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




Bifurcation, Fear, Leslie-Gower model, Permanence, Quadratic fixed effort harvesting, Stability


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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Holling CS. The Functional Response of Predators to Prey Density and its Role in Mimicry and Population Regulation. Mem Entomol Soc Can. Cambridge University Press. 1965; 97(S45): 5–60.

Holling CS. The components of predation as revealed by a study of small mammal predation of the european pine sawfly. Can Entomol. 1959a; 91(5): 293–320.

Ruan S, Xiao D. Global analysis in a predator-prey system with nonmonotonic functional response. SIAM J Appl Math. 2001; 61: 1445–1472.

Panday P, Pal N, Samanta S, Chattopadhyay J. Stability and bifurcation analysis of a three-species food chain model with fear. Int J Bifurc Chaos. 2018; 28: 1850009.

Wang J, Cai Y, Fu S, Wang W. The effect of the fear factor on the dynamics of a predator-prey model incorporating the prey refuge. Chaos. 2019; 29(8): 083109.

Pal S, Pal N, Samanta S, Chattopadhyay J. Fear effect in prey and hunting cooperation among predators in a Leslie-Gower model. Math Biosci Eng. 2019; 16(5): 5146-5179.

Samaddar S, Dhar M, Bhattacharya P. Effect of fear on prey-predator dynamics: Exploring the role of prey refuge and additional food. Chaos. 2020; 30(6): 063129.

Roy J, Barman D, Alam S. Role of fear in a predator-prey system with ratio-dependent functional response in deterministic and stochastic environment. Biosystems. 2020; 197: 104176.

Liu Q, Jiang D. Influence of the fear factor on the dynamics of a stochastic predator–prey model. Appl Math Lett. February 2021; 112: 106756.

Sasmal SK, Takeuchi Y. Dynamics of a predator-prey system with fear and group defense. J Math Anal Appl. 2020; 481(1): 123471.

Meng XY, Li J. Dynamical behavior of a delayed prey-predator-scavenger system with fear effect and linear harvesting. Int J Biomath. 2021; 14(04): 2150024.

Fakhry NH, Naji RK. The Dynamics of A Square Root Prey-Predator Model with Fear. Iraqi J Sci. 2020; 61(1): 139-146.

Sarkar K, Khajanchi S. Impact of fear effect on the growth of prey in a predator-prey interaction model. Ecol Complex. 2020; 42. Article ID 100826.

Maghool FH, Naji RK. The dynamics of a tritrophic Leslie-Gower food-web system with the effect of fear. J Appl Math. 2021; 2021. Article ID 2112814; 21 pages.

Maghool FH, Naji RK. Chaos in the three-species sokol-howell food chain system with fear. Commun Math Biol Neurosci. 2022; 2022: 1-38.

Rahi SA, Kurnaz S, Naji RK. The impact of fear on a stage structure prey–predator system with anti‑predator behavior. Appl Nanosci. 2022.

Lai L, Zhu Z, Chen F. Stability and bifurcation in a predator-prey model with the additive Allee effect and the fear effect. Mathematics. 2020; 8(8): 1280. .

Kaur RP, Sharma A, Sharma AK. Impact of fear effect on plankton-fish system dynamics incorporating zooplankton refuge. Chaos Soliton Fract. 2021; 143(C): 110563.

Xie B. Impact of the fear and Allee effect on a Holling type II prey-predator model. Adv Differ Equ. 2021; 2021: 464.

Xie B, Zhang N. Influence of fear effect on a Holling type III prey-predator system with the prey refuge. AIMS Math. 2022; 7(2): 1811-1830.

Molla H, Sarwardib S, Sajid M. Predator-prey dynamics with Allee effect on predator species subject to intra-specific competition and nonlinear prey refuge. J Math Computer Sci. 2022; 25: 150–165.

Al-Momen S, Naji RK. The Dynamics of Modified Leslie-Gower Predator-Prey Model under the Influence of Nonlinear Harvesting and Fear Effect. Iraqi J Sci. 2022; 63(1): 259-282.

Xie B, Zhang Z, Zhang N. Influence of the Fear Effect on a Holling Type II Prey–Predator System with a Michaelis–Menten Type Harvesting. Int J Bifurcat Chaos. 2021; 31(14): 2150216. .

Mortuja MG, Chaube MK., Kumar S. Dynamic analysis of a predator-prey system with nonlinear prey harvesting and square root functional response. Chaos Soliton Fract. 2021; 148: 111071.

Majumdar P, Debnath S, Mondal B, Sarkar S, Ghosh U. Complex dynamics of a prey-predator interaction model with Holling type-II functional response incorporating the effect of fear on prey and non-linear predator harvesting. Rend Circ Mat Palermo ser 2. 2022.

Aziz-Alaoui MA, Okiye MD. Boundedness and global stability for a predator-prey model with modified Leslie-Gower and Holling-type II schemes. Appl Math Lett. 2003; 16(7): 1069–1075.

Yu S. Global stability of a modified Leslie-Gower model with Beddington-DeAngelis functional response. Adv Differ Equ. 2014; 2014: Article ID 84.

Savitri D, Suryanto A, Kusumawinahyu WM, Abadi. Dynamical Behavior of a Modified Leslie–Gower One Prey–Two Predators with Competition. Mathematics. 2020 Apr 28; 8(5): 669.

Gard TC. Uniform persistence in multispecies population models. Math. Biosci. July 1987; 85(1): 93-104.

Majeed SN, Naji RK. An Analysis of a Partial Temporary Immunity SIR Epidemic Model with Nonlinear Treatment Rate. Baghdad Sci J. 2019; 16(3): 639-647.

Naji RK. On The Dynamical Behavior of a Prey-Predator Model with The Effect of Periodic Forcing. Baghdad Sci J. 2021 Mar. 10; 4(1): 147-5.