Dynamics of Leslie-Gower Predator-Prey Model With Additional Food for Predators

Abstract

Abstract:We consider a Leslie-Gower predator prey model with additional food for predators. Here we investigate the dynamics of the model such as the permanence, determination of equilibrium points and their existence condition as well as their stability properties. It is shown that the model is permanence and has four equilibrium points, i.e., the extinction of both prey and predator point, the extinction of prey point, the extinction of predator and the coexistence point. The point of prey extinction and the coexistence point are conditionally stable while two other equilibrium points are always unstable. It is also shown that the additional food for predators may destabilize the extinction of prey point and at the same time stabilize the coexistence point. Such dynamical behavior agrees with our numerical results.

Analisis Kestabilan pada model prey-predator-super predator dengan fungsi respon Holling tipe I dan Holling tipe II

“…Model ekologi ini menjadi cikal bakal dikembangkannya model prey-predator lain, seperti model Rosenzweig-MacArthur (M. L. Rosenzweig, 1963;M. Moustafa, 2019;Saija, 2020) dan model Leslie-Gower (Y. Lin, 2016;Y.Cai, 2015;H. Ulfa, 2017).…”

Bifurkasi Hopf pada model prey-predator-super predator dengan fungsi respon yang berbeda

“…Pemodelan matematika tentang masalah ekologi berkembang pesat setelah Lotka (1925) dan Volterra (1931) mengajukan model predator-prey yang dikenal sebagai model Lotka-Volterra. Model ekologi klasik ini menjadi cikal bakal diajukannya model predator-prey lain, seperti model Rosenzweig-MacArthur [1][2][3] dan model Leslie-Gower [4][5][6][7][8][9][10][11][12][13][14] yang berfokus pada sistem dengan dua spesies, yaitu satu prey dan satu predator. Lebih lanjut, agar dapat memberikan pemahaman yang lebih baik terhadap dinamika sistem ekologi yang kompleks maka kajian tentang model tiga spesies dipandang menarik untuk dilakukan.…”

Numerical Study of One Prey-Two Predator Model Considering Food Addition and Anti-Predator Defense

“…Panja [12] proposes effects anti-predator defense in a preypredator model using Ratio-dependent functional response to make the model more realistic. Prasad [13], Ulfa [14], and Zhu et al [15] incorporate food additional for predators in their model. Based on the background of several studies of prey-predator models, we developed a one prey-two predators' model to provide an overview of the dynamics of change through numerical simulations.…”