Nonautonomous Lotka Volterra Research Articles

Forwards Attractor Structures in a Planar Cooperative Non-autonomous Lotka–Volterra System

The global attractor of a dissipative dynamical system provides the necessary information to understand the asymptotic dynamics of all the system’s solutions. A crucial question consists in finding the structure of this set. In this paper we provide a full characterization of the structure of attractors for a planar non-autonomous Lotka–Volterra cooperative system. We show sufficient conditions for the existence of forward attractors and give a full description of them by proving the existence of such bounded global solutions that all bounded global solutions join them, i.e. converge towards them when time tends to plus and minus infinity. These results generalize those known in an autonomous framework. The case of particular interest in our work is the situation where globally forward-stable non-autonomous solutions have both coordinates strictly positive. We study this case in detail and obtain sufficient conditions that the problem parameters must satisfy in order to obtain various structures of non-autonomous attractors. This allows us to understand different paths of the solutions towards the unique globally stable one.

Dynamics of a Predator–Prey-Competition System with Pure Delays

This paper deals with the non-autonomous Lotka–Volterra type one prey-two competitive predator systems with pure time delays. Based on the the comparison method and construction of the multiple Lyapunov functional, some new sufficient conditions on the boundedness, permanence, extinction and global attractivity of the system are established. In addition, two examples with numerical simulations are presented to illustrate the obtained theoretical results.

Permanence for a Generalized Nonautonomous Lotka-Volterra Competition System with Delays

Permanence for a Generalized Nonautonomous Lotka-Volterra Competition System with Delays

Positive periodic solutions for Lotka–Volterra systems with a general attack rate

The paper deals with a non-autonomous Lotka–Volterra type system, which in particular may include logistic growth of the prey population and hunting cooperation between predators. We focus on the existence of positive periodic solutions by using an operator approach based on the Krasnosel’skii homotopy expansion theorem. We give sufficient conditions in order that the localized periodic solution does not reduce to a steady state. Particularly, two typical expressions for the functional response of predators are discussed.

A Quantitative Study of the Interactions between Oil Price and Renewable Energy Sources Stock Prices

In this article, we apply an integrable nonautonomous Lotka–Volterra model to study the relationship between oil and renewable energy stock prices between 2006 and 2016. The advantage of this innovative approach is that it allows us to study the simultaneous interaction among n stock indices at any point in time. In line with previous studies, we find that the relationship between oil and renewables is characterized by major structural breaks taking place in 2008 and around 2013. The first structural break might be caused by the financial crisis, whereas more studies are required to advance a hypothesis on the causes behind the second structural break. Our main finding is that oil is always in a predator–prey relationship with wind, whereas it proceeds in mutualism with solar after 2012. Moreover, we find that solar and wind proceed in mutualism between 2008 and 2013 but have a rivalrous interaction before (competition) and after (predator–prey) that period. We explore the possible reasons behind these patterns and their policy implications.

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.

Inter-port interactions in the Le Havre-Hamburg range: A scenario analysis using a nonautonomous Lotka Volterra model

We propose an integrable nonautonomous Lotka-Volterra model to carry out a quantitative study of the interaction among container ports located in the Le Havre-Hamburg range. We find that mutualism is emerging among the ports located in the Benelux area, but not among German ports. Moreover, we develop three alternative scenarios and find that (i) for mutualism to emerge no port must be too strong vis-à-vis the others; (ii) the kind of interaction among ports depends on their geographic location, the services they provide, and demand-side factors; and (iii) upgrading intermodal connections can produce externalities that are not internalized by the investing port/country.

Deterministic modeling in scenario forecasting: estimating the effects of two public policies on intergenerational conflict

In this article, we use a nonautonomous Lotka Volterra model to study the intergenerational conflict within an aging American society between 1974 and 2014. The main findings are that (1) the intensity of the competition among age cohorts is constantly increasing and has crowded out any mutualism, that (2) the elderly have improved their economic status relative to other age cohorts, and that (3) this trend is expected to intensify in the forecasted future (2014–2030). On this background, we test the impact of two stylized policies and of different demographic trends—for a total of 4 alternative scenarios—on the level of intergenerational conflict, and on the performances in terms of income of the relevant age cohorts in the forecasted period. The scenario analysis reveals that without policy intervention it is unlikely that society will revert to mutualistic interactions in the coming fifteen years. At the same time, policy reforms that are sufficiently far-reaching to interrupt the shift of resources from the young to the elderly might face significant political opposition. Politicians that are interested in preventing a gerontocracy and the explosion of intergenerational conflict have to find ways to lessen the opposition of the elderly to policy reforms that are in the interest of younger generations.

Dynamics analysis and numerical simulations of a stochastic non-autonomous predator–prey system with impulsive effects

In this paper, we propose a stochastic non-autonomous Lotka–Volterra predator–prey model with impulsive effects and investigate its stochastic dynamics. We first prove that the subsystem of the system has a unique periodic solution which is globally attractive. Furthermore, we obtain the threshold value in the mean which governs the stochastic persistence and the extinction of the prey–predator system. Our results show that the stochastic noises and impulsive perturbations have crucial effects on the persistence and extinction of each species. Finally, we use the different stochastic noises and impulsive effects parameters to provide a series of numerical simulations to illustrate the analytical results.

A Study of Tourism Dynamics in Three Italian Regions Using a Nonautonomous Integrable Lotka-Volterra Model.

This article is a first application of an integrable nonautonomous Lotka–Volterra (LV) model to the study of tourism dynamics. In particular, we analyze the interaction in terms of touristic flows among three Italian regions. Confirming an hypothesis advanced by recent theoretical works, we find that these regions not only compete against each other, but at times they also proceed in mutualism. Moreover, the kind and the intensity of the interaction changes over time, suggesting that dynamic models can play a vital role in the study of touristic flows.

Extinction of a two species non-autonomous competitive system with Beddington-DeAngelis functional response and the effect of toxic substances

Abstract A two species non-autonomous competitive phytoplankton system with Beddington-DeAngelis functional response and the effect of toxic substances is proposed and studied in this paper. Sufficient conditions which guarantee the extinction of a species and global attractivity of the other one are obtained. The results obtained here generalize the main results of Li and Chen [Extinction in two dimensional nonautonomous Lotka-Volterra systems with the effect of toxic substances, Appl. Math. Comput. 182(2006)684-690]. Numeric simulations are carried out to show the feasibility of our results.

Stability analysis of a non-autonomous Lotka–Volterra competition model with seasonal succession

In this paper, a non-autonomous Lotka–Volterra competition model with seasonal succession is considered. By the stability analysis of equilibria and the theory of monotone dynamical system, the stability of equilibria and periodic solutions are investigated. Finally, the results in this paper are discussed from a new perspective.

Periodic solution for a non-autonomous Lotka–Volterra predator–prey model with random perturbation

This paper studies a stochastic non-autonomous Lotka–Volterra predator–prey model. We prove that there exists at least one positive periodic solution under some simple and reasonable conditions. In addition we obtain sufficient conditions for persistence in mean and extinction for the stochastic non-autonomous system. Our method and results are new and the ideas could be used to study other types of non-autonomous stochastic predator–prey systems.

Local well-posedness for a Lotka–Volterra system in Besov spaces

This paper is devoted to study local existence, uniqueness, and continuous dependence upon the initial data of mild solutions for a diffusive non-autonomous Lotka–Volterra system. Initial data are taken in the Besov space Bp,q,Nσ.

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.

Dynamics of a General Stochastic Nonautonomous Lotka-Volterra Model with Delays and Impulsive Perturbations

A stochastic nonautonomous N-species Lotka-Volterra model with delays and impulsive perturbations is investigated. For this model, sufficient conditions for extinction, nonpersistence in the mean, weak persistence and stochastic permanence are given, respectively. The influences of the stochastic noises, and the impulsive perturbations on the properties of the stochastic model are also discussed. The critical value between weak persistence and extinction is obtained. Finally, numerical simulations are given to support the theoretical analysis results.

Permanence and extinction of non-autonomous Lotka-Volterra facultative systems with jump-diffusion

Using stochastic differential equations with Lévy jumps,this paper studies the effect of environmental stochasticity andrandom catastrophes on the permanenceof Lotka-Volterra facultative systems.Under certain simple assumptions, we establish the sufficient conditionsfor weak permanence in the meanand extinction of the non-autonomous system, respectively.In particular,a necessary and sufficient condition for permanenceand extinction of autonomous system with jump-diffusion are obtained.We generalize some former results under weaker assumptions.Finally, we discuss the biological implications of the mainresults.

Asymptotic behavior of a stochastic non-autonomous predator–prey model with impulsive perturbations

This paper is concerned with a stochastic non-autonomous Lotka–Volterra predator–prey model with impulsive effects. The asymptotic properties are examined. Sufficient conditions for persistence and extinction are obtained, our results demonstrate that the impulse has important effects on the persistence and extinction of the species. We also show that the solution is stochastically ultimate bounded under some conditions. Finally, several simulation figures are introduced to confirm our main results.