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\(N(t)\) and \(P(t)\) stand for the prey and predator density, respectively, at time t. Motivated by the above works, we consider the following predator-prey model : Guin in studied a prey-predator model with logistic growth in both species and using ratio-dependent functional for predators. The author assumed that the predator has logistic growth rate since it has sufficient resources for alternative foods and it is argued that alternative food sources may have an important role in promoting the persistence of predator-prey systems. Haque in proposed a prey-predator model with logistic growth in both species and a linear functional response. Several authors have studied the prey-predator model with logistics growth in both species. Our objective is to understand what is the impact of predation on the dynamics of prey and predator species, in order to avoid any extinction of the two species. It is in this line of thought that we are interested here in the study of the dynamics of prey-predator populations with an alternative food resource for predators, meaning that the predator population can survive if there is no prey. The main feature of predation is therefore a direct impact of the predator on the prey population. Without prey, there would be no predators. Without predators, some prey species would force other species to disappear due to competition. The predator-prey relationship is important to maintain the balance between different animal species. The main questions concerning population dynamics concern the effects of interaction in the regulation of natural populations, the reduction of their size, the reduction of their natural fluctuations, or the destabilization of the equilibria in oscillations of the states of the population. These different types of functional responses present a key element for understanding the dynamics of these populations. Many authors, such as Holling 1959, Getz 1984, and Arditi and Ginzburg 1989, studied the prey-predator system with various functional responses. Mathematical modeling of the population dynamics of a prey-predator system is an important objective of mathematical models in biology, which has attracted the attention of many researchers. In recent decades, mathematics has had a huge impact as a tool for modeling and understanding biological phenomena. solitary predators and prey oscillate over time.The study of the dynamics relationship of the prey-predator system has long been and will continue to be one of the dominant subjects in both ecology and mathematical ecology due to its universal existence and importance. In this situation, the proportions of grouped vs. Therefore, if there is no population of prey or no population of predators, no decrease in the population of prey (also known as predation) can occur. Under some conditions, continuous cycling of the relative frequencies of the different strategies may occur. predators kill prey is proportional to the product of the number of prey and the number of predators, or in other terms, how often the two populations meet. The model predictions are in accordance with empirical evidence that an open habitat encourages group living, and that low risks of predation favor lone prey. machine-learning ai q-learning lstm lstm-neural-networks predator-prey. The agents are controlled by an LSTM which learns with Q-learning. The agents learn to avoid the player from experience in real time. The analysis of the model shows that the intersections of four curves define distinct areas in the parameter space, corresponding to different strategies used by predators and prey at equilibrium. This game lets the player control a predator, whose objective is to devour prey agents.
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Focusing on the "many eyes-many mouths" trade-off, this model considers the benefits and costs of being in a group for hunting predators and foraging prey: predators in a group have more hunting success than solitary predators but they have to share the prey captured prey in a group face a lower risk of predation but greater competition for resources than lone prey. As predators respond strategically to prey behavior and vice versa, the model is based on a co-evolution approach. We present a model of predator and prey grouping strategies using game theory.