Nonautonomous Lotka-Volterra Competitive System Research Articles

Dynamic Behaviors of a Nonautonomous Impulsive Competitive System with the Effect of Toxic Substance

We firstly propose a nonautonomous impulsive Lotka-Volterra competitive system with the effect of toxic substance. Only one of the two species could produce toxic substance. Sufficient condition which guarantees the extinction of one of the species and the global attractivity of the other species is obtained. We also present an example to verify our main results, which show that species still is possibly driven to extinction when only one of the two species produces toxic substances. The results of this paper supplement the existing results.

Extinction in a Nonautonomous Discrete Lotka-Volterra Competitive System with Time Delay

This paper is concerned with a nonautonomous discrete Lotka-Volterra competitive system with time delay. By using some analytical techniques, we prove that, under certain conditions, one of the species will be driven to extinction while the other one will be globally attractive with any positive solution of a discrete logistic equation.

Almost periodic solutions of nonautonomous Lotka–Volterra competitive systems with dominated delays

In this paper, a class of nonautonomous Lotka–Volterra type multispecies competitive systems with delays is studied. By employing Lyapunov functional, some sufficient conditions to guarantee the existence of almost periodic solutions for the Lotka–Volterra system are obtained.

Global asymptotic stability of stochastic competitive system with infinite delays

In this paper, sufficient conditions for global asymptotic stability of a stochastic non-autonomous Lotka–Volterra competitive system with infinite delays are established. Some recent results are improved and generalized.

Note on the Persistence of a Nonautonomous Lotka-Volterra Competitive System with Infinite Delay and Feedback Controls

We study a nonautonomous Lotka-Volterra competitive system with infinite delay and feedback controls. We establish a series of criteria under which a part ofn-species of the systems is driven to extinction while the remaining part of the species is persistent. Particularly, as a special case, a series of new sufficient conditions on the persistence for all species of system are obtained. Several examples together with their numerical simulations show the feasibility of our main results.

Asymptotic behavior of a stochastic nonautonomous Lotka–Volterra competitive system with impulsive perturbations

This paper is concerned with an n-species stochastic nonautonomous Lotka–Volterra competitive system with impulsive effects. Some dynamical properties are investigated and the sufficient conditions for stochastic permanence, extinction and global stability are established. Moreover, the lower-growth rate and the upper-growth rate of the positive solution are studied. In addition, the limit of the average in time of the sample paths of solutions is estimated.

Extinction in a nonautonomous Lotka–Volterra competitive system with infinite delay and feedback controls

In this paper, we propose a Lotka–Volterra competitive system with infinite delay and feedback controls. By using the method of multiple Lyapunov functionals and by developing a new analysis technique, we establish the sufficient conditions which guarantee that some of the n species are driven to extinction. Two examples together with their numerical simulations show the feasibility of our main results and the considerable effects of feedback controls on the extinction of species.

Permanence in Multispecies Nonautonomous Lotka‐Volterra Competitive Systems with Delays and Impulses

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.

Permanence and global attractivity for discrete nonautonomous two-species Lotka-Volterra competitive system with delays and feedback controls

A discrete nonautonomous two-species Lotka–Volterra competitive system with delays and feedback controls is proposed and investigated. By using the method of discrete Lyapunov functionals, new sufficient conditions on the permanence of species and global attractivity of the system are established. Particularly, an interesting fact is found in our results, that is, the feedback controls are harmless to the permanence of species for the considered system.

Formula omitted]-species non-autonomous Lotka–Volterra competitive systems with delays and impulsive perturbations

In this paper, a class of non-autonomous N -species Lotka–Volterra-type competitive system with time delays and impulsive perturbations is investigated. New criteria on coexistence and global attractivity for all species other than some inclining to extinction are established. From our results, we find that the extinction of some species due to competition exclusion and weak adaption to a stochastically variable environment characterized by impulsive perturbations is necessary for the coexistence and global attractivity of other survivors in a limited resource ecosystem. Meanwhile, the dynamic behaviors of competition models with impulse perturbations are more complicated and different from prior research results obtained from continuous competition models. The impulse perturbations impose either negative or positive influences on the survival of species, which results in evidently regulative effects, and even make the inferior competitors exclude or coexist with the superior competitors. The theoretical results are confirmed by a special example and numerical simulations, by which we find some interesting phenomena.

Partial extinction, permanence and global attractivity in nonautonomous n-species Lotka-Volterra competitive systems with impulses

In this paper, the qualitative properties of general nonautonomous Lotka-Volterra n-species competitive systems with impulsive effects are studied. Some new criteria on the permanence, extinction and global attractivity of partial species are established by used the methods of inequalities estimate and Liapunov functions. As applications, nonautonomous two species Lotka-Volterra systems with impulses are discussed.

Permanence and global stability for nonautonomous [formula omitted]-species Lotka–Valterra competitive system with impulses

In this paper, we consider a class of nonautonomoua N -species Lotka–Volterra competitive systems with impulsive effects. Some new criteria on the permanence and global attractivity are established by developing the methods given in [Z. Teng and Z. Li, Permanence and asymptotic behavior of the N -species nonautonomous Lotka–Volterra competitive systems, Comput. Math. Appl. 39 (2000) 107–116; S. Ahmad and I.M. Stamovab, Asymptotic stability of an N -dimensional impulsive competitive system, Nonlinear Anal. RWA 8 (2007) 654–663].

Extinction in Nonautonomous Discrete Lotka-Volterra Competitive System with Pure Delays and Feedback Controls

The paper discusses a nonautonomous discrete time Lotka-Volterra competitive system with pure delays and feedback controls. New sufficient conditions for which a part of then-species is driven to extinction are established by using the method of multiple discrete Lyapunov functionals.

Permanence and stability in multi-species non-autonomous Lotka–Volterra competitive systems with delays and feedback controls

In this paper, we consider a multi-species Lotka–Volterra type competitive system with delays and feedback controls. A general criteria on the permanence is established, which is described by integral form and independent of feedback controls. By constructing suitable Lyapunov functionals, a set of easily verifiable sufficient conditions are derived for global stability of any positive solution to the model.

Extinction in nonautonomous Lotka–Volterra competitive system with pure-delays and feedback controls

In this paper, the extinction of species for general n -species nonautonomous Lotka–Volterra competitive system with pure-delays and feedback controls is studied. New sufficient conditions of which a part of the n species is driven to extinction are established by using the method of multiple Lyapunov functionals and by developing a new analysis technique. The numerical simulation shows that in a competitive system by introducing proper feedback controls we can make an extinct species become permanent.

ON THE PERMANENCE FOR n-SPECIES NON-AUTONOMOUS LOTKA–VOLTERRA COMPETITIVE SYSTEM WITH INFINITE DELAYS AND FEEDBACK CONTROLS

In this paper, a class of n-species nonautonomous Lotka–Volterra competitive system with infinite delays and feedback controls is studied. A new criterion on the permanence of species is established. This result shows that the feedback controls do not influence the permanence of species.

On the permanence in non-autonomous Lotka–Volterra competitive system with pure-delays and feedback controls

This paper,which is a continuation of [H. Hu, Z. Teng, H. Jiang, On the extinction in nonautonomous Lotka–Volterra competitive system with pure-delays and feedback controls, Appl. Math. Comput. (2007) (submitted for publication)], considers general n -species non-autonomous Lotka–Volterra competitive systems with pure-delays and feedback controls. New sufficient conditions for which a part of the n species remains permanent, are established by applying the method of multiple Lyapunov functionals and introducing a new analysis technique. In contrast to previous works (see, for example, references [F. Chen, The permanence and global attractivity of Lotka–Volterra competition system with feedback controls, Nonlinear Anal. RWA 7 (2006) 133–143; F. Chen, Global stability of a single species model with feedback control and distributed time delay, Appl. Math. Comput. 178 (2006) 474–479; F. Chen, Permamence in nonautonomous multi-species predator–prey system with feedback controls, Appl. Math. Comput. 173 (2006) 694–709; F. Chen, Z. Li, Y. Huang, Note on the permamence of a competitive system with infinite delay and feedback controls, Nonlinear Anal. RWA 8 (2007) 680–687]), we introduce a new research method and obtain feedback controls that can not influence the permanence of species.

PERMANENCE IN A DISCRETE n-SPECIES NON-AUTONOMOUS LOTKA–VOLTERRA COMPETITIVE SYSTEMS WITH INFINITE DELAYS AND FEEDBACK CONTROL

In this paper, we deal with a discrete n-species non-autonomous Lotka–Volterra competitive systems with infinite delays and feedback control, obtain sufficient conditions for the permanence of the systems.

Partial permanence and extinction in an N-species nonautonomous Lotka–Volterra competitive system

In this paper, we first consider a general N-species nonautonomous Lotka–Volterra system. We show that certain average conditions involving the respective averages of the growth rates and the interaction coefficients imply the total persistence of all species. Using this result, we then give computable conditions on the coefficients which imply the ultimate extinction of certain species in a N -dimensional Lotka–Volterra system.

Global asymptotic stability in n-species non-autonomous Lotka–Volterra competitive systems with infinite delays and feedback control

Abstract A non-autonomous Lotka–Volterra competition system with infinite delays and feedback control and without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the system. Some new results are obtained.