The effect of maps permutation on the global attractor of a periodic Beverton–Holt model

Al-Ghassani, Asma; AlSharawi, Ziyad

doi:10.1016/j.amc.2019.124905

Cited by 2 publications

(1 citation statement)

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“…The study of periodic solutions has been also studied in the non-impulsive and in the impulsive Beverton-Holt equation since some of its parameterizing parameters, such as, for instance, the carrying capacity or the harvesting quota, are often subject to cyclic variations. See, for instance, [26,32,33] and some of the references therein. The dynamics associated with strong and weak Allee effects are studied in [34]; these lead, respectively, to extinction, for population stocks under a critical density, and to recovery, after small density levels are reached without the presence of a critical value.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2021

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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.

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Section: Introductionmentioning

confidence: 99%

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

et al. 2021

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The Beverton–Hold model on isolated time scales

Böhner

Mesquita

Streipert

2022

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<abstract><p>In this work, we formulate the Beverton–Holt model on isolated time scales and extend existing results known in the discrete and quantum calculus cases. Applying a recently introduced definition of periodicity for arbitrary isolated time scales, we discuss the effects of periodicity onto a population modeled by a dynamic version of the Beverton–Holt equation. The first main theorem provides conditions for the existence of a unique $ \omega $ -periodic solution that is globally asymptotically stable, which addresses the first Cushing–Henson conjecture on isolated time scales. The second main theorem concerns the generalization of the second Cushing–Henson conjecture. It investigates the effects of periodicity by deriving an upper bound for the average of the unique periodic solution. The obtained upper bound reveals a dependence on the underlying time structure, not apparent in the classical case. This work also extends existing results for the Beverton–Holt model in the discrete and quantum cases, and it complements existing conclusions on periodic time scales. This work can furthermore guide other applications of the recently introduced periodicity on isolated time scales.</p></abstract>

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The effect of maps permutation on the global attractor of a periodic Beverton–Holt model

Cited by 2 publications

References 25 publications

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

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

The Beverton–Hold model on isolated time scales

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