Related papers: Enrichment paradox and applications
The paradox of enrichment was observed by M. Rosenzweig in a class of predator-prey models. Two of the parameters in the models are crucial for the paradox. These two parameters are the prey's carrying capacity and prey's half-saturation…
We consider a modified Rosenzweig-MacArthur predator-prey model, based on the premise that the search rate of predators is dependent on the prey density, rather than constant. A complete analysis of the global behavior of the model is…
In the last years, predator-prey systems have increased their applications and have given rise to systems which represent more accurately different biological issues that appear in the context of interacting species. Our aim in this paper…
We consider a three-level food chain in which an epidemics affects the intermediate population. Two models are presented, respectively either allowing for unlimited food supply for the bottom prey, or instead assuming for it a logistic…
The broad application range of the predator-prey modelling enabled us to apply it to represent the dynamics of the work-employment system. For the adopted period, we conclude that this dynamics is chaotic in the beginning of the time series…
This article adopts game theory to build a model for explaining the predation behavior of animals.We assume that both the prey and the preydator have two stratigies in this game,the active one and the passive one.By calculating the outcome…
Consider the coupling of $2$ evolution equations, each generating a global process. We prove that the resulting system generates a new global process. This statement can be applied to differential equations of various kinds. In particular,…
A generalized seasonally-varying predator-prey model with Allee effect in the prey growth is investigated. The analysis is performed only on the basis of some properties determining the shape of the prey growth rate and the trophic…
Dormancy is a costly adaptive strategy that is widespread among living organisms inhabiting diverse environments. We explore mathematical models of predator-prey systems, in order to assess the impact of prey dormancy on the competition…
The field of AI alignment aims to steer AI systems toward human goals, preferences, and ethical principles. Its contributions have been instrumental for improving the output quality, safety, and trustworthiness of today's AI models. This…
The dynamics of a prey-predator system with foraging facilitation among predators are investigated. The analysis involves the computation of many semi-algebraic systems of large degrees. We apply the pseudo-division reduction, real-root…
We address the question of an averaging principle for a general class of multi-scale hybrid predator-prey models. We consider prey-predator models where the kinetic of the prey population, described by a differential equation, is faster…
A general framework for age-structured predator-prey systems is introduced. Individuals are distinguished into two classes, juveniles and adults, and several possible interactions are considered. The initial system of partial differential…
We present a dynamical model for the price evolution of financial assets. The model is based in a two level structure. In the first stage one finds an agent-based model that describes the present state of the investors' beliefs,…
We construct a global bifurcation diagram of the plane differential system $$ {l} \dot x = x(1-x)-x y/(a+x^2), \dot y = y(\delta-\beta y/x), x(t)>0, y(t)>0, a>0, \delta>0, \beta>0, $$ which describes the predator-prey interaction.
The goal of this paper is to explain how to derive the classical Rosenzweig-MacArthur's model by using a model with two groups of predators in which we can separate the vital dynamic and consumption of prey to describe the behavior of the…
We propose a novel definition of model exploitation in reinforcement learning. Informally, a world model is exploitable if it implies that one policy should be strictly preferred over another while the environment's true transition model…
In this paper, we consider a stochastic ratio-dependent predator-prey model. We firstly prove the existence, uniqueness and positivity of the solutions. Then, the boundedness of moments of population are studied. Finally, we show the…
We develop a mathematical model of extinction and coexistence in a generic predator-prey ecosystem composed of two herbivores in asymmetrical competition and a hunter exerting a predatory pressure on both species. With the aim of…
Theory purports that animal foraging choices evolve to maximize returns, such as net energy intake. Empirical research in both human and nonhuman animals reveals that individuals often attend to the foraging choices of their competitors…