一类扩展的协作竞争模型及其定性分析  

An Extended Mutualism-competition Model and its Qualitative Analysis

作　　者：吴红[1] 王远世[1] 

机构地区：[1]中山大学数学与计算科学学院,广东广州510275

出　　处：《中山大学学报（自然科学版）》2008年第5期11-13,17,共4页Acta Scientiarum Naturalium Universitatis Sunyatseni

基　　金：国家自然科学基金资助项目(10771223)

摘　　要：将已有文献中一类特殊的两种群协作竞争模型扩展到一般的多种群协作竞争模型。证明在一般的两种群协作竞争模型中,竞争种群在低密度时的相互协作能促进双方的共生,并能提高其环境容纳量,从而证明并拓展了已有结论;同时,完整分析一类具体的两种群协作竞争模型,证明该系统不存在周期解,并从定性与定量两方面揭示了协作关系在促进竞争者共生及环境容纳量提升方面的内在机理,深化了已有结论。A previous competition and mutualism model of two species is extended to a general competition and mutualism model of multiple species. By the analysis of the general competition and mutualism model of two species, it is proved that mutualism promotes coexistence and carrying capacities of the competitors. The mechanism that how mutualism promotes coexistence and carrying capacities of the competitors is shown by analyzing a special competition and mutualism model. It is also shown that both the species benefit from the mutualism at low density.

关 键 词：种群协作 竞争模型 周期解 稳定性 

分 类 号：O175.13[理学—数学]