Classification of Stably Dissipative 3D Lotka-Volterra Systems and Their Necessary and Sufficient Condition for Being Stably Dissipative |
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| Authors: | LIU Hai-ying |
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| Affiliation: | School of Public Adminitration, Southwest Jiaotong University, Chengdu 610031, China;School of Finance and Economics, Yunnan University of Finance and Economics, Kunming 650021, China |
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| Abstract: | By introducing the concepts of stably dissipative matrix and graph, some criteria conditions for stably dissipative matrix were given. On this basis, the method of graph theory was used to classify all stably dissipative 3D Lotka-Volterra systems and five classes of maximal stably dissipative graphs were obtained for these systems. Finally, the necessary and sufficient condition of being stably dissipative for every class was studied, under which the matrix associated with the graph is stably dissipative. |
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| Keywords: | Lotka-Voterra system Stably dissipative Reduced graph Equilibrium point |
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