Dynamics and bifurcations of a ratio-dependent predator-prey model

Boletim da Sociedade Paranaense de Matemática ◽

10.5269/bspm.41174 ◽

2022 ◽

Vol 40 ◽

pp. 1-20

Author(s):

Parisa Azizi ◽

Reza Khoshsiar Ghaziani

Keyword(s):

Normal Form ◽

Limit Cycles ◽

Numerical Continuation ◽

Predator Prey ◽

Bifurcation Points ◽

Predator Prey Model ◽

Prey Model ◽

Ratio Dependent

In this paper, we study a ratio-dependent predator-prey model with modied Holling-Tanner formalism, by using dynamical techniques and numerical continuation algorithms implemented in Matcont. We determine codim-1 and 2 bifurcation points and their corresponding normal form coecients. We also compute a curve of limit cycles of the system emanating from a Hopf point.

Download Full-text

Spatiotemporal dynamics in a diffusive ratio-dependent predator–prey model near a Hopf–Turing bifurcation point

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2014.04.015 ◽

2014 ◽

Vol 67 (10) ◽

pp. 1978-1997 ◽

Cited By ~ 41

Author(s):

Yongli Song ◽

Xingfu Zou

Keyword(s):

Bifurcation Point ◽

Spatiotemporal Dynamics ◽

Predator Prey ◽

Turing Bifurcation ◽

Predator Prey Model ◽

Prey Model ◽

Ratio Dependent

Download Full-text

Spatial Pattern of Ratio-Dependent Predator–Prey Model with Prey Harvesting and Cross-Diffusion

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127419500366 ◽

2019 ◽

Vol 29 (03) ◽

pp. 1950036 ◽

Cited By ~ 1

Author(s):

R. Sivasamy ◽

M. Sivakumar ◽

K. Balachandran ◽

K. Sathiyanathan

Keyword(s):

Temporal Dynamics ◽

Intake Rate ◽

Diffusion Term ◽

Predator Prey ◽

Cross Diffusion ◽

Predator Prey Model ◽

Prey Model ◽

Nonlinear Harvesting ◽

Ratio Dependent ◽

The Cross

This study focuses on the spatial-temporal dynamics of predator–prey model with cross-diffusion where the intake rate of prey is per capita predator according to ratio-dependent functional response and the prey is harvested through nonlinear harvesting strategy. The permanence analysis and local stability analysis of the proposed model without cross-diffusion are analyzed. We derive the conditions for the appearance of diffusion-driven instability and global stability of the considered model. Also the parameter space for Turing region is specified by keeping the cross-diffusion coefficient as one of the crucial parameters. Numerical simulations are given to justify the proposed theoretical results and to show that the cross-diffusion term plays a significant role in the pattern formation.

Download Full-text

Stability analysis and nonstandard Grünwald-Letnikov scheme for a fractional order predator-prey model with ratio-dependent functional response

10.1063/1.5016645 ◽

2017 ◽

Cited By ~ 4

Author(s):

Agus Suryanto ◽

Isnani Darti

Keyword(s):

Stability Analysis ◽

Functional Response ◽

Fractional Order ◽

Predator Prey ◽

Predator Prey Model ◽

Prey Model ◽

Ratio Dependent

Download Full-text

Hopf and steady state bifurcation analysis in a ratio-dependent predator–prey model

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2016.07.027 ◽

2017 ◽

Vol 44 ◽

pp. 52-73 ◽

Cited By ~ 19

Author(s):

Lai Zhang ◽

Jia Liu ◽

Malay Banerjee

Keyword(s):

Steady State ◽

Bifurcation Analysis ◽

Predator Prey ◽

Predator Prey Model ◽

Prey Model ◽

Steady State Bifurcation ◽

Ratio Dependent

Download Full-text

Dynamical analysis of a ratio-dependent predator–prey model with Holling III type functional response and nonlinear harvesting in a random environment

Advances in Difference Equations ◽

10.1186/s13662-018-1625-8 ◽

2018 ◽

Vol 2018 (1) ◽

Cited By ~ 5

Author(s):

Guijie Lan ◽

Yingjie Fu ◽

Chunjin Wei ◽

Shuwen Zhang

Keyword(s):

Functional Response ◽

Random Environment ◽

Dynamical Analysis ◽

Predator Prey ◽

Predator Prey Model ◽

Prey Model ◽

Nonlinear Harvesting ◽

Ratio Dependent

Download Full-text

Review of a predator-prey model with two limit cycles

International Journal of Mathematical Education in Science and Technology ◽

10.1080/0020739x.2018.1510553 ◽

2018 ◽

Vol 50 (6) ◽

pp. 921-933

Author(s):

Q. van der Hoff ◽

A. Harding

Keyword(s):

Limit Cycles ◽

Predator Prey ◽

Predator Prey Model ◽

Prey Model

Download Full-text

Globally Attractive of a Ratio-Dependent Lotka-Volterra Predator-Prey Model with Feedback Control

Advances in Bioscience and Bioengineering ◽

10.11648/j.abb.20160405.13 ◽

2016 ◽

Vol 4 (5) ◽

pp. 59 ◽

Cited By ~ 1

Author(s):

Changyou Wang

Keyword(s):

Feedback Control ◽

Predator Prey ◽

Predator Prey Model ◽

Prey Model ◽

Ratio Dependent ◽

Globally Attractive

Download Full-text

GLOBAL STABILITY OF A DELAYED RATIO-DEPENDENT PREDATOR-PREY MODEL WITH GOMPERTZ GROWTH FOR PREY

Journal of Applied Analysis & Computation ◽

10.11948/2015003 ◽

2015 ◽

Vol 5 (1) ◽

pp. 28-37

Author(s):

Shihua Zhang ◽

◽

Rui Xu

Keyword(s):

Global Stability ◽

Predator Prey ◽

Predator Prey Model ◽

Prey Model ◽

Ratio Dependent

Download Full-text

Turing instability for a ratio-dependent predator–prey model with diffusion

Applied Mathematics and Computation ◽

10.1016/j.amc.2011.02.018 ◽

2011 ◽

Vol 217 (17) ◽

pp. 7265-7281 ◽

Cited By ~ 23

Author(s):

Shaban Aly ◽

Imbunm Kim ◽

Dongwoo Sheen

Keyword(s):

Turing Instability ◽

Predator Prey ◽

Predator Prey Model ◽

Prey Model ◽

Ratio Dependent

Download Full-text

Parametric analysis of the ratio-dependent predator-prey model

Journal of Mathematical Biology ◽

10.1007/s002850000078 ◽

2001 ◽

Vol 43 (3) ◽

pp. 221-246 ◽

Cited By ~ 122

Author(s):

F. Berezovskaya ◽

G. Karev ◽

R. Arditi

Keyword(s):

Parametric Analysis ◽

Predator Prey ◽

Predator Prey Model ◽

Prey Model ◽

Ratio Dependent

Download Full-text