Special Session 4: Qualitative and Quantitative Features of Delay Differential Equations and Their Applications

On stability and asymptotics of equations and systems with distributed unbounded delays

Elena Braverman
University of Calgary
Canada
Co-Author(s):    Leonid Berezansky
Abstract:
Many differential equations of mathematical biology assume delayed production process and the instantaneous mortality. Introduction of delay can destabilize the unique positive equilibrium and even lead to chaos. However, for some types of equations and systems, lags in the reproduction term do not change stability properties. Consideration of variable, unbounded and distributed delays emphasizes robustness of this `absolute stability` property. Influence of an infinite, not just unbounded, delay is also outlined.