华南师范大学学报(自然科学版)
華南師範大學學報(自然科學版)
화남사범대학학보(자연과학판)
JOURNAL OF SOUTH CHINA NORMAL UNIVERSITY (NATURAL SCIENCE EDITION)
2014年
6期
16-22
,共7页
曹佳敏%温俊浩%翁佩萱
曹佳敏%溫俊浩%翁珮萱
조가민%온준호%옹패훤
反应扩散方程%先锋-顶级种群模型%平衡点%线性稳定性
反應擴散方程%先鋒-頂級種群模型%平衡點%線性穩定性
반응확산방정%선봉-정급충군모형%평형점%선성은정성
reaction-diffusion equation%pioneer and climax species competition model%constants equilibria%line-ar stability
研究扩散的先锋-顶级种群竞争模型的平衡态线性稳定性。所讨论的系统有4~6个平衡点,其中最多有2个正平衡点,其动力学性态十分丰富。运用线性化方法和特征根分析技巧等,对系统可能的各个常数平衡点的线性稳定性进行分析并给出每个平衡点稳定的充分条件或充分必要条件,最后举例说明结论的应用并进行了数值模拟和讨论。
研究擴散的先鋒-頂級種群競爭模型的平衡態線性穩定性。所討論的繫統有4~6箇平衡點,其中最多有2箇正平衡點,其動力學性態十分豐富。運用線性化方法和特徵根分析技巧等,對繫統可能的各箇常數平衡點的線性穩定性進行分析併給齣每箇平衡點穩定的充分條件或充分必要條件,最後舉例說明結論的應用併進行瞭數值模擬和討論。
연구확산적선봉-정급충군경쟁모형적평형태선성은정성。소토론적계통유4~6개평형점,기중최다유2개정평형점,기동역학성태십분봉부。운용선성화방법화특정근분석기교등,대계통가능적각개상수평형점적선성은정성진행분석병급출매개평형점은정적충분조건혹충분필요조건,최후거례설명결론적응용병진행료수치모의화토론。
The linear stability of equilibria for a diffused pioneer and climax species competition model is dis-cussed.This system has at least 4 and at most 6 equilibria with two possible positive equilibria, and thus the dy-namical behaviors are very rich.All the constant equilibria of the model are given in the second section, and then the linear stabilities of these equilibria are analyzed in the third section.The sufficient condition or sufficient and necessary condition of the stability for every equilibrium is given.The linearization method is used accompanied with the eigenvalue skill.At last, an example is given to illustrate the application of the results with numerical sim-ulation and conclusion discussion.