Abstract
Experiments on the living environment of vertebrate ecosystems, it has been shown that predators have a massive influence on the demographic growth rate of prey. The proposed fear effect is a mathematical model that affects the reproductive growth rate of prey with the Holling Type I interaction model. Mathematical analysis of the prey-predator model shows that a strong anti-predator response can provide stability for prey-predator interactions. The parameter area taken will be shown for the extinction of the prey population, the balance of population survival, and the balance between the prey birth rate and the predator death rate. Numerical simulations were given to investigate the biological parameters of the population (birth rate, natural mortality of prey, and predators). Another numerical illustration that is seen is the behavior of prey which is less sensitive in considering the risk of predators with the growth rate of prey.
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