scholarly journals Stability and Hopf bifurcation of the coexistence equilibrium for a differential-algebraic biological economic system with predator harvesting

2021 ◽  
Vol 29 (1) ◽  
pp. 1641-1660
Author(s):  
Kerioui Nadjah ◽  
◽  
Abdelouahab Mohammed Salah
Keyword(s):  
Hopf Bifurcation ◽  
Economic System ◽  
Coexistence Equilibrium

Periodic Solutions of a Delayed Eco-Epidemiological Model with Infection-Age Structure and Holling Type II Functional Response

2020 ◽  
Vol 30 (01) ◽  
pp. 2050011 ◽  
Author(s):  
Peng Yang ◽  
Yuanshi Wang
Keyword(s):  
Hopf Bifurcation ◽  
Functional Response ◽  
Age Structure ◽  
Epidemiological Model ◽  
Type Ii ◽  
Epidemic Disease ◽  
Semilinear Equations ◽  
Infection Age ◽  
Coexistence Equilibrium ◽  
Type Ii Functional Response

This paper is devoted to the study of a new delayed eco-epidemiological model with infection-age structure and Holling type II functional response. Firstly, the disease transmission rate function among the predator population is treated as the piecewise function concerning the incubation period [Formula: see text] of the epidemic disease and the model is rewritten as an abstract nondensely defined Cauchy problem. Besides, the prerequisite which guarantees the presence of the coexistence equilibrium is achieved. Secondly, via utilizing the theory of integrated semigroup and the Hopf bifurcation theorem for semilinear equations with nondense domain, it is found that the model exhibits a Hopf bifurcation near the coexistence equilibrium, which suggests that this model has a nontrivial periodic solution that bifurcates from the coexistence equilibrium as the bifurcation parameter [Formula: see text] crosses the bifurcation critical value [Formula: see text]. That is, there is a continuous periodic oscillation phenomenon. Finally, some numerical simulations are shown to support and extend the analytical results and visualize the interesting phenomenon.

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.

scholarly journals Hopf Bifurcation Analysis of a Predator-Prey Biological Economic System with Nonselective Harvesting

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
Biwen Li ◽  
Zhenwei Li ◽  
Boshan Chen ◽  
Gan Wang
Keyword(s):  
Hopf Bifurcation ◽  
Economic System ◽  
Bifurcation Analysis ◽  
Economic Perspective ◽  
Modified Model ◽  
Bifurcation Theorem ◽  
Predator Prey ◽  
Economic Profit ◽  
Prey System ◽  
Nonselective Harvesting

A modified predator-prey biological economic system with nonselective harvesting is investigated. An important mathematical feature of the system is that the economic profit on the predator-prey system is investigated from an economic perspective. By using the local parameterization method and Hopf bifurcation theorem, we analyze the Hopf bifurcation of the proposed system. In addition, the modified model enriches the database for the predator-prey biological economic system. Finally, numerical simulations illustrate the effectiveness of our results.

Hopf bifurcation for a differential–algebraic biological economic system with time delay

2012 ◽  
Vol 218 (15) ◽  
pp. 7717-7726 ◽  
Author(s):  
Guodong Zhang ◽  
Boshan Chen ◽  
Lulu Zhu ◽  
Yi Shen
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Economic System ◽  
System With Time Delay
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