Stability in a Holling-Tanner predator-prey model like a Kolmogorov system without periodic orbits via Dulac functions

2018 ◽  
Vol 11 (45) ◽  
pp. 2219-2224
Author(s):  
A. M. Marin ◽  
R. D. Ortiz ◽  
S. B. Gutierrez
Keyword(s):  
Periodic Orbits ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Kolmogorov System

scholarly journals Stable Periodic Orbits for a Predator–Prey Model with Delay

2000 ◽  
Vol 249 (2) ◽  
pp. 324-339 ◽  
Author(s):  
Mario Cavani ◽  
Marcos Lizana ◽  
Hal L. Smith
Keyword(s):  
Periodic Orbits ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Stable Periodic

Nonlinear Dynamical Behaviour in a Predator-Prey Model with Harvesting

2017 ◽  
Vol 7 (2) ◽  
pp. 376-395
Author(s):  
Wei Liu ◽  
Yaolin Jiang
Keyword(s):  
Hopf Bifurcation ◽  
Periodic Orbits ◽  
Sufficient Conditions ◽  
Dynamical Behaviour ◽  
Nonlinear Dynamical ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Damped Oscillations ◽  
Prey Model ◽  
The Stability

AbstractWe investigate the stability and periodic orbits of a predator-prey model with harvesting. The model has a biologically-meaningful interior, an attractor undergoing damped oscillations, and can become destabilised to produce periodic orbits via a Hopf bifurcation. Some sufficient conditions for the existence of the Hopf bifurcation are established, and a stability analysis for the periodic solutions using a Lyapunov function is presented. Finally, some computer simulations illustrate our theoretical results.

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