A discrete evolutionary Beverton–Holt population model

Ch-Chaoui, Mohamed; Mokni, Karima

doi:10.1007/s40435-022-01035-y

Cited by 8 publications

(2 citation statements)

References 36 publications

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“…The following Lemma is required to analyze stability and bifurcation using the eigenvalues analysis method [5] (see also [32][33][34]). Now, the eigenvalues of the boundary fixed point A(K, 0) are γ 1 = exp(−rδ) and γ 2 = 1.…”

Section: Stability Analysis Of System (4)-(5)mentioning

confidence: 99%

Complex dynamics and chaos control in a nonlinear discrete prey–predator model

Mokni¹,

Ali²,

Ch-Chaoui³

2023

Math. Model. Comput.

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The dynamics of prey–predator interactions are often modeled using differential or difference equations. In this paper, we investigate the dynamical behavior of a two-dimensional discrete prey–predator system. The model is formulated in terms of difference equations and derived by using a nonstandard finite difference scheme (NSFD), which takes into consideration the non-overlapping generations. The existence of fixed points as well as their local asymptotic stability are proved. Further, it is shown that the model experiences Neimark–Sacker bifurcation (NSB for short) and period-doubling bifurcation (PDB) in a small neighborhood of the unique positive fixed point under certain parametric conditions. This analysis utilizes bifurcation theory and the center manifold theorem. The chaos produced by NSB and PDB is stabilized. Finally, we use numerical simulations and computer analysis to check our theories and show more complex behaviors.

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Section: Stability Analysis Of System (4)-(5)mentioning

confidence: 99%

Complex dynamics and chaos control in a nonlinear discrete prey–predator model

Mokni¹,

Ali²,

Ch-Chaoui³

2023

Math. Model. Comput.

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“…Finally, in [14], M. Ch-Chaoui and K. Mokni presented a derivation of a discrete-time evolutionary Beverton-Holt model. The authors discussed the existence of the positive fixed point and explored its asymptotic stability.…”

Section: Introductionmentioning

confidence: 99%

Open Problems and Conjectures in the Evolutionary Periodic Ricker Competition Model

Luís

2024

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In this paper, we present a survey about the latest results in global stability concerning the discrete-time evolutionary Ricker competition model with n species, in both, autonomous and periodic models. The main purpose is to convey some arguments and new ideas concerning the techniques for showing global asymptotic stability of fixed points or periodic cycles in these kind of discrete-time models. In order to achieve this, some open problems and conjectures related to the evolutionary Ricker competition model are presented, which may be a starting point to study global stability, not only in other competition models, but in predator–prey models and Leslie–Gower-type models as well.

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