Abstract
We define and study a tritrophic bioeconomic model of Lotka-Volterra with a prey, middle predator, and top predator populations. These fish populations are exploited by two fishermen. We study the existence and the stability of the equilibrium points by using eigenvalues analysis and Routh-Hurwitz criterion. We determine the equilibrium point that maximizes the profit of each fisherman by solving the Nash equilibrium problem. Finally, following some numerical simulations, we observe that if the price varies, then the profit behavior of each fisherman will be changed; also, we conclude that the price change mechanism improves the fishing effort of the fishermen.
Highlights
The problem of modelization is, perhaps, the most challenging in modern ecology, biology, chemistry, and many other sciences
In [2], the authors have formulated and studied a stage-structured predator-prey model of BeddingtonDeAngelis type functional response to investigate the impact of predation over the immature prey by the juvenile predator
We note that Hij = qjEijXj represent the catches of species j by the fisherman i (X1 = x, X2 = y, and X3 = z), and Eij is the effort of the fisherman i to exploit the species j
Summary
The problem of modelization is, perhaps, the most challenging in modern ecology, biology, chemistry, and many other sciences. The first basic classic prey-predator model is renowned by Lotka-Volterra model and mathematical formulation of this model is directly related to the great work of Lotka (in 1925) and Volterra (in 1926). Thanks to this prey-predator model, other models have been proposed and studied [1,2,3]. In [2], the authors have formulated and studied a stage-structured predator-prey model of BeddingtonDeAngelis type functional response to investigate the impact of predation over the immature prey by the juvenile predator.
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