Related papers: Predator-prey models with memory and kicks: Exact …

Accelerators with power-law memory are proposed in the framework of the discrete time approach. To describe discrete accelerators we use the capital stock adjustment principle, which has been suggested by Matthews.The suggested discrete…

Starting from kicked equations of motion with derivatives of non-integer orders, we obtain "fractional" discrete maps. These maps are generalizations of well-known universal, standard, dissipative, kicked damped rotator maps. The main…

The Lotka-Volterra predator-prey model still represents the paradigm for the description of the competition in population dynamics. Despite its extreme simplicity, it does not admit an analytical solution, and for this reason, numerical…

Derivatives of fractional order with respect to time describe long-term memory effects. Using nonlinear differential equation with Caputo fractional derivative of arbitrary order $\alpha>0$, we obtain discrete maps with power-law memory.…

We first present a predator-prey model for two species and then extend the model to three species where the two predator species engage in mutualistic predation. Constant effort harvesting and the impact of by-catch issue are also…

A generalization of the economic model of logistic growth, which takes into account the effects of memory and crises, is suggested. Memory effect means that the economic factors and parameters at any given time depend not only on their…

The study of systems with memory requires methods which are different from the methods used in regular dynamics. Systems with power-law memory in many cases can be described by fractional differential equations, which are…

We consider a modified Lotka-Volterra model applied to the predator-prey system that can also be applied to other areas, for instance the bank system. We show that the model is well-posed (non-negativity of solutions and conservation law)…

The forces which drive growth, development, survival and change within an ecological system involving a predator and prey specie are not easily addressed in the field. To better understand the dynamics in the system, ecologists have turned…

In this article, we proposed new discrete maps with memory (DMM). These maps are derived from fractional differential equations (FDE) with the Hilfer fractional derivatives of non-integer orders and periodic sequence of kicks. The suggested…

Attention mechanisms are widely used in artificial intelligence to enhance performance and interpretability. In this paper, we investigate their utility in modeling classical dynamical systems -- specifically, a noisy predator-prey…

Discrete maps with long-term memory are obtained from nonlinear differential equations with Riemann-Liouville and Caputo fractional derivatives. These maps are generalizations of the well-known universal map. The memory means that their…

This paper presents a study of the two-predators-two-preys discrete-time Lotka-Volterra model with self- inhibition terms for preys with direct applications to ecological problems. Parameters in the model are modified so that each of them…

The classical Lotka-Volterra predator-prey system is often used in species competition modeling. An exact, closed-form solution is derived when the natural growth rate of the prey species and decay rate of the predators are equal in…

Nonlinear mathematical models introduce the relation between various physical and biological interactions present in nature. One of the most famous models is the Lotka-Volterra model which defined the interaction between predator and prey…

Intersectoral dynamic models with power-law memory are proposed. The equations of open and closed intersectoral models, in which the memory effects are described by the Caputo derivatives of non-integer orders, are derived. We suggest…

Many physical, biological, and engineered systems exhibit memory effects that challenge Markovian models. Fractional calculus provides nonlocal operators to capture hereditary dynamics. This survey connects modeling, analysis, and…

In this paper, we consider the inverse problem of determining the coefficients of interaction terms within some Lotka-Volterra models, with support from boundary observation of its non-negative solutions. In the physical background, the…

This study uses the Lotka Volterra Predator-Prey model to offer a notion of piecewise patterns for the various piecewise derivatives. Using the piecewise derivatives, we produced numerical solutions that are referred to as the…

We consider a broad class of stochastic lattice predator-prey models, whose main features are overviewed. In particular, this article aims at drawing a picture of the influence of spatial fluctuations, which are not accounted for by the…