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On Instability in Componentwise Partitioned Systems

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Abstract

Asymptotic behavior of solutions of componentwise partitioned systems is studied. Sufficient conditions in terms of the properties of asymptotic localization of the right-hand sides of equations under which the solutions are not logarithmically bounded are obtained. Results obtained by the application of the developed theory to the generalized Lotka–Volterra system are presented. In the Appendix, auxiliary issues of the theory related to properties of convex sets are discussed.

Keywords:

componentwise partitioned system asymptotic localization of Malthusian vector function logarithmic boundedness of solutions Lotka–Volterra system. 

Notes

ACKNOWLEDGMENTS

This work was supported by the Russian Foundation for Basic Research, project no. 15-07-06947.

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Dorodnicyn Computing Center, Federal Research Center “Computer Science and Control,” Russian Academy of SciencesMoscowRussia

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