题目: Time Delay Induced Instabilities and Hopf Bifurcations
摘要: 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 generalreaction-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.
English
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