On Instability in Componentwise Partitioned Systems

Resumo

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.