Theoretical study and control optimization of an integrated pest management predator–prey model with power growth rate

2016 ◽  
Vol 279 ◽  
pp. 13-26 ◽  
Author(s):  
Kaibiao Sun ◽  
Tonghua Zhang ◽  
Yuan Tian
Keyword(s):  
Growth Rate ◽  
Integrated Pest Management ◽  
Pest Management ◽  
Theoretical Study ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Power Growth ◽  
Control Optimization ◽  
Prey Model ◽  
And Control

scholarly journals A stochastic predator–prey model for integrated pest management

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Lidong Huang ◽  
Xingshu Chen ◽  
Xuewen Tan ◽  
Xiaochou Chen ◽  
Xinzhi Liu
Keyword(s):  
Integrated Pest Management ◽  
Pest Management ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

scholarly journals Complex dynamics and coexistence of period-doubling and period-halving bifurcations in an integrated pest management model with nonlinear impulsive control

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Changtong Li ◽  
Sanyi Tang ◽  
Robert A. Cheke
Keyword(s):  
Periodic Solution ◽  
Integrated Pest Management ◽  
Pest Management ◽  
Pest Control ◽  
Impulsive Control ◽  
Period Doubling ◽  
Dynamical Behaviour ◽  
Period Doubling Bifurcation ◽  
Predator Prey ◽  
Predator Prey Model

Abstract An expectation for optimal integrated pest management is that the instantaneous numbers of natural enemies released should depend on the densities of both pest and natural enemy in the field. For this, a generalised predator–prey model with nonlinear impulsive control tactics is proposed and its dynamics is investigated. The threshold conditions for the global stability of the pest-free periodic solution are obtained based on the Floquet theorem and analytic methods. Also, the sufficient conditions for permanence are given. Additionally, the problem of finding a nontrivial periodic solution is confirmed by showing the existence of a nontrivial fixed point of the model’s stroboscopic map determined by a time snapshot equal to the common impulsive period. In order to address the effects of nonlinear pulse control on the dynamics and success of pest control, a predator–prey model incorporating the Holling type II functional response function as an example is investigated. Finally, numerical simulations show that the proposed model has very complex dynamical behaviour, including period-doubling bifurcation, chaotic solutions, chaos crisis, period-halving bifurcations and periodic windows. Moreover, there exists an interesting phenomenon whereby period-doubling bifurcation and period-halving bifurcation always coexist when nonlinear impulsive controls are adopted, which makes the dynamical behaviour of the model more complicated, resulting in difficulties when designing successful pest control strategies.

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