Abstract
Abstract A predator-prey model interaction under fluctuating water level with non-selective harvesting is proposed and studied in this paper. Sufficient conditions for the permanence of two populations and the extinction of predator population are provided. The non-negative equilibrium points are given, and their stability is studied by using the Jacobian matrix. By constructing a suitable Lyapunov function, sufficient conditions that ensure the global stability of the positive equilibrium are obtained. The bionomic equilibrium and the optimal harvesting policy are also presented. Numerical simulations are carried out to show the feasibility of the main results.
Highlights
Dx dt = x (a10 − a11x) − a12 xy, (1.1) ddyt = y (a20 − a22 y) + a21xy, where x and y denote the density of the prey population and predator population, respectively, and aij (i, j = 1, 2 ...) are all positive constants
For the predator-prey system with nonselective harvesting we studied, the existence of the bionomic equilibrium is of great significance
We study a prey-predator system interaction under fluctuating water level with nonselective harvesting
Summary
Lotka-Volterra systems are one of the most classical and important systems in the field of mathematical biology research and were initially independently proposed in the 1920s by the American biophysicist Lotka when studying a chemical reaction and the Italian mathematician Volterra when studying competition between fish. Ddyt = −βy + α min y b+xD , γ y − q2 mEy, where x(t) and y(t) denote the densities of the prey and predator, respectively, at time t and r, K, b, α, β, γ, q1, q2, m, D, E are positive constants: r means the intrinsic growth rate of prey, K means the carrying capacity for prey, b is the mean function for the predation rate of prey, β is the death rate of predator, γ means the maximum consumption rate of resource by predator, α means the conversion rate from prey that was eaten by the predator to newborn predators, D measures other causes of mortality outside of predation, q1 and q2 denote the catchability coefficients of the prey and predator species, respectively, E is the effort devoted to the harvesting of human beings, and m is the fraction of the stock available for harvesting and 0 < m < 1.
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