Additional food supplements as a tool for biological conservation of predator-prey systems involving type III functional response: A qualitative and quantitative investigation

2018 ◽  
Vol 455 ◽  
pp. 303-318 ◽  
Author(s):  
P.D.N. Srinivasu ◽  
D.K.K. Vamsi ◽  
V.S. Ananth
Keyword(s):  
Functional Response ◽  
Food Supplements ◽  
Biological Conservation ◽  
Quantitative Investigation ◽  
Additional Food ◽  
Predator Prey ◽  
Qualitative And Quantitative ◽  
Type Iii

BIFURCATION AND CHAOS IN A DISCRETE PREDATOR–PREY MODEL WITH HOLLING TYPE-III FUNCTIONAL RESPONSE AND HARVESTING EFFECT

2021 ◽  
pp. 1-28
Author(s):  
ANURAJ SINGH ◽  
PREETI DEOLIA
Keyword(s):  
Functional Response ◽  
Sufficient Conditions ◽  
Flip Bifurcation ◽  
Bifurcation Structure ◽  
Bifurcation And Chaos ◽  
Predator Prey ◽  
Type Iii ◽  
Predator Prey Model ◽  
Prey Model ◽  
Wide Range

In this paper, we study a discrete-time predator–prey model with Holling type-III functional response and harvesting in both species. A detailed bifurcation analysis, depending on some parameter, reveals a rich bifurcation structure, including transcritical bifurcation, flip bifurcation and Neimark–Sacker bifurcation. However, some sufficient conditions to guarantee the global asymptotic stability of the trivial fixed point and unique positive fixed points are also given. The existence of chaos in the sense of Li–Yorke has been established for the discrete system. The extensive numerical simulations are given to support the analytical findings. The system exhibits flip bifurcation and Neimark–Sacker bifurcation followed by wide range of dense chaos. Further, the chaos occurred in the system can be controlled by choosing suitable value of prey harvesting.

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 Warming can destabilise predator-prey interactions by shifting the functional response from Type III to Type II

2018 ◽  
Author(s):  
Uriah Daugaard ◽  
Owen Petchey ◽  
Frank Pennekamp
Keyword(s):  
Population Dynamics ◽  
Functional Response ◽  
Conversion Efficiency ◽  
Trophic Interactions ◽  
Clearance Rate ◽  
Temperature Effects ◽  
Type Ii ◽  
Predator Prey ◽  
Type Iii ◽  
Population Dynamic Model

The potential for climate change and temperature shifts to affect community stability remains relatively unknown. One mechanism by which temperature may affect stability is by altering trophic interactions. The functional response quantifies the per capita resource consumption by the consumer as a function of resource abundance and is a suitable framework for the description of nonlinear trophic interactions. We studied the effect of temperature on a ciliate predator-prey pair (Spathidium sp. and Dexiostoma campylum) by estimating warming effects on the functional response and on the associated conversion efficiency of the predator. We recorded prey and predator dynamics over 24 hours and at three temperature levels (15, 20 and 25 C). To these data we fitted a population dynamic model including the predator functional response, such that the functional response parameters (space clearance rate, handling time, and density dependence of space clearance rate) were estimated for each temperature separately. To evaluate the ecological significance of temperature effects on the functional response parameters we simulated predator-prey population dynamics. We considered the predator-prey system to be destabilised, if the prey was driven extinct by the predator. Effects of increased temperature included a transition of the functional response from a Type III to a Type II and an increase of the conversion efficiency of the predator. The simulated population dynamics showed a destabilisation of the system with warming, with greater risk of prey extinction at higher temperatures likely caused by the transition from a Type III to a Type II functional response. Warming-induced shifts from a Type III to II are not commonly considered in modelling studies that investigate how population dynamics respond to warming. Future studies should investigate the mechanism and generality of the effect we observed and simulate temperature effects in complex food webs including shifts in the type of the functional response as well as consider the possibility of a temperature dependent conversion efficiency.

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