一类带有扩散项和阶段结构的非自治捕食-食饵系统解的渐近行为
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摘要
研究一类带有扩散项和阶段结构的非自治捕食-食饵系统解的渐近行为,包括解的向前和拉回行为及拉回吸引子的存在性.利用上下解方法和线性椭圆方程谱理论以及非自治吸引子理论,得到系统解的估计以及拉回吸引子的存在性.
In this paper,we study the asymptotic behavior of solutions for a class of non-autonomous predator-prey systems with diffusion and stage structure,including the forward and pullback behavior and the existence of pullback attractors. By using the sub-super solution method,the spectral theory for linear elliptic equations and the theory of attractors for non-autonomous differential equations,we obtain the solution estimates and the existence of pullback attractors.
In this paper,we study the asymptotic behavior of solutions for a class of non-autonomous predator-prey systems with diffusion and stage structure,including the forward and pullback behavior and the existence of pullback attractors. By using the sub-super solution method,the spectral theory for linear elliptic equations and the theory of attractors for non-autonomous differential equations,we obtain the solution estimates and the existence of pullback attractors.
引文
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[8]LIU S,CHEN L,AGARWAL R. Recent progress on stage-structured population dynamics[J]. Math Comput Modelling,2002,36(11):1319-1360.
[9]WANG W. Global Dynamics of a Population Model With Stage Structure for Predator[M]. Singapore:Word Scientific,1997:253-257.
[10]XIAO Y N,CHEN L. Global stability of a predator-prey system with stage structure for the predator[J]. Acta Math Sin(Engl Ser),2004,20(1):63-70.
[11]CRAUEL H,DEBUSSCHE A,FLANDOLI F. Random attractors[J]. J Dynam Diff Eqns,1997,9(2):307-341.
[12]SCHMALFUSS B. Attractors for the non-autonomous dynamical systems[J]. Social Studies,2015,98(6):226-227.
[13]PAO C V. Nonlinear Parabolic and Elliptic Equations[M]. New York:Plenum Press,1992.
[14]LOPEZ-GOMEZ J. The maximum principle and the existence of principal eigenvalues for some linear weighted boundary value problems[J]. J Diff Eqns,1996,127(1):263-294.
[15]MORE X. Semilinear parabolic problem define semiflows on Ckspaces[J]. Trans Am Math Soc,1983,278(1):21-55.
[16]CANTRELL R S,HUTSON C C V. Permanence in ecological systems with spatial heterogeneity[J]. Proc Roy Soc Edinburgh,1993,123(3):533-559.
[2]LANGA J A,ROBINSON J C,SUAREZ A. Forwards and pullback behaviour of a non-autonomous Lotka-Volterra system[J].Nonlinearity,2003,16(4):1277-1293.
[3]LANGA J A,ROBINSON J C,SUAREZ A. Pullback permanence in a non-autonomous competitive Lotka-Volterra model[J]. J Diff Eqns,2003,190(1):214-238.
[4]LANGA J A,ROBINSON J C,RODRIGUEZ-BERNAL A,et al. Permanence and asymptotically stable complete trajectories for non-autonomous Lotka-Volterra models with diffusion[J]. SIAM J Math Anal,2009,40(6):2179-2216.
[5]LANGA J A,RODRIGUEZ-BERNAL A,SUAREZ A. On the long time behavior of non-autonomous Lotka-Volterra models with diffusion via the sub-supertrajectory method[J]. J Diff Eqns,2010,249(2):414-445.
[6]KUANG Y. Basic properties of mathematical population models[J]. J Biomath,2002,26(2):129-142.
[7]ARDITI R,MICHALSKI J. Nonlinear Food Web Models and Their Response to Increased Basal Productivity[M]. New York:Springer-Verlag,1996:122-133.
[8]LIU S,CHEN L,AGARWAL R. Recent progress on stage-structured population dynamics[J]. Math Comput Modelling,2002,36(11):1319-1360.
[9]WANG W. Global Dynamics of a Population Model With Stage Structure for Predator[M]. Singapore:Word Scientific,1997:253-257.
[10]XIAO Y N,CHEN L. Global stability of a predator-prey system with stage structure for the predator[J]. Acta Math Sin(Engl Ser),2004,20(1):63-70.
[11]CRAUEL H,DEBUSSCHE A,FLANDOLI F. Random attractors[J]. J Dynam Diff Eqns,1997,9(2):307-341.
[12]SCHMALFUSS B. Attractors for the non-autonomous dynamical systems[J]. Social Studies,2015,98(6):226-227.
[13]PAO C V. Nonlinear Parabolic and Elliptic Equations[M]. New York:Plenum Press,1992.
[14]LOPEZ-GOMEZ J. The maximum principle and the existence of principal eigenvalues for some linear weighted boundary value problems[J]. J Diff Eqns,1996,127(1):263-294.
[15]MORE X. Semilinear parabolic problem define semiflows on Ckspaces[J]. Trans Am Math Soc,1983,278(1):21-55.
[16]CANTRELL R S,HUTSON C C V. Permanence in ecological systems with spatial heterogeneity[J]. Proc Roy Soc Edinburgh,1993,123(3):533-559.