Dynamic patterns in herding predator–prey system: Analyzing the impact of inertial delays and harvesting DOI
Santanu Bhattacharya, Santu Ghorai, Nandadulal Bairagi

et al.

Chaos An Interdisciplinary Journal of Nonlinear Science, Journal Year: 2024, Volume and Issue: 34(12)

Published: Dec. 1, 2024

This study expands traditional reaction–diffusion models by incorporating hyperbolic dynamics to explore the effects of inertial delays on pattern formation. The kinetic system considers a harvested predator–prey model where predator and prey populations gather in herds. Diffusion are subsequently introduced. Theoretical frameworks establish conditions for stability, revealing that delay notably alters diffusion-induced instabilities Hopf bifurcations. inclusion narrows stability region wave instability, which cannot arise two-variable spatiotemporal without inertia. Computational simulations demonstrate Turing lead diverse spatial patterns. highlights initial influence generating distinct patterns based different values, while other remain unaffected. Additionally, patterns, such as hot spots, cold stripes, observed within region. impact harvesting is also examined, showing increased efforts can shift systems between unstable uniform states. findings provide practical implications ecological modeling, offering insights into how practices affect formation natural populations.

Language: Английский

Stationary and Oscillatory patterned solutions in three-compartment reaction–diffusion systems: Theory and application to dryland ecology DOI Creative Commons
Giancarlo Consolo, Carmela Curró, Gabriele Grifó

et al.

Chaos Solitons & Fractals, Journal Year: 2024, Volume and Issue: 186, P. 115287 - 115287

Published: July 23, 2024

This work aims at elucidating the conditions under which stationary and oscillatory periodic patterns may emerge in a class of one-dimensional three-compartments reaction–diffusion models where one interacting species does not undergo any spatial dispersal. To this purpose, linear stability analysis is firstly employed to deduce system undergoes Turing or wave instability as well extract information on main features that characterize corresponding patterned solutions onset. Then, multiple-scale weakly nonlinear carried out describe time evolution pattern amplitude close bifurcation thresholds above-mentioned instabilities. Finally, provide quantitative estimation most relevant features, an illustrative example context dryland ecology addressed. It deals with generalization Klausmeier vegetation model for flat arid environments describes interaction among biomass, soil water toxic compounds. Numerical simulations are also used corroborate theoretical findings gain some useful insights into ecological response ecosystems variable environmental conditions.

Language: Английский

Citations

5
Sustainable management of predatory fish affected by an Allee effect through marine protected areas and taxation DOI

Xiaoyue Yuan,

Wenjun Liu, Guangying Lv

et al.

Mathematical Biosciences, Journal Year: 2024, Volume and Issue: 373, P. 109220 - 109220

Published: May 24, 2024

Language: Английский

Citations

2
Evolution of Turing patterns of a predator–prey system with variable carrying capacity and harvesting DOI
Lakpa Thendup Bhutia, Samir Biswas, Esita Das

et al.

Chaos Solitons & Fractals, Journal Year: 2024, Volume and Issue: 191, P. 115790 - 115790

Published: Dec. 5, 2024

Language: Английский

Citations

1
Bifurcation analysis of a Leslie-type predator–prey system with prey harvesting and group defense DOI Creative Commons
Yongxin Zhang, Jianfeng Luo

Frontiers in Physics, Journal Year: 2024, Volume and Issue: 12

Published: June 19, 2024

In this paper, we investigate a Leslie-type predator–prey model that incorporates prey harvesting and group defense, leading to modified functional response. Our analysis focuses on the existence stability of system’s equilibria, which are essential for coexistence predator populations maintenance ecological balance. We identify maximum sustainable yield, critical factor achieving Through thorough examination positive equilibrium stability, determine conditions initial values promote survival both species. delve into dynamics by analyzing saddle-node Hopf bifurcations, crucial understanding system transitions between various states. To evaluate bifurcation, calculate first Lyapunov exponent offer quantitative assessment stability. Furthermore, explore Bogdanov–Takens (BT) co-dimension 2 scenario, employing universal unfolding technique near cusp point. This method simplifies complex reveals trigger such bifurcations. substantiate our theoretical findings, conduct numerical simulations, serve as practical validation predictions. These simulations not only confirm results but also showcase potential predicting real-world scenarios. in-depth contributes nuanced within interactions advances field modeling.

Language: Английский

Citations

1
Effective detection of early warning signal with power spectrum in climate change system DOI
Zheng Chen, Peiyi Fan,

Xintong Hou

et al.

Chaos Solitons & Fractals, Journal Year: 2024, Volume and Issue: 187, P. 115409 - 115409

Published: Aug. 22, 2024

Language: Английский

Citations

1
Bifurcations analysis and pattern formation in a plant-water model with nonlocal grazing DOI
Yong Wang, Jia‐Xin Yin, Rui Yuan

et al.

Nonlinear Dynamics, Journal Year: 2024, Volume and Issue: unknown

Published: Oct. 17, 2024

Language: Английский

Citations

1
Spatiotemporal fluctuation induces Turing pattern formation in the chemical Brusselator DOI Open Access
Quan Yuan, Sizhe Wang,

Ting Lai

et al.

Mathematical Methods in the Applied Sciences, Journal Year: 2024, Volume and Issue: unknown

Published: Oct. 8, 2024

Chemical reactions are embedded in spatiotemporal fluctuations instead of a constant environment. Here, we aimed to assess reaction–diffusion (RD) with dichotomous noise‐controlling system parameters the Brusselator and examine effect these on dynamic behavior chemical reactions. By performing multiscale perturbation analysis, demonstrated that correlated noise can broaden Turing region even if molecular memory (autocorrelation time) exists. However, for small noise, short‐term promotes instability. The instability is determined by strength, which belongs optimal diffusion coefficient fixed. pattern selection stability also governed character amplitude equation, entire shifts right phase space perturbation. Finally, numerical simulations validate theoretical derivation amplify formation maintain distinct patterns.

Language: Английский

Citations

0
Dynamic patterns in herding predator–prey system: Analyzing the impact of inertial delays and harvesting DOI
Santanu Bhattacharya, Santu Ghorai, Nandadulal Bairagi

et al.

Chaos An Interdisciplinary Journal of Nonlinear Science, Journal Year: 2024, Volume and Issue: 34(12)

Published: Dec. 1, 2024

This study expands traditional reaction–diffusion models by incorporating hyperbolic dynamics to explore the effects of inertial delays on pattern formation. The kinetic system considers a harvested predator–prey model where predator and prey populations gather in herds. Diffusion are subsequently introduced. Theoretical frameworks establish conditions for stability, revealing that delay notably alters diffusion-induced instabilities Hopf bifurcations. inclusion narrows stability region wave instability, which cannot arise two-variable spatiotemporal without inertia. Computational simulations demonstrate Turing lead diverse spatial patterns. highlights initial influence generating distinct patterns based different values, while other remain unaffected. Additionally, patterns, such as hot spots, cold stripes, observed within region. impact harvesting is also examined, showing increased efforts can shift systems between unstable uniform states. findings provide practical implications ecological modeling, offering insights into how practices affect formation natural populations.

Language: Английский

Citations

0