Dynamic analysis of a predator-prey system with nonlinear prey harvesting and square root functional response

Mortuja, Golam; Chaube, Mithilesh Kumar; Kumar, Santosh

doi:10.1016/j.chaos.2021.111071

Cited by 31 publications

(14 citation statements)

References 29 publications

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“…There have been a variety of harvesting tactics used. Some of them used fixed harvesting, fixed effort harvesting (or proportional harvesting), and continuous threshold harvesting, while others examined nonlinear harvesting [22][23][24][25] .…”

Section: Introductionmentioning

confidence: 99%

Modeling and Analyzing the Influence of Fear on the Harvested Modified Leslie-Gower Model

Jamil

Naji²

2023

Baghdad Sci.J

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A modified Leslie-Gower predator-prey model with a Beddington-DeAngelis functional response is proposed and studied. The purpose is to examine the effects of fear and quadratic fixed effort harvesting on the system's dynamic behavior. The model's qualitative properties, such as local equilibria stability, permanence, and global stability, are examined. The analysis of local bifurcation has been studied. It is discovered that the system experiences a saddle-node bifurcation at the survival equilibrium point whereas a transcritical bifurcation occurs at the boundary equilibrium point. Additionally established are the prerequisites for Hopf bifurcation existence. Finally, using MATLAB, a numerical investigation is conducted to verify the validity of the theoretical analysis and visualize the model dynamics.

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Section: Introductionmentioning

confidence: 99%

Modeling and Analyzing the Influence of Fear on the Harvested Modified Leslie-Gower Model

Jamil

Naji²

2023

Baghdad Sci.J

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“…It is thereby more reasonable to take into account the element in predator-prey models, which is usually depicted by non-differentiable nonlinear functional responses (see e.g. [Ajraldi et al, 2011;Braza, 2012;Pal et al, 2016;Venturino & Petrovskii, 2013;Vilches et al, 2018;Xu et al, 2016]). For instance, Rosenzweig [1971] proposed functional response ax α with α ∈ (0, 1) called Rosenzweig functional response to model the prey herd behavior, where exponent α stands for a kind of aggregation efficiency.…”

Section: Introductionmentioning

confidence: 99%

“…For the more specific situation that the prey of some species does exhibit the herd behavior when they simultaneously encounter human intervention and predation, some predator-prey models were established to simulate this situation (see e.g. [Hacini et al, 2021;Kumar & Kharbanda, 2019;Luo & Zhao, 2017;Mortuja et al, 2021]). For example, Luo and Zhao in [Luo & Zhao, 2017] considered a predator-prey model with prey herd behavior and harvesting under two cases, i.e., prey harvesting only and predator harvesting only.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a Leslie-Gower predator-prey system with hunting cooperation and prey harvesting

Yao

Liu

2022

DCDS-B

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<p style='text-indent:20px;'>In this paper, we study the dynamics of a Leslie-Gower predator-prey system with hunting cooperation among predator population and constant-rate harvesting for prey population. It is shown that there are a weak focus of multiplicity up to three and a cusp of codimension at most two for various parameter values, and the system exhibits two saddle-node bifurcations, a Bogdanov-Takens bifurcation of codimension two and a Hopf bifurcation as the bifurcation parameters vary. The results developed in this article reveal far more complex dynamics compared to the Leslie-Gower system and show how the prey harvesting and the hunting cooperation affect the dynamics of the system. In particular, there exist some critical values of prey harvesting and hunting cooperation such that the predator and prey populations are at risk of extinction if the intensities of harvesting and hunting cooperation are greater than these critical values. Moreover, numerical simulations are presented to illustrate our theoretical results.</p>

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“…In fact, with the development of the economy, humans will harvest biological populations and develop related biological resources to obtain economic benefits, such as fisheries, forestry, and wildlife management (see [9][10][11]). In recent years, many scholars have introduced the harvesting terms into biological systems to study the system modeling and related dynamic characteristics [12][13][14][15]. May et al [16] established the following model to analyse the interaction between populations under different harvesting strategies:…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal Evolution Characteristics of Time‐Delay Ecological Competition Systems with Food‐Limited and Diffusion

et al. 2022

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In this paper, we put forward a time-delay ecological competition system with food restriction and diffusion terms under Neumann boundary conditions. For the case without delay, the conditions for local asymptotic stability and Turing instability are constructed. For the case with delay, the existence of Hopf bifurcation is demonstrated by analyzing the root distribution of the corresponding characteristic equations. Furthermore, by using the normal form theory and the center manifold reduction of partial functional differential equations, explicit formulas are obtained to determine the direction of bifurcations and the stability of bifurcating periodic solutions. Finally, some simulation examples are provided to substantiate our analysis.

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Dynamic analysis of a predator-prey system with nonlinear prey harvesting and square root functional response

Cited by 31 publications

References 29 publications

Modeling and Analyzing the Influence of Fear on the Harvested Modified Leslie-Gower Model

Modeling and Analyzing the Influence of Fear on the Harvested Modified Leslie-Gower Model

Dynamics of a Leslie-Gower predator-prey system with hunting cooperation and prey harvesting

Spatiotemporal Evolution Characteristics of Time‐Delay Ecological Competition Systems with Food‐Limited and Diffusion

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