Title: Harmless off-diagonal delays in delay differential equations

Authors: Ravinder Kumar; Yogendra Singh

Addresses: Department of Mathematics, Dayalbagh Educational Institute (Deemed University), Dayalbagh, Agra, U.P., 282005, India ' Department of Mathematics, Dayalbagh Educational Institute (Deemed University), Dayalbagh, Agra, U.P., 282005, India

Abstract: Systems of linear differential equations with delays in the off-diagonal entries and constant coefficients are considered. Sufficient conditions for the delays to be harmless and for the preservation of instability are obtained. This is applied to systems of two preys and two mutualistic predators with time delays due to gestation, and to a time delay model with increasing returns.

Keywords: time delays; harmless delays; normal matrix; diagonally dominant matrix; Gershgorin theorem; Implicit Function Theorem; mutualism; system with increasing returns.

DOI: 10.1504/IJDSDE.2022.127809

International Journal of Dynamical Systems and Differential Equations, 2022 Vol.12 No.5, pp.402 - 411

Accepted: 05 Aug 2021
Published online: 19 Dec 2022 *

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