Increased Regions of Stability for a Two-Delay Differential Equation

Start: 11/28/2012 - 4:15pm
End  : 11/28/2012 - 5:15pm


Joseph Mahaffy (San Diego State University)


Delay differential equations (DDEs) are used in a number of applications. Stability analysis of DDEs can be quite complex, particularly when multiple delays occur. We examine the scalar two-delay differential equation:
y ̇(t) = A y(t) + B y(t − 1) + C y(t − R).
The stability region for this DDE has some very interesting features that this talk will explore. There are four parameters, A, B, C, and R, which can be varied. The stability region can be disconnected in the BC-space though for fixed R the 3D stability surface in the ABC-parameter space is connected. One of the most intriguing features is that when R is rational, this stability surface becomes larger. We demonstrate how certain rational values of R significantly increase the stability region, then show this significance in a nonlinear application. Understanding the details of this analysis can help mathematical modelers appreciate sensitivity in their stability analysis and the complexity of numerical solutions as delays vary in a model with multiple delays.

Millikan 134, Pomona College

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