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

Abstract

This paper is devoted to a type of combined impulsive discrete Beverton–Holt equations in ecology when eventual discontinuities at sampling time instants are considered. Such discontinuities could be interpreted as impulses in the corresponding continuous-time logistic equations. The set of equations involve competition-type coupled dynamics among a finite set of species. It is assumed that, in general, the intrinsic growth rates and the carrying capacities are eventually distinct for the various species. The impulsive parts of the equations are parameterized by harvesting quotas and independent consumptions which are also eventually distinct for the various species and which control the populations’ evolution. The performed study includes the existence of extinction and non-extinction equilibrium points, the conditions of non-negativity and boundedness of the solutions for given finite non-negative initial conditions and the conditions of asymptotic stability without or with extinction of the solutions.

On an Extended Time-Varying Beverton–Holt Equation Subject to Harvesting Monitoring and Population Excess Penalty

“…It is discussed in [7] how, in practice, the intrinsic growth rate can be dependent on the environment carrying capacity. Also, it is discussed in [8] an impulsive extended competition Beverton-Holt model between species from the stability point of view. Te usefulness of the Beverton-Holt and other mathematical models in maritime biology is described in [9].…”

“…Normally, harvesting refers to fshing or hunting which is subjected to authorities regulation but it can also be total or partially illegal while associated to furtive uncontrolled actions. See also some references therein and [6,8]. Other related studies consider alternative generalizations concerned with periodic behaviors, associated, for instance, to seasonality [14,15], global dynamics analysis of some extended equation versions [16], presence of bifurcations [17,18] or resonances [19], and perturbations of the basic model.…”

On a Coupled Time-Varying Beverton–Holt Model with Two Habitats Subject to Harvesting, Repopulation, and Mixed Migratory Flows of Populations

“…It can be pointed out that the intrinsic growth rate and the environment carrying capacity can be related to each other, in real situations, as discussed in [7]. On the other hand, it has also been proposed an impulsive extended competition Beverton-Holt model among species from the stability point of view [8]. Beverton-Holt models as well as other mathematical related models like, for instance, Ricker's-type models are often used in Maritime Biology for population evolution studies and population management.…”

“…See, for instance [9]. In [6][7][8][10][11][12][13], harvesting actions have been investigated in the framework of extended Beverton-Holt models. Typically, harvesting is related to legal regulated fshing or hunting but illegal poaching might also be included [6,8].…”

“…In [6][7][8][10][11][12][13], harvesting actions have been investigated in the framework of extended Beverton-Holt models. Typically, harvesting is related to legal regulated fshing or hunting but illegal poaching might also be included [6,8]. Periodicity of the solutions of the Beverton-Holt equation due to seasonality has been focused on in [14,15].…”