Time delay-induced instabilities and Hopf bifurcations in general reaction-diffusion systems (Q1941057)

From authors' abstract: The distribution of the roots of a second order transcendental polynomial is analyzed, and is used to find the purely imaginary eigenvalue 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 a system of ODEs with delay effects. Examples from biochemical reaction and predator-prey models are analyzed using the new techniques.