Approximation Theory in Computer and Computational Sciences

Open AccessArticle

Influence of Spatial Dispersal among Species in a Prey–Predator Model with Miniature Predator Groups

and

Symmetry 2023, 15(5), 986; https://doi.org/10.3390/sym15050986 - 26 Apr 2023

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Abstract

Dispersal among species is an important factor that can govern the prey–predator model’s dynamics and cause a variety of spatial structures on a geographical scale. These structures form when passive diffusion interacts with the reaction part of the reaction–diffusion system in such a way that even if the reaction lacks symmetry-breaking capabilities, diffusion can destabilize the symmetry and allow the system to have them. In this article, we look at how dispersal affects the prey–predator model with a Hassell–Varley-type functional response when predators do not form tight groups. By considering linear stability, the temporal stability of the model and the conditions for Hopf bifurcation at feasible equilibrium are derived. We explored spatial stability in the presence of diffusion and developed the criterion for diffusion-driven instability. Using amplitude equations, we then investigated the selection of Turing patterns around the Turing bifurcation threshold. The examination of the stability of these amplitude equations led to the discovery of numerous Turing patterns. Finally, numerical simulations were performed to validate the outcomes of the analysis. The outcomes of the theoretical study and numerical simulation were accorded. Our findings demonstrate that spatial patterns are sensitive to dispersal and predator death rates. Full article

(This article belongs to the Topic Approximation Theory in Computer and Computational Sciences)

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Open AccessArticle

On the Approximation by Bivariate Szász–Jakimovski–Leviatan-Type Operators of Unbounded Sequences of Positive Numbers

Abdullah Alotaibi

Mathematics 2023, 11(4), 1009; https://doi.org/10.3390/math11041009 - 16 Feb 2023

Viewed by 476

Abstract

In this paper, we construct the bivariate Szász–Jakimovski–Leviatan-type operators in Dunkl form using the unbounded sequences

α_{n}

β_{m}

and

ξ_{m}

of positive numbers. Then, we obtain the rate of convergence in terms of the weighted modulus of continuity of [...] Read more.

In this paper, we construct the bivariate Szász–Jakimovski–Leviatan-type operators in Dunkl form using the unbounded sequences

α_{n}

β_{m}

and

ξ_{m}

of positive numbers. Then, we obtain the rate of convergence in terms of the weighted modulus of continuity of two variables and weighted approximation theorems for our operators. Moreover, we provide the degree of convergence with the help of bivariate Lipschitz-maximal functions and obtain the direct theorem. Full article

(This article belongs to the Topic Approximation Theory in Computer and Computational Sciences)

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Algorithms algorithms	-	3.3	2008	17.6 Days	1600 CHF	Submit
Axioms axioms	1.824	2.6	2012	17.8 Days	1600 CHF	Submit
Fractal and Fractional fractalfract	3.577	2.8	2017	18.3 Days	1800 CHF	Submit
Mathematics mathematics	2.592	2.9	2013	16.8 Days	2100 CHF	Submit
Symmetry symmetry	2.940	4.3	2009	14.2 Days	2000 CHF	Submit

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