AN IMPROVEMENT OF THE HOLLING TYPE III FUNCTIONAL RESPONSE IN ENTOMOPHAGOUS SPECIES MODEL

2007 ◽  
Vol 15 (04) ◽  
pp. 515-524 ◽  
Author(s):  
T. CABELLO ◽  
M. GÁMEZ ◽  
Z. VARGA
Keyword(s):  
Biological Control ◽  
Functional Response ◽  
Type I ◽  
Parasitoid Species ◽  
Predator Species ◽  
Predator Prey ◽  
Type Iii ◽  
Prey System ◽  
Biological Interpretation ◽  
Chelonus Blackburni

In this study, we analyze the functional response for a parasitoid-host and a predator-prey system, as a tool of biological control of pests to evaluate the potential of bio-control agents. A possible biological interpretation was given to the adjustment coefficients of type I and II functional response by Hassell.1 Based on this, we propose new expressions for type III in terms of a new parameter that we call entomophagous potential (parasitoid or predator), providing examples using actual data from trials carried out previously for parasitoid species Chelonus blackburni Cameron (Hym.: Braconidae) and predator species Joppeicus paradoxus Puton (Het.: Joppeicidae). The novelty of the paper consists in the fact that these new expressions for Holling type III functional response have a biological interpretation, and result in a better fit to data than Hassel's model.

scholarly journals Dynamics Behaviors of a Discrete Ratio-Dependent Predator-Prey System with Holling Type III Functional Response and Feedback Controls

2008 ◽  
Vol 2008 ◽  
pp. 1-19 ◽  
Author(s):  
Jinghui Yang
Keyword(s):  
Lyapunov Function ◽  
Functional Response ◽  
Global Attractivity ◽  
Sufficient Conditions ◽  
Feedback Controls ◽  
Predator Species ◽  
Predator Prey ◽  
Type Iii ◽  
Prey System ◽  
Ratio Dependent

A ratio-dependent predator-prey system with Holling type III functional response and feedback controls is proposed. By constructing a suitable Lyapunov function and using the comparison theorem of difference equation, sufficient conditions which ensure the permanence and global attractivity of the system are obtained. After that, under some suitable conditions, we show that the predator speciesywill be driven to extinction. Examples together with their numerical simulations show that the main results are verifiable.

scholarly journals The Dynamics of an Impulsive Predator-Prey System with Stage Structure and Holling Type III Functional Response

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Zhixiang Ju ◽  
Yuanfu Shao ◽  
Xiaolan Xie ◽  
Xiangmin Ma ◽  
Xianjia Fang
Keyword(s):  
Functional Response ◽  
Global Attractivity ◽  
Stage Structure ◽  
Biological Resource ◽  
Predator Prey ◽  
Analysis Techniques ◽  
Type Iii ◽  
Predator Prey Model ◽  
Prey System ◽  
Impulsive Harvesting

Based on the biological resource management of natural resources, a stage-structured predator-prey model with Holling type III functional response, birth pulse, and impulsive harvesting at different moments is proposed in this paper. By applying comparison theorem and some analysis techniques, the global attractivity of predator-extinction periodic solution and the permanence of this system are studied. At last, examples and numerical simulations are given to verify the validity of the main results.

scholarly journals Dynamic Behaviors of a Nonautonomous Discrete Predator-Prey System Incorporating a Prey Refuge and Holling Type II Functional Response

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yumin Wu ◽  
Fengde Chen ◽  
Wanlin Chen ◽  
Yuhua Lin
Keyword(s):  
Global Stability ◽  
Numerical Simulations ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Type Ii ◽  
Prey Refuge ◽  
Predator Species ◽  
Predator Prey ◽  
Prey System ◽  
Type Ii Functional Response

A nonautonomous discrete predator-prey system incorporating a prey refuge and Holling type II functional response is studied in this paper. A set of sufficient conditions which guarantee the persistence and global stability of the system are obtained, respectively. Our results show that if refuge is large enough then predator species will be driven to extinction due to the lack of enough food. Two examples together with their numerical simulations show the feasibility of the main results.

scholarly journals Permanence for a Discrete Ratio-Dependent Predator-Prey System with Holling Type III Functional Response and Feedback Controls

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Jiangbin Chen ◽  
Shengbin Yu
Keyword(s):  
Feedback Control ◽  
Functional Response ◽  
Sufficient Conditions ◽  
Feedback Controls ◽  
Control Variables ◽  
Predator Prey ◽  
Type Iii ◽  
Prey System ◽  
Ratio Dependent

A new set of sufficient conditions for the permanence of a ratio-dependent predator-prey system with Holling type III functional response and feedback controls are obtained. The result shows that feedback control variables have no influence on the persistent property of the system, thus improving and supplementing the main result of Yang (2008).

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