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Conditions for Absolute Delay Stability

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Tuesday, March 21, 2023 4pm to 5pm

Fashion by Marina Debris

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Tuesday, March 21, 2023 4pm to 5pm

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Polly Yu, Harvard University

Some chemical and biological models use a system of delay differential equations (DDEs) instead of the usual ODEs, with the assumption of instantaneous consumption but delayed production. Stability of DDEs can be determined by solutions to a transcendental equation (similar to locating the roots of the characteristic equations in the case of ODEs). In this talk, I will motivate and introduce delay models for chemical systems, and provide a sufficient algebraic condition that guarantees its delay stability independent of parameters (i.e., absolute delay stability). In particular, this condition also implies asymptotic stability when there is no delay in the system. Time permitting, I will introduce a graph-theoretic condition for absolute delay stability that in certain cases is easier to check. This is joint work with Gheorghe Craciun, Maya Mincheva, Casian Pantea.

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