Dynamics and optimal Harvesting strategy for biological models with Beverton –Holt growth

Abstract

In this work, the dynamic behavior of discrete models is analyzed with Beverton- Holt function growth . All equilibria are found . The existence and local stability are investigated of all its equilibria.. The optimal harvest strategy is done for the system by using Pontryagin’s maximum principle to solve the optimality problem. Finally numerical simulations are used to solve the optimality problem and to enhance the results of mathematical analysis

On the Properties of a Class of Impulsive Competition Beverton–Holt Equations

“…and x3 = 175.90, in accordance with Theorem 3, since Condition C1 of Theorem 3(ii) holds. Furthermore, these values are close to the ones calculated from(31) and given by x1 =288.46, x2 = 182.58 and x3 = 175.42, since the elements of the matrix C are sufficiently small and satisfy the conditions(27).…”

“…Note that Theorem 6 gives extinction conditions for intrinsic growth rates exceeding unity, which is an usual condition in the background literature on Beverton-Holt equations [5][6][7][8][9][10][11][12]18,[26][27][28][29]33]. In this section, the asymptotic extinction is studied for the case of intrinsic growth rates being less than unity.…”

“…The subsequent impulsive discrete Beverton-Holt equation for a single species, [26,27,33] extends the standard one, which has been described in the introduction:…”

“…It has to be clarified that, since input impulses in continuous-time dynamic systems translate into bounded discontinuities in the state (see, for instance, [23][24][25]), it is usual to refer to their counterpart discretized versions (with bounded steps at sampling time instants) as impulsive discrete systems. See, for instance, [13,26,27]. The Beverton-Holt equation has also been studied from a control point of view.…”

Dynamical Behaviours of Stage-Structured Fractional-Order Prey-Predator Model with Crowley–Martin Functional Response

“…e Crowley-Martin functional response is simpli ed to Michaelis-Menten which has involved one more term explaining mutual interferences of predators for the case where the predator feeding rate is decreased by a higher predator density even when the prey density is high [28,29]. e subject of the optimal harvesting is very important in managing the renewable resources due to the economic aspect and to keep population at level far from the extinct, so that many researchers and authors have widely investigated and studied this subject in their works, see [30][31][32][33][34] and the references therein.…”