数学年刊A辑
數學年刊A輯
수학년간A집
CHINESE ANNALS OF MATHEMATICS,SERIES A
2009年
6期
845-856
,共12页
恒化器%Beddington-DeAngelis功能反应项%共存解%稳定性%扰动理论
恆化器%Beddington-DeAngelis功能反應項%共存解%穩定性%擾動理論
항화기%Beddington-DeAngelis공능반응항%공존해%은정성%우동이론
Chemostat%Beddington-DeAngelis functional response%Coexistence solution%Stability%Perturbation theory
研究了一类具有抑制剂和Beddington-DeAngelis功能反应项的非均匀恒化器模型.根据单调动力系统理论得到了正平衡解的存在性.利用度理论、分歧理论以及摄动理论,分析了抑制剂对系统正平衡解及渐近行为的影响.结果表明当体现抑制作用的参数μ充分大时,此模型或者没有正解,并且一个半平凡晌非负解是全局吸引的;或者模型的所有正解均由一个极限问题决定.
研究瞭一類具有抑製劑和Beddington-DeAngelis功能反應項的非均勻恆化器模型.根據單調動力繫統理論得到瞭正平衡解的存在性.利用度理論、分歧理論以及攝動理論,分析瞭抑製劑對繫統正平衡解及漸近行為的影響.結果錶明噹體現抑製作用的參數μ充分大時,此模型或者沒有正解,併且一箇半平凡晌非負解是全跼吸引的;或者模型的所有正解均由一箇極限問題決定.
연구료일류구유억제제화Beddington-DeAngelis공능반응항적비균균항화기모형.근거단조동력계통이론득도료정평형해적존재성.이용도이론、분기이론이급섭동이론,분석료억제제대계통정평형해급점근행위적영향.결과표명당체현억제작용적삼수μ충분대시,차모형혹자몰유정해,병차일개반평범상비부해시전국흡인적;혹자모형적소유정해균유일개겁한문제결정.
An unstirred chemostat model with inhibitor and Beddington-DeAngelis func-tional response is discussed. The existence of positive steady-state solutions is given by monotone system theory. The effects of the inhibitor are considered by making use of the degree theory, bifurcation theory and perturbation technique. It turns out that if the pa-rameter μ, which measures the effect of the inhibitor, is sufficiently large, either this model has no coexistence solution and a semitrivial global attractor, or all positive solutions of this model are governed by a limit problem.