A Cydia Pomonella Integrated Management Predator-Prey Model With Smith Growth and Linear Feedback Control

Cydia Pomonella has great influence on the output and quality of apple, therefore, it is an interesting subject to find out the optimum control strategy of Cydia Pomonella. A Cydia Pomonella integrated management predator-prey model with Smith growth and linear feedback control is established in this paper, and the pulse parameter linearity is dependent on controlling level. Firstly, we prove the existence and uniqueness of order one periodic solution (OOPS) by using differential equation geometry theory and successor function method. Secondly, the stability of OOPS is proved by using the geometric method. Finally, with the discussion of different parameters, we verify the theoretical results by numerical simulations, and demonstrate the advantages and disadvantages of biological control strategy, chemical control strategy and integrated control strategy. Moreover, the optimization model with minimum cost is established by using OOPS and optimal control level of the model is obtained.

[1]  Bing Liu,et al.  The dynamical behaviors of a Lotka–Volterra predator–prey model concerning integrated pest management ☆ , 2005 .

[2]  Feng Liu,et al.  Rough maximal singular integral and maximal operators supported by subvarieties on Triebel–Lizorkin spaces , 2018, Nonlinear Analysis.

[3]  Frederick E. Smith,et al.  Population Dynamics in Daphnia magna and a New Model for Population Growth , 1963 .

[4]  Yan Zhang,et al.  Adaptive Finite-Time Control of Nonlinear Quantized Systems With Actuator Dead-Zone , 2019, IEEE Access.

[5]  J. J. Shepherd,et al.  Logistic growth with a slowly varying Holling type II harvesting term , 2017, Commun. Nonlinear Sci. Numer. Simul..

[6]  Fei Li,et al.  Analysis and Numerical Simulations of a Stochastic SEIQR Epidemic System with Quarantine-Adjusted Incidence and Imperfect Vaccination , 2018, Comput. Math. Methods Medicine.

[7]  Paul Georgescu,et al.  IMPULSIVE CONTROL STRATEGIES FOR PEST MANAGEMENT , 2007 .

[8]  Yongfeng Li,et al.  Complex dynamics of a predator-prey model with impulsive state feedback control , 2014, Appl. Math. Comput..

[9]  Lansun Chen,et al.  State-Dependent Pulse Vaccination and Therapeutic Strategy in an SI Epidemic Model with Nonlinear Incidence Rate , 2019, Comput. Math. Methods Medicine.

[10]  Xinzhu Meng,et al.  Geometrical analysis and control optimization of a predator-prey model with multi state-dependent impulse , 2017, Advances in Difference Equations.

[11]  Fang Wang,et al.  Multi-State Dependent Impulsive Control for Holling I Predator-Prey Model , 2012 .

[12]  Tongqian Zhang,et al.  A new predator-prey model with a profitless delay of digestion and impulsive perturbation on the prey , 2011, Appl. Math. Comput..

[13]  Huidong Cheng,et al.  A Lycaon pictus impulsive state feedback control model with Allee effect and continuous time delay , 2018, Advances in Difference Equations.

[14]  Tzy-Wei Hwang,et al.  Global analysis of the predator–prey system with Beddington–DeAngelis functional response , 2003 .

[15]  Ruiqing Shi,et al.  A predator-prey model with disease in the prey and two impulses for integrated pest management , 2009 .

[16]  Yuan Tian,et al.  Dynamics analysis and control optimization of a pest management predator-prey model with an integrated control strategy , 2017, Appl. Math. Comput..

[17]  Alan J. Terry,et al.  Biocontrol in an impulsive predator-prey model. , 2014, Mathematical biosciences.

[18]  Xinzhu Meng,et al.  Application of stochastic inequalities to global analysis of a nonlinear stochastic SIRS epidemic model with saturated treatment function , 2018, Advances in Difference Equations.

[19]  Zhenzhen Shi,et al.  Dynamic Analysis of a Pest Management Smith Model with Impulsive State Feedback Control and Continuous Delay , 2019, Mathematics.

[20]  Jianmei Wang,et al.  Periodic solution and control optimization of a prey-predator model with two types of harvesting , 2018 .

[21]  Prashanta Kumar Mandal,et al.  Spatial pattern in a diffusive predator–prey model with sigmoid ratio-dependent functional response , 2014 .

[22]  Zhidong Teng,et al.  Existence and stability of periodic solution of a predator-prey model with state-dependent impulsive effects , 2009, Math. Comput. Simul..

[23]  F. Wang,et al.  Entropy-expansiveness of geodesic flows on closed manifolds without conjugate points , 2016 .

[24]  Feng Liu,et al.  Continuity and approximate differentiability of multisublinear fractional maximal functions , 2018 .

[25]  Jianmei Wang,et al.  Control optimization and homoclinic bifurcation of a prey–predator model with ratio-dependent , 2019, Advances in Difference Equations.

[26]  Vladimir Igorevich Arnold,et al.  Geometrical Methods in the Theory of Ordinary Differential Equations , 1983 .

[27]  Chen Lan-sun.  Pest Control and Geometric Theory of Semi-Continuous Dynamical System , 2011 .

[28]  Lansun Chen,et al.  The dynamics of an epidemic model for pest control with impulsive effect , 2010 .

[29]  Jian Zhang,et al.  Dynamics of a stochastic SIR model with both horizontal and vertical transmission , 2018 .

[30]  S. Walde.  Immigration and the dynamics of a predator-prey interaction in biological control , 1994 .

[31]  Bing Liu,et al.  Extinction and permanence of a two-prey one-predator system with impulsive effect. , 2003, Mathematical medicine and biology : a journal of the IMA.

[32]  Wenshun Lv,et al.  Adaptive tracking control for a class of uncertain nonlinear systems with infinite number of actuator failures using neural networks , 2017, Advances in Difference Equations.

[33]  Yanhui Wang,et al.  Beyond regular semigroups , 2016 .

[34]  Joydev Chattopadhyay,et al.  Infection in prey population may act as a biological control in ratio-dependent predator?prey models , 2004 .

[35]  Tonghua Zhang,et al.  GLOBAL ANALYSIS FOR A DELAYED SIV MODEL WITH DIRECT AND ENVIRONMENTAL TRANSMISSIONS , 2015 .

[36]  Xiaoning Zhang,et al.  The geometrical analysis of a predator-prey model with multi-state dependent impulsive , 2018 .

[37]  Tonghua Zhang,et al.  Theoretical study and control optimization of an integrated pest management predator-prey model with power growth rate. , 2016, Mathematical biosciences.

[38]  Tonghua Zhang,et al.  Dynamics analysis of a pest management prey–predator model by means of interval state monitoring and control , 2017 .

[39]  Frédéric Grognard,et al.  Global stability and optimisation of a general impulsive biological control model. , 2008, Mathematical biosciences.

[40]  Qingling Zhang,et al.  The geometrical analysis of a predator-prey model with two state impulses. , 2012, Mathematical biosciences.

[41]  Lansun Chen,et al.  On the impulsive controllability and bifurcation of a predator-pest model of IPM , 2008, Biosyst..

[42]  Lu Wang,et al.  Global analysis of a new nonlinear stochastic differential competition system with impulsive effect , 2017 .

[43]  Rui Liu,et al.  Periodic solution of a pest management Gompertz model with impulsive state feedback control , 2014 .

[44]  Yi Song,et al.  The dynamics of a high-dimensional delayed pest management model with impulsive pesticide input and harvesting prey at different fixed moments , 2011 .

[45]  Zhiqing Liang,et al.  Qualitative analysis of a predator–prey system with mutual interference and impulsive state feedback control , 2017 .

[46]  Xinzeng Wang,et al.  Dynamics of a stochastic SIS epidemic model with nonlinear incidence rates , 2019, Advances in Difference Equations.

[47]  Yongzhen Pei,et al.  Species extinction and permanence in a prey–predator model with two-type functional responses and impulsive biological control , 2008 .

[48]  Yuan Tian,et al.  Geometric approach to the stability analysis of the periodic solution in a semi-continuous dynamic system , 2014 .

[49]  Guodong Liu,et al.  Extinction and Persistence in Mean of a Novel Delay Impulsive Stochastic Infected Predator-Prey System with Jumps , 2017, Complex..

[50]  Jianmei Wang,et al.  Dynamic analysis of unilateral diffusion Gompertz model with impulsive control strategy , 2018 .