[PAST EVENT] Time Delay Induced Instabilities and Hopf Bifurcations

February 8, 2013
2pm - 3pm
Jones Hall, Room 301
200 Ukrop Way
Williamsburg, VA 23185Map this location
I will give a brief introduction of delayed differential
equations, and show that the question of stability of an equilibrium solution is equivalent to an algebraic equation with transcendental terms. Then I will show the new method of solving the purely imaginary eigenvalues of a transcendental characteristic equation with two transcendental terms.

The results are applied to the stability and associated Hopf bifurcation of a constant equilibrium of a general reaction-diffusion system or ordinary differential equation with delay effects. Examples from chemical reaction and predator-prey models are analyzed using the new techniques. In particular the stability and associate Hopf bifurcation of a Gierer-Meinhardt system with the gene expression time delays is analyzed by using our method.

This is a joint work with Shanshan Chen, and Junjie Wei. The talk is accessible to advanced undergraduate students.