具有非线性密度死亡率的时滞Nicholson飞蝇方程的持久性
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摘要
利用微分不等式的技巧和函数上下极限的性质,建立了一类具有非线性密度死亡率的时滞Nicholson飞蝇方程解的正性和整体存在性,借此提出保证系统具有持久性的充分性判据,改进和推广了已有文献的相应结果,并结合实际的生物模型验证了理论结果的有效性。
This paper deals with a generalized Nicholson's blowflies model involving a nonlinear density-dependent mortality term. By using the differential inequality technique and the properties of upper and lower limits of functions, some sufficient conditions are obtained to show the positive, global existence and permanence of the addressed model, which complement some previous works. In the end, an example is carried out to substantiate the correctness of the theoretical findings.
This paper deals with a generalized Nicholson's blowflies model involving a nonlinear density-dependent mortality term. By using the differential inequality technique and the properties of upper and lower limits of functions, some sufficient conditions are obtained to show the positive, global existence and permanence of the addressed model, which complement some previous works. In the end, an example is carried out to substantiate the correctness of the theoretical findings.
引文
[1]A J Nicholson.An outline of the dynamics of animal populations[J].Australian Journal of Zoology,1954,2(1):9-65.
[2]W S Gurney,S P Blythe,R M Nisbet.Nicholson's blowflies(revisited)[J].Nature,1980,287:17-21.
[3]Yi T,Zou X.Global attractivity of the diffusive Nicholson blowflies equation with Neumann boundary condition:Anon-monotone case[J].Journal of Differential Equations,2008,245(11):3 376-3 388.
[4]Liu B.Global stability of a class of Nicholson's blowflies model with patch structure and multiple time-varying delays[J].Nonlinear Analysis:Real World Applications,2010,11:2 557-2 562.
[5]T Faria.Asymptotic behaviour for a class of delayed cooperative models with patch structure[J].Discrete and Continuous Dynamical Systems,2013,18(6):1 567-1 579.
[6]L Berezansky,E Braverman,L Idels.Nicholson's blowflies differential equations revisited:Main results and open problems[J].Applied Mathematical Modelling,2010,34(6):1 405-1 417.
[7]黄祖达.一类具有非线性死亡率的时滞Nicholson飞蝇方程的持久性[J].四川师范大学学报(自然科学版),2012,35(1):86-89.
[8]Chen Z.Periodic solutions for Nicholson-type delay system with nonlinear density dependent mortality terms[J].Electronic Journal of Qualitative Theory of Differential Equatio,2013(1):1-10.
[9]Liu B.Positive periodic solutions for a nonlinear density-dependent mortality Nicholson's blowflies model[J].Kodai Mathematical Seminar Reports,2014,37(1):157-173.
[10]Yao L.Dynamics of Nicholson's blowflies models with a nonlinear density-dependent mortality[J].Applied Mathematical Modelling,2018,64:185-195.
[11]J K Hale,S M Verduyn Lunel.Introduction to Functional Differential Equations[M].New York:Springer-Verlag,1993.
[2]W S Gurney,S P Blythe,R M Nisbet.Nicholson's blowflies(revisited)[J].Nature,1980,287:17-21.
[3]Yi T,Zou X.Global attractivity of the diffusive Nicholson blowflies equation with Neumann boundary condition:Anon-monotone case[J].Journal of Differential Equations,2008,245(11):3 376-3 388.
[4]Liu B.Global stability of a class of Nicholson's blowflies model with patch structure and multiple time-varying delays[J].Nonlinear Analysis:Real World Applications,2010,11:2 557-2 562.
[5]T Faria.Asymptotic behaviour for a class of delayed cooperative models with patch structure[J].Discrete and Continuous Dynamical Systems,2013,18(6):1 567-1 579.
[6]L Berezansky,E Braverman,L Idels.Nicholson's blowflies differential equations revisited:Main results and open problems[J].Applied Mathematical Modelling,2010,34(6):1 405-1 417.
[7]黄祖达.一类具有非线性死亡率的时滞Nicholson飞蝇方程的持久性[J].四川师范大学学报(自然科学版),2012,35(1):86-89.
[8]Chen Z.Periodic solutions for Nicholson-type delay system with nonlinear density dependent mortality terms[J].Electronic Journal of Qualitative Theory of Differential Equatio,2013(1):1-10.
[9]Liu B.Positive periodic solutions for a nonlinear density-dependent mortality Nicholson's blowflies model[J].Kodai Mathematical Seminar Reports,2014,37(1):157-173.
[10]Yao L.Dynamics of Nicholson's blowflies models with a nonlinear density-dependent mortality[J].Applied Mathematical Modelling,2018,64:185-195.
[11]J K Hale,S M Verduyn Lunel.Introduction to Functional Differential Equations[M].New York:Springer-Verlag,1993.