Fear effect in discrete prey-predator model incorporating square root functional response

Abstract

In this work, an interaction between prey and its predator involving the effect of fear in presence of the predator and the square root functional response is investigated. Fixed points and their stability condition are calculated. The conditions for the occurrence of some phenomena namely Neimark-Sacker, Flip, and Fold bifurcations are given. Base on some hypothetical data, the numerical simulations consist of phase portraits and bifurcation diagrams are demonstrated to picturise the dynamical behavior. It is also shown numerically that rich dynamics are obtained by the discrete model as the effect of fear.

A Fractional-Order Predator-Prey Model with Age Structure on Predator and Nonlinear Harvesting on Prey

“…Biological equilibria is basically the equilibrium point of model (7) which exists in R 3 + := (x, y, z) : x ≥ 0, y ≥ 0, z ≥ 0, (x, y, z) ∈ R 3 . Therefore, the following equations are needed to solve.…”

“…Some modifications based on the biological behaviors are integrated to construct a better model. For example, the predator-prey model involving the effect of fear [1][2][3][4], the impact of Allee to the existence of prey and predator [5][6][7][8], and the exploitation of biological resources by harvesting [9][10][11].…”

Implementasi algoritma genetika dalam mengestimasi kepadatan populasi jackrabbit dan coyote

“…Hasil simulasi menunjukkan bahwa setiap solusi dengan nilai awal yang berbeda selalu memberikan orbit tertutup berupa kurva periodik. Model prey-predator yang digunakan dalam artikel ini belum mempertimbangkan daya dukung lingkungan maupun variasi fungsi respon yang telah dibahas pada beberapa modifikasi seperti pada [21][22][23][24][25] dan beberapa referensi di dalamnya. Oleh karena itu, apabila dikaji lebih lanjut tentang kondisi biologis jackrabbit dan coyote sehingga diperoleh model yang lebih tepat menggambarkan interaksi antara keduanya, maka estimasi parameter yang diperoleh akan lebih baik lagi.…”

Complexity of a Discrete-Time Predator-Prey Model Involving Prey Refuge Proportional to Predator

“…Several investigators studied the predator-prey model in the continuous-time domain. Depending on time, we can divide predator-prey model into two types, discrete domain system [1][2][3][4][5][6][7][8][9] and continuous domain system [10][11][12][13][14][15]. The discrete-time predator-prey model has reached dynamics, and interesting qualitative behavior for the study incorporating refuge, different functional responses, harvesting, delays, etc.…”