Session S12 - Delay and functional differential equations and applications

Wednesday, July 21, 16:35 ~ 17:10 UTC-3

Chaotic behavior in a functional differential equation

Sergei Trofimchuk

Universidad de Talca , Chile   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

Differential equations with maxima can be regarded as a special subclass of differential equations with state-dependent lags. This kind of delay equations and related differential inequalities are known mainly due to the Halanay inequality and Myshkis-Yorke 3/2-stability theorems [1,2,3]. These equations also appear in a natural way in applications coming from the real world: one of them will be analysed in our talk. For this particular application, we prove the existence of solutions with complicated behaviour and discuss their relevance to the original real world model.

References:

1. N. Bantsur and E. Trofimchuk, Existence and stability of the periodic and almost periodic solutions of quasilinear systems with maxima, Ukrainian Math. J., 50 (1998), 847-856.

2. A. Ivanov, E. Liz and S. Trofimchuk, Halanay inequality, Yorke 3/2 stability criterion, and differential equations with maxima, Tohoku Mathematical Journal, 54 (2002) 277--295.

3. M. Pinto and S. Trofimchuk, Stability and existence of multiple periodic solutions for a quasilinear differential equation with maxima, Proc. Roy. Soc. Edinburgh Sect. A, {130} (2000), 1103-1118.

Joint work with Eduardo Liz (Universidade de Vigo, Spain) and Elena Trofimchuk (Igor Sikorsky Kyiv Polytechnic Institute, Ukraine).

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