工程数学学报
工程數學學報
공정수학학보
CHINESE JOURNAL OF ENGINEERING MATHEMATICS
2012年
3期
462-468
,共7页
捕食系统%Holling-Ⅲ型功能反应%食饵保护%扩散%稳定性
捕食繫統%Holling-Ⅲ型功能反應%食餌保護%擴散%穩定性
포식계통%Holling-Ⅲ형공능반응%식이보호%확산%은정성
predator-prey system%Holling-Ⅲ type functional response%prey refuge%diffusion%stability
本文研究了一类具食饵保护的Holling-Ⅲ型扩散捕食系统,带有齐次Neumann边界条件.首先,讨论了系统的全局吸引性;其次,给出了系统正常数平衡态局部/全局渐近稳定的充分条件,这些条件依赖于食饵保护参数;特别地,获得了扩散对系统常数平衡态稳定性的影响,即当扩散系数较大时可使得常数平衡态不稳定.
本文研究瞭一類具食餌保護的Holling-Ⅲ型擴散捕食繫統,帶有齊次Neumann邊界條件.首先,討論瞭繫統的全跼吸引性;其次,給齣瞭繫統正常數平衡態跼部/全跼漸近穩定的充分條件,這些條件依賴于食餌保護參數;特彆地,穫得瞭擴散對繫統常數平衡態穩定性的影響,即噹擴散繫數較大時可使得常數平衡態不穩定.
본문연구료일류구식이보호적Holling-Ⅲ형확산포식계통,대유제차Neumann변계조건.수선,토론료계통적전국흡인성;기차,급출료계통정상수평형태국부/전국점근은정적충분조건,저사조건의뢰우식이보호삼수;특별지,획득료확산대계통상수평형태은정성적영향,즉당확산계수교대시가사득상수평형태불은정.
This paper is concerned with a diffusive predator-prey system with Holling Ⅲ type functional response incorporating a prey refuge under homogeneous Neumann boundary conditions.Firstly,the global attractivity of this system is discussed.Then,some sufficient conditions which are dependent on the prey refuge parameter for the local/global asymptotic stability of the positive constant steady state are given.In particular,the effect of diffusion on the stability of positive constant steady state is observed,that is,the large diffusion can make the positive constant steady state to be unstable.