scholarly journals DYNAMIC COMPLEXITY OF A PREDATOR-PREY MODEL FOR IPM WITH NONLINEAR IMPULSIVE CONTROL INCORPORATING A REGULATORY FACTOR FOR PREDATOR RELEASES

2019 ◽  
Vol 24 (1) ◽  
pp. 134-154 ◽  
Author(s):  
Sanyi Tang ◽  
Yuan Tian ◽  
Robert A. Cheke
Keyword(s):  
Natural Enemies ◽  
Impulsive Control ◽  
Control Measures ◽  
Threshold Condition ◽  
Random Perturbations ◽  
Regulatory Factor ◽  
Multiple Attractors ◽  
Dynamic Complexity ◽  
Predator Prey Model ◽  
Pest Outbreaks

The success of integrated pest management (IPM) depends on spraying the correct amount of pesticides at an appropriate time and releases of natural enemies or pathogens of the pest in appropriate proportions at critical times, with little cost and minimal effects on the environment. Therefore, control decisions require information on instantaneous killing rates of pesticides and numbers of natural enemies to be released, variables that should depend on the densities of both pest and natural enemy population densities in the field. To describe such a control strategy we have proposed a mathematical model of IPM involving releases of natural enemies in relation to a regulatory factor. The threshold condition for the existence and stability of the pest free periodic solution is provided using a cobweb model, the comparison principle and Floquet theory, which reveals the effects of nonlinear control actions on pest outbreaks. Bifurcation analyses show that the dynamics of the proposed model can be very complex, including multiple attractors and switch-like transition patterns following small random perturbations. Moreover, the random perturbations and nonlinear impulsive control measures could generate complex switching patterns, which show that the pest population could have outbreaks in complex ways due to environmental noise.

scholarly journals Generalized Predator-Prey Model with Nonlinear Impulsive Control Strategy

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Wenjie Qin ◽  
Guangyao Tang ◽  
Sanyi Tang
Keyword(s):  
Pest Control ◽  
Impulsive Control ◽  
Dynamical Behavior ◽  
Limited Resource ◽  
Control Measures ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model ◽  
Pest Outbreaks ◽  
Wide Range

A generalized predator-prey model concerning integrated pest management and nonlinear impulsive control measures is proposed and analyzed. The main purpose is to understand how resource limitation affects the successful pest control and pest outbreaks. The threshold conditions for the stability of the pest-free periodic solution are given firstly. Once the threshold value exceeds a critical level, both pest and its natural enemy populations can oscillate periodically. Secondly, in order to address how the limited resources affect the pest control, as an example the Holling II functional response function is chosen. The numerical results show that predator-prey model with limited resource has complex dynamical behavior. In addition, it is confirmed that the model has the coexistence of pests and natural enemies for a wide range of parameters.

scholarly journals A Holling Type II Pest and Natural Enemy Model with Density Dependent IPM Strategy

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Xia Wang ◽  
Yuan Tian ◽  
Sanyi Tang
Keyword(s):  
Periodic Solution ◽  
Integrated Pest Management ◽  
Pest Management ◽  
Pest Control ◽  
Natural Enemies ◽  
Natural Enemy ◽  
Impulsive Control ◽  
Control Measures ◽  
Threshold Condition ◽  
Density Dependent

Resource limitations and density dependent releasing of natural enemies during the pest control and integrated pest management will undoubtedly result in nonlinear impulsive control. In order to investigate the effects of those nonlinear control strategies on the successful pest control, we have proposed a pest-natural enemy system concerning integrated pest management with density dependent instant killing rate and releasing rate. In particular, the releasing rate depicts how the number of natural enemy populations released was guided by their current density at the fixed moment. The threshold condition which ensures the existence and global stability of pest-free periodic solution has been discussed first, and the effects of key parameters on the threshold condition reveal that reducing the pulse period does not always benefit pest control; that is, frequent releasing of natural enemies may not be beneficial to the eradication of pests when the density dependent releasing method has been implemented. Moreover, the forward and backward bifurcations could occur once the pest-free periodic solution becomes unstable, and the system could exist with very complex dynamics. All those results confirm that the control actions should be carefully designed once the nonlinear impulsive control measures have been taken for pest management.

scholarly journals The Effects of Resource Limitation on a Predator-Prey Model with Control Measures as Nonlinear Pulses

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Wenjie Qin ◽  
Sanyi Tang ◽  
Robert A. Cheke
Keyword(s):  
Natural Enemies ◽  
Dynamical Behavior ◽  
Rank Correlation ◽  
Resource Limitation ◽  
Latin Hypercube Sampling ◽  
Threshold Value ◽  
Control Measures ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

The dynamical behavior of a Holling II predator-prey model with control measures as nonlinear pulses is proposed and analyzed theoretically and numerically to understand how resource limitation affects pest population outbreaks. The threshold conditions for the stability of the pest-free periodic solution are given. Latin hypercube sampling/partial rank correlation coefficients are used to perform sensitivity analysis for the threshold concerning pest extinction to determine the significance of each parameter. Comparing this threshold value with that without resource limitation, our results indicate that it is essential to increase the pesticide’s efficacy against the pest and reduce its effectiveness against the natural enemy, while enhancing the efficiency of the natural enemies. Once the threshold value exceeds a critical level, both pest and its natural enemies populations can oscillate periodically. Further-more, when the pulse period and constant stocking number as a bifurcation parameter, the predator-prey model reveals complex dynamics. In addition, numerical results are presented to illustrate the feasibility of our main results.

scholarly journals Seaweed aquaculture: a preliminary assessment of biosecurity measures for controlling the ice-ice syndrome and pest outbreaks of a Kappaphycus farm

2021 ◽  
Author(s):  
Cicilia S. B. Kambey ◽  
Iona Campbell ◽  
Elizabeth J. Cottier-Cook ◽  
Adibi R. M. Nor ◽  
Azhar Kassim ◽  
...  
Keyword(s):  
Hazard Analysis ◽  
Kappaphycus Alvarezii ◽  
Control Point ◽  
Control Measures ◽  
Seaweed Aquaculture ◽  
Critical Control Point ◽  
Management Measures ◽  
Long Line ◽  
Pest Outbreaks ◽  
The Impact

AbstractThe application of biosecurity in seaweed aquaculture plays an important role in reducing the impact of disease and pest outbreaks. The continuous occurrence of seaweed pests including the macroalgal epiphytes, epi-endophytic filamentous algae and biofilms on Kappaphycus farms may also potentially induce further incidences of the ice-ice syndrome. In this study, on-farm biosecurity management measures were tested on the commercially grown seaweeds Kappaphycus malesianus and Kappaphycus alvarezii during peak ice-ice season at Gallam-Gallam Village, Sabah, Malaysia. The investigation was focused on preventative control measures including the early detection of the ice-ice syndrome and pests through propagule health checks, regular cleaning of the crop thallus and associated long-line ropes and monitoring of the environment. Farm procedures and practices were also assessed in terms of their biosecurity ‘risk’ using the hazard analysis and critical control point (HCCAP) approach. Observations were replicated in two different farm management systems; one system adopted routine biosecurity measures and the other had no biosecurity measures. The results showed that the ice-ice syndrome and pest outbreak was significantly decreased by 60–75% for K. malesianus and 29–71% for K. alvarezii at the farm which adopted the routine biosecurity measures compared with the no biosecurity treatment. The biosecurity measures also significantly improved growth rate and seaweed quality. The infection levels of the epi-endophyte Melanothamnus sp. contributed to the ice-ice syndrome in K. malesianus, whilst the epiphyte coverage was correlated to the ice-ice incidence in K. alvarezii. This study provides the first evidence of biosecurity management measures significantly decreasing the incidence of the ice-ice syndrome and pests on a commercial seaweed farm.

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.

scholarly journals The Dynamic Complexity of a Holling Type-IV Predator-Prey System with Stage Structure and Double Delays

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Yakui Xue ◽  
Xiafeng Duan
Keyword(s):  
Time Delay ◽  
Equilibrium Point ◽  
Dynamical Behavior ◽  
Stage Structure ◽  
Point Of View ◽  
Maturation Time ◽  
Dynamic Complexity ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Type Iv

We invest a predator-prey model of Holling type-IV functional response with stage structure and double delays due to maturation time for both prey and predator. The dynamical behavior of the system is investigated from the point of view of stability switches aspects. We assume that the immature and mature individuals of each species are divided by a fixed age, and the mature predator only attacks the mature prey. Based on some comparison arguments, sharp threshold conditions which are both necessary and sufficient for the global stability of the equilibrium point of predator extinction are obtained. The most important outcome of this paper is that the variation of predator stage structure can affect the existence of the interior equilibrium point and drive the predator into extinction by changing the maturation (through-stage) time delay. Our linear stability work and numerical results show that if the resource is dynamic, as in nature, there is a window in maturation time delay parameters that generate sustainable oscillatory dynamics.

AN INTEGRATED PEST MANAGEMENT MODEL WITH DOSE-RESPONSE EFFECT OF PESTICIDES

2018 ◽  
Vol 26 (01) ◽  
pp. 59-86 ◽  
Author(s):  
BAOLIN KANG ◽  
BING LIU ◽  
FENGMEI TAO
Keyword(s):  
Asymptotic Stability ◽  
Pest Management ◽  
Natural Enemies ◽  
Control Strategies ◽  
Sufficient Conditions ◽  
Residual Effects ◽  
Delayed Response ◽  
Threshold Condition ◽  
Significant Control ◽  
Dose Response Effect

Considering the delayed response to pesticide applications and the long-term residual effects of pesticides after the deployment of a pest management strategy, this paper develops a pollutant-discharge model to simulate pesticide spraying and analyze the effect of releasing natural enemies of the pest. The following two different control strategies are discussed: (1) the frequency of spraying pesticides is higher than that of releasing natural enemies, and (2) the frequency of releasing natural enemies is higher than that of spraying pesticides. For different control strategies, the sufficient conditions of locally asymptotic stability and globally asymptotic stability of the pest-eradication periodic solution are obtained. Using numerical simulations, we analyze the sensitivity of the threshold condition with respect to the parameters, identify the major factors affecting pest control and provide guidance for decision-making in pest management. Finally, we compare the control strategies and analyze which strategy is optimal as the most significant control parameters are varying.

scholarly journals Dynamics of a Beddington-DeAngelis Type Predator-Prey Model with Impulsive Effect

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Sun Shulin ◽  
Guo Cuihua
Keyword(s):  
Small Amplitude ◽  
Floquet Theory ◽  
Impulsive Control ◽  
Control Strategies ◽  
Impulsive Effect ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Impulsive Equation ◽  
Predator System ◽  
Comparison Technique

In view of the logical consistence, the model of a two-prey one-predator system with Beddington-DeAngelis functional response and impulsive control strategies is formulated and studied systematically. By using the Floquet theory of impulsive equation, small amplitude perturbation method, and comparison technique, we obtain the conditions which guarantee the global asymptotic stability of the two-prey eradication periodic solution. We also proved that the system is permanent under some conditions. Numerical simulations find that the system appears the phenomenon of competition exclusion.

DYNAMICS ON A HOLLING II PREDATOR–PREY MODEL WITH STATE-DEPENDENT IMPULSIVE CONTROL

2012 ◽  
Vol 05 (03) ◽  
pp. 1260006 ◽  
Author(s):  
BING LIU ◽  
YE TIAN ◽  
BAOLIN KANG
Keyword(s):  
Periodic Solution ◽  
Chemical Control ◽  
Impulsive Control ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
State Dependent ◽  
Continuous Dynamic System ◽  
Continuous Dynamic ◽  
Holling Ii Functional Response

According to biological and chemical control strategy for pest control, a Holling II functional response predator–prey system concerning state-dependent impulsive control is investigated. We define the successor functions of semi-continuous dynamic system and give an existence theorem of order 1 periodic solution of such a system. By means of sequence convergence rules and qualitative analysis, we successfully get the conditions of existence and attractiveness of order 1 periodic solution. Our results show that our method used in this paper is more efficient and easier than the existing methods to prove the existence and attractiveness of order 1 periodic solution.

scholarly journals Dynamic Analysis of a Predator-Prey (Pest) Model with Disease in Prey and Involving an Impulsive Control Strategy

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Min Zhao ◽  
Yanzhen Wang ◽  
Lansun Chen
Keyword(s):  
Integrated Pest Management ◽  
Pest Management ◽  
Control Strategy ◽  
Impulsive Control ◽  
Critical Parameters ◽  
Critical Conditions ◽  
Dynamic Complexity ◽  
Predator Prey ◽  
Impulsive Control Strategy ◽  
Disease In Prey

The dynamic behaviors of a predator-prey (pest) model with disease in prey and involving an impulsive control strategy to release infected prey at fixed times are investigated for the purpose of integrated pest management. Mathematical theoretical works have been pursuing the investigation of the local asymptotical stability and global attractivity for the semitrivial periodic solution and population persistent, which depicts the threshold expression of some critical parameters for carrying out integrated pest management. Numerical analysis indicates that the impulsive control strategy has a strong effect on the dynamical complexity and population persistent using bifurcation diagrams and power spectra diagrams. These results show that if the release amount of infective prey can satisfy some critical conditions, then all biological populations will coexist. All these results are expected to be of use in the study of the dynamic complexity of ecosystems.

Sign in / Sign up

Export Citation Format

Share Document