Effect of Nonlocal Delay With Strong Kernel on Vegetation Pattern

Liang, Juan; ,; Sun, Guiquan; ,; ,; ,

doi:10.11948/20230290

jaac

2024

DOI: 10.11948/20230290

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Effect of Nonlocal Delay With Strong Kernel on Vegetation Pattern

Juan Liang,

Guiquan Sun

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2024

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Cited by 3 publications

References 68 publications

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Bifurcations analysis and pattern formation in a plant-water model with nonlocal grazing

Wang,

Yin,

Yuan

2024

Nonlinear Dyn

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Bifurcations analysis and pattern formation in a plant-water model with nonlocal grazing

Wang,

Yin,

Yuan

2024

Nonlinear Dyn

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Dynamic patterns in herding predator–prey system: Analyzing the impact of inertial delays and harvesting

Bhattacharya,

Ghorai,

Bairagi

2024

Chaos: An Interdisciplinary Journal of Nonlinear Science

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

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Bifurcation analysis of a Leslie-type predator–prey system with prey harvesting and group defense

Zhang,

Luo

2024

Front. Phys.

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

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Effect of Nonlocal Delay With Strong Kernel on Vegetation Pattern

Cited by 3 publications

References 68 publications

Bifurcations analysis and pattern formation in a plant-water model with nonlocal grazing

Bifurcations analysis and pattern formation in a plant-water model with nonlocal grazing

Dynamic patterns in herding predator–prey system: Analyzing the impact of inertial delays and harvesting

Bifurcation analysis of a Leslie-type predator–prey system with prey harvesting and group defense

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