Mathematical Model of the Dynamics of three Different Species in Predator-Prey System (original) (raw)

In studying the interrelationships of organisms and their environment, there is need to investigate science of coexistence of two or more species. To this end, it is natural to seek a mathematical formulation of this prey-predator problem and to use it to forecast the behavior of populations of various species at different times (Vahidin, et al., 2017; Ma et al., 2017). Nonlinear differential equations are utilized in the study of Lotka-Volterra prey-predator relationships (Canale, 1970). Mathematical models of the interaction between predator and prey populations are generally expressed as systems of nonlinear ordinary differential equations (Bai and Zhang, 2022; Canale, 1970; Xu and Wu, 2013). In animal ecosystems, interspecies interaction is inevitable (Ashine and Gebru, 2017). Interactions between various species occur on a regular basis when they live in comparable habitats. By offering havens, the natural world can offer a certain level of defense to prey populations (Ashine and Gebru, 2017). Such refugia can help in prolonging prey-predator interactions by reducing the chance of extinction due to predation (Ashine and Gebru, 2017). Italian mathematician Vito Volterra developed a differential equation model in the 1920s to explain the population dynamics of a predator and its prey (Vahidin et al., 2017; Xia and Cao, 2006). Predators can sustain a higher population if there is a huge number of prey. But when the number of predators becomes too much, the prey starts to disappear, which likewise causes the number of predators to decline (Vahidin et al., 2017). Vahidin et al. (2017) studied the system of differential equations modeling the population dynamics of a predator y , a scavenger z , and a prey x to demonstrate the possible population trends when a predator, a prey and a scavenger population interact. Their study shows that, the predator and the prey can coexist in the absence of the scavenger, and the scavenger and the prey can coexist in the absence of the predator. However, the scavenger and the predator cannot coexist without the prey. Biologically, this is reasonable, because without the prey, the predator will have no