Dynamics of a predator-prey ecological system with nonlinear harvesting rate

2015 ◽  
Vol 20 (1) ◽  
pp. 25-33 ◽  
Author(s):  
Weiyi Liu ◽  
Biwen Li ◽  
Chaojin Fu ◽  
Boshan Chen
Keyword(s):  
Ecological System ◽  
Predator Prey ◽  
Nonlinear Harvesting ◽  
Nonlinear Harvesting Rate

Stability and Hopf Bifurcation of a Predator–Prey Biological Economic System with Nonlinear Harvesting Rate

2015 ◽  
Vol 16 (6) ◽  
pp. 249-258 ◽  
Author(s):  
Weiyi Liu ◽  
Chaojin Fu ◽  
Boshan Chen
Keyword(s):  
Hopf Bifurcation ◽  
Economic System ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Matlab Simulation ◽  
Predator Prey ◽  
Complex Models ◽  
Nonlinear Harvesting ◽  
Nonlinear Harvesting Rate ◽  
The Stability

AbstractIn this paper, we analyze the stability and Hopf bifurcation of a biological economic system with harvesting effort on prey. The model we consider is described by differential-algebraic equations because of economic revenue. We choose economic revenue as a positive bifurcation parameter here. Different from previous researchers’ models, this model with nonlinear harvesting rate is more general. Furthermore, the improved calculation process of parameterization is much simpler and it can handle more complex models which could not be dealt with by their algorithms because of enormous calculation. Finally, by MATLAB simulation, the validity and feasibility of the obtained results are illustrated.

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

2019 ◽  
Vol 29 (03) ◽  
pp. 1950036 ◽  
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.

Stability analysis of a delayed predator–prey model with nonlinear harvesting efforts using imprecise biological parameters

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Amit K. Pal
Keyword(s):  
Equilibrium Points ◽  
Stable Limit Cycle ◽  
Limit Cycle Oscillation ◽  
Stable Limit ◽  
Biological Parameters ◽  
Delay Model ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Nonlinear Harvesting

Abstract In this paper, the dynamical behaviors of a delayed predator–prey model (PPM) with nonlinear harvesting efforts by using imprecise biological parameters are studied. A method is proposed to handle these imprecise parameters by using a parametric form of interval numbers. The proposed PPM is presented with Crowley–Martin type of predation and Michaelis–Menten type prey harvesting. The existence of various equilibrium points and the stability of the system at these equilibrium points are investigated. Analytical study reveals that the delay model exhibits a stable limit cycle oscillation. Computer simulations are carried out to illustrate the main analytical findings.

scholarly journals On a predator prey model with nonlinear harvesting and distributed delay

2018 ◽  
Vol 17 (6) ◽  
pp. 2703-2727 ◽  
Author(s):  
Tomás Caraballo ◽  
◽  
Renato Colucci ◽  
Luca Guerrini ◽  
◽  
...  
Keyword(s):  
Distributed Delay ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Nonlinear Harvesting
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