A class of non-autonomous predator-prey system with Crowley–Martin functional response is discussed. Some sufficient conditions on the boundedness
permanence
extinction
existence of periodic solution and global attractivity of the system are established by using the comparison method and Lyapunov function method.
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references
LOTKA A J.Elements of physical biology,williams and wilkins[M].London:Baltimore,1925.
VOLTERRA V.Fluctuations in the abundance of a species considered mathematically[J].Nature,1926,118:558-560.
UPADHYAY R K,RAWSN R V.Dynamic complexities in a tri-trophic food chainmodel with Holling type II and Crowley-Martin functional response[J].Nonlinear Anal:Model Control,2010,15:361-75.
TRIPATHI J P,ABBAS S,THAKUR M.Dynamical analysis of a prey-predator model with Beddington-De Angelis type function response incorporating a prey refuge[J].Nonlinear Dyn,2014,80:177-96.
JAI P T,SWATI T,SYED A.Global analysis of a delayed density dependent predator-prey model with Crowley-Martin functional response[J].Commun Nonlinear Sci Numer Simulat,2016,30:45-69.
SARWARDI S,HAQUE M,MANDAL P K.Persistence and global stability of Baazykin predator-preymodel with Beddington-De Angelis response function[J].Commun Nonlinear Sci Numer Simulat,2014,19:189-209.
TRIPATHI J P,ABBAS S,THAKUR M.A density dependent delayed predator-prey model with Beddington-De Angelis type function response incorporating a prey refuge[J].Commun Nonlinear Sci Numer Simulat,2015,22:427-50.
Muhammadhaji A,TENG Z.Permanence and extinction analysis for a periodic competing predator-prey system with stage structure[J].International Journal of Dynamics and Control,2017,5(3):858-871.
艾合麦提·麦麦提阿吉.具有离散时滞和反馈控制的Lotka-Volterra合作系统的动力学行为研究[J].数学的实践与认识,2018,48(5):276-285.Muhammadhaji A.Dynamics of a periodic Lotka-Volterra cooperative system with delays and feedback controls[J].Journal of Mathematics in Practice and Theory,2018,48(5):276-285.(in Chinese)
艾合麦提·麦麦提阿吉.含时滞和比例依赖的Lotka-Volterra合作系统的动力学行为研究[J].数学的实践与认识,2019,49(22):316-320.Muhammadhaji A.Dynamics of a ratio-dependent Lotka-Volterra cooperative system with delays[J].Journal of Mathematics in Practice and Theory,2019,49(22):316-320.(in Chinese)
艾合麦提·麦麦提阿吉.含时滞非线性扩散合作系统的正周期解存在性与全局吸引性[J].新疆大学学报(自然科学版),2019,36(1):1-10.Muhammadhaji A.On the existence and global attractivity of p ositive perioic solution for a cooperative system with nonlinear diffusion and delays[J].Journal of Xinjiang University(Natural Science Edition),2019,36(1):1-10.(in Chinese)