ESS,NIS and GIS for matrix games in n‐species systems |
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Authors: | Zhanwen Ding Yanxiang Peng Honglin Yang |
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Institution: | Faculty of Science, Jiangsu University, Zhenjiang 212013, People's Republic of China |
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Abstract: | In this paper, we discuss the concepts of evolutionarily stable strategy (ESS), neighborhood invader strategy (NIS) and global invader strategy (GIS) in n‐species systems. We give their definitions both on system level and species level. Although the definition on system level and that on species level are apparently different, it is found that they are equivalent to one another. About the relationships among an ESS, an NIS and a GIS for n‐species systems, we obtain the results similar to the ones for single species models: a GIS must be an NIS; an NIS must be an ESS; an ESS may not be a GIS; a GIS must be unique. The stability in the frequency dynamics with two phenotypes is also considered and the global stability of a GIS is shown. Copyright © 2010 John Wiley & Sons, Ltd. |
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Keywords: | evolutionarily stable strategy neighborhood invader strategy global invader strategy matrix game n‐species system dynamical stability |
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