Attractivity Of Positive Periodic Solution Research Articles

Further Studies on the Dynamics of a Lotka–Volterra Competitor–Competitor–Mutualist System with Time-Varying Delays

In this paper, a Lotka–Volterra (L-V) competitor–competitor–mutualist system with time-varying delays is studied. Some dynamical behaviors of the considered system are investigated. Firstly, we obtain the boundedness, permanence and periodic solution of the system using the comparison principle of differential equations and inequality estimation method. Then, the global attractiveness of the system is analyzed by multiple Lyapunov functionals. Meanwhile, the existence and global attractivity of positive periodic solutions is derived. In the third section, in order to validate the practicability and feasibility of the obtained theoretical results, we conducted numerical simulations using MATLAB function ddesd. Finally, the fourth section is where conclusions are drawn.

A delay nonautonomous model for the effects of fear and refuge on predator–prey interactions with water-level fluctuations

The interaction of prey (small fish) and predator (large fish) in lakes/ ponds at temperate and tropical regions varies when water level fluctuates naturally during seasonal time. We relate the perceptible effect of fear and anti-predator behavior of prey with the water-level fluctuations and describe how these are influenced by the seasonal changing of water level. So, we consider these as time-dependent functions to make the system more realistic. Also, we incorporate the time-dependent delay in the negative growth rate of prey in predator–prey model with Crowley–Martin-type functional response. We clearly provide the basic dynamics of the system such as positiveness, permanence and nonpersistence. The existence of positive periodic solution is studied using Continuation theorem, and suffiecient conditions for globally attractivity of positive periodic solution are also derived. To make the system more comprehensive, we establish numerical simulations, and compare the dynamics of autonomous and nonautonomous systems in the absence as well as the presence of time delay. Our results show that seasonality and time delay create the occurrence of complex behavior such as prevalence of chaotic disorder which can be potentially suppressed by the cost of fear and prey refuge. Also, if time delay increases, then system leads a boundary periodic solution. Our findings assert that the predation, fear of predator and prey refuge are correlated with water-level variations, and give some reasonable biological interpretations for persistence as well as extinction of species due to water-level variations.

Dynamic Analysis of a Model for Spruce Budworm Populations with Delay

A class of delayed spruce budworm population model is considered. Compared with previous studies, both autonomous and nonautonomous delayed spruce budworm population models are considered. By using the inequality techniques, continuation theorem, and the construction of suitable Lyapunov functional, we establish a set of easily verifiable sufficient conditions on the permanence, existence, and global attractivity of positive periodic solutions for the considered system. Finally, an example and its numerical simulation are given to illustrate our main results.

Global attractivity of positive periodic solution of a delayed Nicholson model with nonlinear density-dependent mortality term

Global attractivity of positive periodic solution of a delayed Nicholson model with nonlinear density-dependent mortality term

Existence and global attractivity of positive periodic solutions for a delayed predator-prey model with mutual interference and functional response

Existence and global attractivity of positive periodic solutions for a delayed predator-prey model with mutual interference and functional response

On a periodic predator-prey system with nonlinear diffusion and delays

In this paper, we consider a two species Lotka–Volterra type predator-prey system with nonlinear diffusion and distributed time delays. Based on the continuation theorem of the coincidence degree theory and the Liapunov function method, some new sufficient conditions on the existence and global attractivity of positive periodic solutions are established.

A periodic single species model with intermittent unilateral diffusion in two patches

In this paper, we consider a periodic single species model with intermittent unilateral diffusion in two patches. By using analytic method, Poincare mapping, Lyapunov function approach, sufficient and necessary conditions on the existence, uniqueness and global attractivity of positive periodic solution and the extinction of species for the considered system are established. Two examples and numerical simulations are presented to validate our theoretical results.

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

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.

Existence and global attractivity of the unique positive periodic solution for discrete hematopoiesis model

In this paper, a discrete Hematopoiesis model is studied. By using fixed point theorem of decreasing operator, we obtain sufficient conditions for the existence of unique positive periodic solution. Particularly,we give iterative sequence which converges to the positive periodic solution. In addition, the global attractivity of positive periodic solution is also investigated.

Existence and global stability of positive periodic solution of tri-trophic food chain with middle predator migratory in nature

Predator avoidance is the most important factor inducing vertical migration among zooplankton. Light intensity at the surface water also plays an important role to shape the predation pressure on zooplankton as most of the fishes show visually oriented predation. In the present paper, we assume that zooplankton can switch between vulnerable and invulnerable state through vertical migration. This switching is regulated by light intensity, predator abundance and food abundance in surface water. We propose a tri-trophic food chain model incorporating migratory behavior of middle predator. Further, we study the non-autonomous version of the proposed model by incorporating the seasonal variation of the rate parameters of the model. The sufficient conditions for the existence of positive periodic solutions are obtained. We also obtain the conditions for the global attractivity of positive periodic solutions. The numerical experiments are carried out to substantiate analytical findings.

Global attractivity of positive periodic solution for a predator–prey model with modified Leslie–Gower Holling-type II schemes and a deviating argument

In this paper, by utilizing the comparison theorem and constructing a suitable Lyapunov functional the predator–prey model with modified Leslie–Gower Holling-type II schemes and a deviating argument is studied. Some sufficient conditions are obtained for uniform persistence and global attractivity of positive periodic solutions for this model. Furthermore, an example shows that the obtained criteria are easily verifiable.

Dynamic analysis of an impulsive differential equation with time-varying delays

An impulsive differential equation with time varying delay is proposed in this paper. By using some analysis techniques with combination of coincidence degree theory, sufficient conditions for the permanence, the existence and global attractivity of positive periodic solution are established. The results of this paper improve and generalize some previously known results.

Global Attractivity of Positive Periodic Solution for a Delayed Predator-Prey System with Diffusion and Impulses

By constructing a suitable Lyapunov functional, the global attractivity of positive periodic solutions for a delayed predator-prey system with diffusion and impulses is studied in this paper. Finally, an example and numerical analysis are given to show the effectiveness of the main results.

Existence and Global Attractivity of Positive Periodic Solutions for The Neutral Multidelay Logarithmic Population Model with Impulse

Suffiicient and realistic conditions are established in this paper for the existence and global attractivity of a positive periodic solution to the neutral multidelay logarithmic population model with impulse by using the theory of abstract continuous theorem of k-set contractive operator and some inequality techniques. The results improve and generalize the known ones in Li 1999, Lu and Ge 2004, Y. Luo and Z. G. Luo 2010, and Wang et al. 2009. As an application, we also give an example to illustrate the feasibility of our main results.

Existence and global attractivity of positive periodic solutions for a delayed competitive system with the effect of toxic substances and impulses

In this paper, a class of non-autonomous delayed competitive systems with the effect of toxic substances and impulses is considered. By using the continuation theorem of coincidence degree theory, we derive a set of easily verifiable sufficient conditions that guarantees the existence of at least one positive periodic solution, and by constructing a suitable Lyapunov functional, the uniqueness and global attractivity of the positive periodic solution are established.

Existence and Uniqueness of Positive (Almost) Periodic Solutions for a Neutral Multi-Species Logarithmic Population Model with Multiple Delays and Impulses

In this paper, by using the contraction mapping principle and constructing a suitable Lyapunov functional, we established a set of easily applicable criteria for the existence, uniqueness and global attractivity of positive periodic solution and positive almost periodic solution of a neutral multi-species Logarithmic population model with multiple delays and impulses. The results improve and generalize the known ones in [1], as an application, we also give an example to illustrate the feasibility of our main results.

Existence and Stability of Positive Periodic Solutions for a Neutral Multispecies Logarithmic Population Model with Feedback Control and Impulse

We investigate a neutral multispecies logarithmic population model with feedback control and impulse. By applying the contraction mapping principle and some inequality techniques, a set of easily applicable criteria for the existence, uniqueness, and global attractivity of positive periodic solution are established. The conditions we obtained are weaker than the previously known ones and can be easily reduced to several special cases. We also give an example to illustrate the applicability of our results.

Global Attractivity of a Periodic DelayedN-Species Model of Facultative Mutualism

Two classes of periodicN-species Lotka-Volterra facultative mutualism systems with distributed delays are discussed. Based on the continuation theorem of the coincidence degree theory developed by Gaines and Mawhin and the Lyapunov function method, some new sufficient conditions on the existence and global attractivity of positive periodic solutions are established.

Existence and global attractivity of positive periodic solutions for a Holling II two-prey one-predator system

In this paper, a Holling II two-pery one-predator system is investigated. Based on the continuation theorem of coincidence degree theory and by constructing a suitable Lyapunov function, we derive a set of sufficient conditions that guarantee the existence of at least a positive periodic solution and global attractivity of periodic solutions.Mathematics Subject Classification 2000: 34K20; 34C25

Bionomics dynamic model of a class of competition systems

Differential equation problem is an important research topic in the international academia. In accordance with certain ecological phenomena, previous research was conducted based on simple observational and statistical data. But this approach does not effectively study the essence of the ecological phenomena. Recently, one dynamic approach has been proposed for the study of ecology in the international academia. According to this approach, first of all, the ecology is reduced to the differential equation model which represents the essential phenomenon, and then the dynamic law and rules of mathematics and biology will be studied. Currently, an extensive research is conducted on the differential equation problem. This paper primarily explores a type of competitive ecological model, which is a system of differential equation with infinite integral. we first study the existence of positive periodic solution to this model, and then present sufficient conditions for the global attractivity of positive periodic solutions.