liapunov Functions ◽  
Partial Extinction ◽  
New Criteria

The qualitative properties of general nonautonomousn-species Gilpin-Ayala competitive systems with impulsive effects are studied. Some new criteria on the permanence, extinction, and global attractivity of partial species are established by using the methods of inequalities estimate and Liapunov functions.

scholarly journals Global attractivity in a “food-limited” population model with impulsive effects

2004 ◽  
Vol 292 (1) ◽  
pp. 211-221 ◽  
Author(s):  
Sanyi Tang ◽  
Lansun Chen
Keyword(s):  
Population Model ◽  
Global Attractivity ◽  
Impulsive Effects

scholarly journals An analysis on the controllability and stability to some fractional delay dynamical systems on time scales with impulsive effects

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Bakhtawar Pervaiz ◽  
Akbar Zada ◽  
Sina Etemad ◽  
Shahram Rezapour
Keyword(s):  
Time Scales ◽  
Dynamic Systems ◽  
Fixed Point Theorems ◽  
Impulsive Effects ◽  
Qualitative Properties ◽  
Existence And Uniqueness Results ◽  
New Class ◽  
Uniqueness Results ◽  
Fractional Delay ◽  
The Stability

AbstractIn this article, we establish a new class of mixed integral fractional delay dynamic systems with impulsive effects on time scales. We investigate the qualitative properties of the considered systems. In fact, the article contains three segments, and the first segment is devoted to investigating the existence and uniqueness results. In the second segment, we study the stability analysis, while the third segment is devoted to investigating the controllability criterion. We use the Leray–Schauder and Banach fixed point theorems to prove our results. Moreover, the obtained results are examined with the help of an example.

scholarly journals Dynamic Behaviors in a Droop Model for Phytoplankton Growth in a Chemostat with Nutrient Periodically Pulsed Input

2012 ◽  
Vol 2012 ◽  
pp. 1-25
Author(s):  
Kai Wang ◽  
Zhidong Teng ◽  
Xueliang Zhang
Keyword(s):  
Periodic Solution ◽  
Global Attractivity ◽  
Positive Periodic Solution ◽  
Phytoplankton Growth ◽  
Dynamic Behaviors ◽  
Droop Model ◽  
New Criteria

The dynamic behaviors in a droop model for phytoplankton growth in a chemostat with nutrient periodically pulsed input are studied. A series of new criteria on the boundedness, permanence, extinction, existence of positive periodic solution, and global attractivity for the model are established. Finally, an example is given to demonstrate the effectiveness of the results in this paper.

Asymptotic Behavior of a Stochastic Two-Species Competition System with Impulsive Effects

2018 ◽  
Vol 19 (5) ◽  
pp. 427-438
Author(s):  
Pan Wang ◽  
Bing Li ◽  
Yongkun Li
Keyword(s):  
Asymptotic Behavior ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Impulsive Effects ◽  
Species Competition ◽  
Stochastic Permanence ◽  
Competition System ◽  
Stochastic Boundedness ◽  
Dynamical Properties ◽  
Persistent In Mean

AbstractIn this paper, we consider a stochastic two-species competition system with impulsive effects. Some dynamical properties are investigated and sufficient conditions for the stochastic boundedness, stochastic permanence and global attractivity are established. Under some conditions, we conclude that the stochastic model is persistent in mean and extinction. An example is given to illustrate the main result.

scholarly journals Periodic Solutions for n-Species Lotka-Volterra Competitive Systems with Pure Delays

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Ahmadjan Muhammadhaji ◽  
Rouzimaimaiti Mahemuti ◽  
Zhidong Teng
Keyword(s):  
Periodic Solutions ◽  
Lyapunov Functional ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Positive Periodic Solutions ◽  
Competitive Systems ◽  
Volterra Systems ◽  
Special Cases

We study a class of periodic general n-species competitive Lotka-Volterra systems with pure delays. Based on the continuation theorem of the coincidence degree theory and Lyapunov functional, some new sufficient conditions on the existence and global attractivity of positive periodic solutions for the n-species competitive Lotka-Volterra systems are established. As an application, we also examine some special cases of the system, which have been studied extensively in the literature.

scholarly journals Analysis of a Periodic Impulsive Predator-Prey System with Disease in the Prey

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Lianwen Wang ◽  
Zhijun Liu
Keyword(s):  
Prey Species ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Functional Method ◽  
Predator Prey ◽  
Prey System ◽  
Lyapunov Functional Method ◽  
Partial Extinction ◽  
Impulsive Perturbations

We investigate a periodic predator-prey system subject to impulsive perturbations, in which a disease can be transmitted among the prey species only, in this paper. With the help of the theory of impulsive differential equations and Lyapunov functional method, sufficient conditions for the permanence, global attractivity, and partial extinction of system are established, respectively. It is shown that impulsive perturbations contribute to the above dynamics of the system. Numerical simulations are presented to substantiate the analytical results.

scholarly journals Global attractivity and extinction for Lotka–Volterra systems with infinite delay and feedback controls

2015 ◽  
Vol 145 (2) ◽  
pp. 301-330 ◽  
Author(s):  
Teresa Faria ◽  
Yoshiaki Muroya
Keyword(s):  
Global Attractivity ◽  
Infinite Delay ◽  
Sufficient Conditions ◽  
Weak Form ◽  
Volterra Model ◽  
Delay Effect ◽  
Feedback Controls ◽  
Competitive Systems ◽  
Volterra Systems ◽  
Multiple Species

The paper deals with a multiple species Lotka–Volterra model with infinite distributed delays and feedback controls, for which we assume a weak form of diagonal dominance of the instantaneous negative intra-specific terms over the infinite delay effect in both the population variables and controls. General sufficient conditions for the existence and attractivity of a saturated equilibrium are established. When the saturated equilibrium is on the boundary of , sharper criteria for the extinction of all or part of the populations are given. While the literature usually treats the case of competitive systems only, here no restrictions on the signs of the intra- and inter-specific delayed terms are imposed. Moreover, our technique does not require the construction of Lyapunov functionals.

scholarly journals Permanence in Multispecies Nonautonomous Lotka-Volterra Competitive Systems with Delays and Impulses

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaomei Feng ◽  
Fengqin Zhang ◽  
Kai Wang ◽  
Xiaoxia Li
Keyword(s):  
Sufficient Conditions ◽  
Fixed Time ◽  
Impulsive Effects ◽  
Competitive Systems ◽  
Integrable Form

This paper studies multispecies nonautonomous Lotka-Volterra competitive systems with delays and fixed-time impulsive effects. The sufficient conditions of integrable form on the permanence of species are established.

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