Session S12 - Delay and functional differential equations and applications

Tuesday, July 13, 15:25 ~ 16:00 UTC-3

Analysis of stability in neutral delay differential equations through different approaches

Griselda Rut Itovich

Universidad Nacional de Río Negro, Argentina   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

This work is about the analysis of equilibrium stability in certain neutral delay differential equations (ndde), which include several bifurcation parameters. In the considered cases, the associated characteristic equation is an exponential polynomial one with a principal term, so some Pontryagin results [1,2] are a convenient tool to locate its roots. Then, it is possible to set up certain regions in the parameter space where asymptotic stability can be guaranteed. Besides, the outcomes are all in agreement with those coming from a sophisticated application of the Nyquist stability criterion (based on the Cauchy's argument principle) and also with others found in the literature, related with some real systems modelled by ndde.

References

[1] Bellman R. and Cooke, K. Differential-Difference Equations, Academic Press, New York, 1963.

[2] Pontryagin, L. S. On the zeros of some elementary transcendental functions, American Math. Society Translations 21 (1), pp. 95-110, 1955.

Joint work with Franco Sebastián Gentile (Universidad Nacional del Sur, Argentina) and Jorge Luis Moiola (Universidad Nacional del Sur, Argentina).

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