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efectos allee » efecto allee (Expander búsqueda), efectos al (Expander búsqueda), efectos amfe (Expander búsqueda)
efectos allee » efecto allee (Expander búsqueda), efectos al (Expander búsqueda), efectos amfe (Expander búsqueda)
1
artículo
Publicado 2022
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In this paper, a modified Leslie-Gower type predator-prey model introducing in prey population growth a delayed strong Allee effect is studied. Estabilidad de un modelo depredador-presa tipo Leslie Gower con un efecto Allee fuerte con retardo The Leslie-Gower model with Allee effect has none, one or two positive equilibrium points but the incorporation of a time delay in the growth rate destabilizes the system, breaking the stability when the delay cross a critical point. The existence of a Hopf bifurcation is studied in detail and the numerical simulations confirm the theoretical results showing the different scenarios. We present biological interpretations for species prey-predator type.
2
artículo
Publicado 2022
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A predator-prey model of Gause type is an extension of the classical Lotka-Volterra predator-prey model. In this work, we study a predator-prey model of Gause type, where the prey growth rate is subject to an Allee effect and the action of the predator over the prey is given by a square-root functional response, which is non-differentiable at the y-axis. This kind of functional response appropriately models systems in which the prey have a strong herd structure, as the predators mostly interact with the prey on the boundary of the herd. Because of the square root term in the functional response, studying the behavior of the solutions near the origin is more subtle and interesting than other standard models.Our study is divided into two parts: the local classification of the equilibrium points, and the behavior of the solutions in certain invariant set when the model has a strong Allee ef...
3
artículo
Publicado 2023
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This research concerns with analysis of a class of modified predator- prey type Leslie-Gower models. The model is described by an autonomous nonlinear ordinary differential equation system. The functional response of predators is Holling IV type or non-monotone, and the growth of prey is affected by the Allee effect. An important aspect is the study of the point (0, 0) since it has a strong influence on the behavior of the system being essential for the existence and extinction of both species, although the proposed system is not define there.
4
artículo
Publicado 2025
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Mathematical models are a very useful tool to understand, describe or predict the population dynamics of species interacting. Ecologists and mathematicians have extensively studied the predator-prey, victim-exploiter, competition and mutualistic relationships. However, mutualism between species has not received the same attention as the other ecological interactions. In this work, we exclude periodic solutions of three types of systems by the construction of Dulac functions. These systems can be used to describe the population dynamics of mutualistic species. The system type I includes a wide variety of mutualistic models in which both the intrinsic rate of increase and the carrying capacity of each species increase by the interaction between species. In particular, the system type I can be applied to exclude periodic solutions of models with conditioned interactions such ...
5
artículo
Publicado 2022
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The interactions between predators and their prey in the real world are usually affected by diverse ecological phenomena acting on both the prey and the predators. Collaboration or cooperation between predators is one of those behaviors, which has received less attention from researchers than competition among consumers. These contacts are important aspects of the dynamics of food chains and trophic webs. In this work, we will study the influence of collaboration or cooperation (hunting cooperation) between predators to consume (or capture) their favorite prey, which are affected by an effect Allee weak. We extend the results obtained in a previously published model, considering only collaboration between predators and in which the Allee effect is absent.
6
artículo
Publicado 2021
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The main feature of the Leslie-Gower-type predation model is that the predator’s growth function is one of logistic-type. Thus, it is a model assuming implicitly the competition among predators. In this work the dynamics of a modified Leslie-Gower type predator-prey model is analyzed, considering two important aspects: (i) the predators capture an alternative food when the quantity of prey is scarce and (ii) the prey population is affected by an Allee effect. Considering a topological equivalent system, the main properties of the system are established. Necessary and sufficient conditions for the existence and local stability of equilibria are determined, also showing the existence of a homoclinic orbit and of at least a limit cycle. When the predators are generalists the dynamics of the model differ enough respecting the model considering predators specialist ...
7
artículo
Publicado 2020
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It is well known that predator-prey interactions are strongly dependent on the functional response as well as the population growth rates of prey and predators.In this work, the study will be based on a Leslie-Gower type predation model, described by a twodimensional system of ordinary differential equations (ODEs), assuming the prey population is affected by a strong Allee effect and that predators have an alternative food.The functional response will be assumed linear, which is prey-dependent and monotonously increasing. In turn, the equation of growth of predators will also be considered of the logistic type, where the environmental carrying capacity for predators is assumed proportional to the prey population size. Among the most important results obtained is that for a same set of parameters, there are different behaviors of the system solutions, since two attractor equilibrium poin...
8
artículo
Publicado 2020
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It is well known that predator-prey interactions are strongly dependent on the functional response as well as the population growth rates of prey and predators.In this work, the study will be based on a Leslie-Gower type predation model, described by a twodimensional system of ordinary differential equations (ODEs), assuming the prey population is affected by a strong Allee effect and that predators have an alternative food.The functional response will be assumed linear, which is prey-dependent and monotonously increasing. In turn, the equation of growth of predators will also be considered of the logistic type, where the environmental carrying capacity for predators is assumed proportional to the prey population size. Among the most important results obtained is that for a same set of parameters, there are different behaviors of the system solutions, since two attractor equilibrium poin...
9
artículo
Publicado 2024
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In this work, the well-possednes of a predator-prey model with reaction-diffusion will be studied where the Allee effect in prey reproduction will be included and predation dynamics will be considered a functional response dependent on the species (prey and predator) with the incorporation of the refuge in the dam. In this way, the existence, uniqueness and positivity of the system's solutions as the main result will be guaranteed.
