Spatiotemporal Dynamics of a Reaction Diffusive Predator-Prey Model: A Weak Nonlinear Analysis

International Journal of Differential Equations, Journal Year: 2023, Volume and Issue: 2023, P. 1 - 23

Published: Oct. 10, 2023

In the realm of ecology, species naturally strive to enhance their own survival odds. This study introduces and investigates a predator-prey model incorporating reaction-diffusion through system differential equations. We scrutinize how diffusion impacts model’s stability. By analysing stability uniform equilibrium state, we identify condition leading Turing instability. The delves into influences pattern formation within system. Our findings reveal that various spatiotemporal patterns, such as patches, spots, even chaos, emerge based on rates. derive amplitude equation by employing weak nonlinear multiple scales analysis technique Taylor series expansion. A novel sinc interpolation approach is introduced. Numerical simulations elucidate interplay between parameters. two-dimensional domain, spatial illustrates population density dynamics resulting in isolated groups, stripes, or labyrinthine patterns. Simulation results underscore method’s effectiveness. article concludes discussing biological implications these outcomes.

Language: Английский

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Stability and bifurcation analysis of predator-prey model with Allee effect using conformable derivatives

Journal of Mathematics and Computer Science, Journal Year: 2024, Volume and Issue: 36(03), P. 299 - 316

Published: Aug. 7, 2024

Some organisms coexist on the expense of others.This coexistence is called predation which has been successfully investigated using differential equations.In this work, we aim to analyse a fractional order predator-prey dynamical system with Allee effect bifurcation theory.The density-dependent phenomenon where population growth and individual fitness increase as density increases.Several mechanisms, such cooperative feeding, mate limitation, predator satiation, can cause effects.The piecewise-constant approximation method conformable derivatives are utilized discretise propose model.We explore equilibrium points, local stability, Neimark-Sacker bifurcation, periodic-doubling chaos control, numerical simulations proposed model.The linear theory stability used examine attractivity fixed points.Our findings include that point locally stable, source, unstable under certain constraints.We also prove considered discrete model goes through bifurcations according specific conditions.The techniques be applied for other nonlinear systems.

Language: Английский

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Generalized Lerch polynomials: application in fractional model of CAR-T cells for T-cell leukemia

The European Physical Journal Plus, Journal Year: 2023, Volume and Issue: 138(12)

Published: Dec. 26, 2023

Language: Английский

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The impact of vaccination strategy on the spatiotemporal pattern dynamics of a COVID-19 epidemic model

The European Physical Journal Plus, Journal Year: 2024, Volume and Issue: 139(2)

Published: Feb. 19, 2024

Language: Английский

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Bifurcation Analysis and Chaos Control of a Discrete Fractional-Order Modified Leslie–Gower Model with Nonlinear Harvesting Effects

Fractal and Fractional, Journal Year: 2024, Volume and Issue: 8(12), P. 744 - 744

Published: Dec. 16, 2024

This paper investigates the dynamical behavior of a discrete fractional-order modified Leslie–Gower model with Michaelis–Menten-type harvesting mechanism and Holling-II functional response. We analyze existence stability nonnegative equilibrium points. For interior points, we study conditions for period-doubling Neimark–Sacker bifurcations using center manifold theorem bifurcation theory. To control chaos arising from these bifurcations, two strategies are proposed. Numerical simulations performed to validate theoretical results. The findings provide valuable insights into sustainable management conservation ecological systems.

Language: Английский

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Modeling Study of the Effects of Ageratum conyzoides on the Transmission and Control of Citrus Huanglongbing

Plants, Journal Year: 2023, Volume and Issue: 12(20), P. 3659 - 3659

Published: Oct. 23, 2023

Ageratum conyzoides (A. conyzoides) is commonly found or intentionally planted in citrus orchards due to its ability provide habitat and breeding grounds for the natural enemies of pests. This study aims expand from a switching Huanglongbing model by incorporating effects A. conyzoides, vector preferences settling, pesticide application intervals on disease transmission. Additionally, we establish basic reproduction number R0 calculation general compartmental epidemic model. Theoretical findings demonstrate that serves as threshold parameter characterize dynamics models: if R0<1, will disappear, whereas R0>1, it spread. Numerical results indicate recruitment rate not only affects spread speed but also leads paradoxical effects. Specifically, cases high infection rates, low can result decrease, rather than an increase, number. Conversely, accelerate Huanglongbing. Furthermore, show how different bias spraying periods affect

Language: Английский

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Laplace transform method for logistic growth in a population and predator models with fractional order

Open Journal of Mathematical Sciences, Journal Year: 2023, Volume and Issue: 7(1), P. 339 - 345

Published: Dec. 27, 2023

In this paper, we develop a new application of the Laplace transform method (LTM) using series expansion dependent variable for solving fractional logistic growth models in population as well prey-predator models. The derivatives are described Caputo sense. To illustrate reliability some examples provided. results reveal that technique introduced here is very effective and convenient fractional-order nonlinear differential equations.

Language: Английский

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