To write differential equations with respect to discontinuous noises like Z one needs. The one nonzero critical point is stable. The model is a nonlinear system of two equations, where one species grows exponentially and the other decays exponentially in the absence of the other. The following system of ordinary differential equations represents the famous Volterra prey–predator model. They characterize a Levy type of stochastic differential equation 19. It has also been applied to many other fields, including economics. Based on linear per capita growth rates, the Volterra system is the simplest model of predator–prey interactions. With the help of the Floquet theory of impulsive differential equations, local stability and global attractivity of the boundary periodic solution of the system are derived, and then sufficient conditions for global asymptotic stability of the boundary periodic. Volterra established a model in 1931 to represent the connection between predators and their preys in an ecological system by developing a system of two autonomous ordinary differential equations. A predator-prey model with Holling II functional response incorporating a prey refuge with impulse effect is considered in this paper. Due to its universal existence and importance, a large number of investigations have already examined the predator–prey models (see, for examples). When populations have non-overlapping generations, the discrete-time models are more reasonable than the continuous-time models. The differential and difference equations are used to explain the majority of dynamic population models. half-saturation prey density for predation lambda 1 predator death rate. Many ecologists, mathematicians, and biologists have studied this during the last few decades. In this research article, a two prey-one predator system with intra specific competition and self-interaction is investigated and its dynamics are. Step 2: Rewrite the differential equation and multiply both sides by: dP dt 0.2311P(1, 072, 764 P 1, 072, 764) dP 0.2311P(1, 072, 764 P 1, 072, 764)dt dP P(1, 072, 764 P) 0.2311 1, 072, 764dt. of a 2-dimensional differential equation model (for example, as in Fig. The predator–prey interaction among the population is well known to be one of the most difficult inquiry areas for the biology and ecology population.
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