Global stability results for models of commensalism  

作　　者：Paul Georgescu Daniel Maxin Hong Zhang 

机构地区：[1]Department of Mathematics, Technical University of Iasi Bld. Copou 11A, 700506 Iasi, Romania [2]Department of Mathematics and Computer Science Valparaiso University, 1900 Chapel Drive Valparaiso, IN 56383, USA [3]Department of Financial Mathematics, Jiangsu University Zhenjiang, Jiangsu 212013, P. R. China

出　　处：《International Journal of Biomathematics》2017年第3期125-149,共25页生物数学学报（英文版）

基　　金：The work of P. Georgescu was supported by a Grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-ID- PCE-2011-3-0557. D. Maxin acknowledges funding from Wheat Ridge Ministries -- O. P. Kretzmann Grant for Research in the Healing Arts and Sciences. The work of H. Zhang was supported by the National Natural Science Foundation of China, Grant ID 11201187, the Scientific Research Foundation for the Returned Overseas Chinese Scholars and the China Scholarship Council.

摘　　要：We analyze the global stability of the coexisting equilibria for several models of commensalism, first by devising a procedure to modify several Lyapunov functionals which were introduced earlier for corresponding models of mutualism, further confirming their usefulness. It is seen that commensalism promotes global stability, in connection with higher-order self-limiting terms which prevent unboundedness. We then use the theory of asymptotically autonomous systems to prove global stability results for models of commensalism which are subject to Allee effects, finding that commensalisms of appropriate strength can overcome the influence of strong Allee effects.

关 键 词：COMMENSALISM global stability Lyapunov functional Allee effects asymptotically autonomous systems. 

分 类 号：G[文化科学]