Arts & Sciences Events
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Arts & Sciences
[PAST EVENT] Time Delay Induced Instabilities and Hopf Bifurcations
February 8, 2013
2pm - 3pm
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.
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.