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Classification and Dynamics of Stably Dissipative Three-Dimensional Lotka-Volterra Systems

  • Conference paper
High Performance Networking, Computing, and Communication Systems (ICHCC 2011)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 163))

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Abstract

By introducing the concepts of stably dissipative matrix and graph, some criteria conditions for stably dissipative matrix are 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. Simultaneously, 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. Then, the corresponding dynamical properties of stably dissipative three-dimensional Lotka-Volterra system for each class are investigated. Finally, through the possible changes between the dynamical properties of different classes of Lotka-Volterra systems, the corresponding biological significance and control strategies under perturbations are discussed.

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Author information

Authors and Affiliations

  1. Law and Politics School, Ocean University of China, Qingdao, 266100, China

    Liu Haiying

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  1. Liu Haiying
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Editors and Affiliations

  1. Huazhong Normal University, Luoyu Road 452, 430079, Wuhan, Hubei, China

    Yanwen Wu

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Haiying, L. (2011). Classification and Dynamics of Stably Dissipative Three-Dimensional Lotka-Volterra Systems. In: Wu, Y. (eds) High Performance Networking, Computing, and Communication Systems. ICHCC 2011. Communications in Computer and Information Science, vol 163. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25002-6_22

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  • DOI: https://doi.org/10.1007/978-3-642-25002-6_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25001-9

  • Online ISBN: 978-3-642-25002-6

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