# Hopf bifurcation

Consider the scalar linear retarded equation (with infinite delay) $$x^{\prime}(t)=-ax(t)+b\int_{0}^{\infty}x(t-\tau)f(\tau)d\tau\;,$$ where $a,b\in\mathbb{R}$, $\tau\in\mathbb{R}^{+}$, and $f$ is an appropriate delay kernel. The book by Cushing covers a lot of these types of equations. I've always wondered why it doesn't make sense to talk about Hopf bifurcation in linear systems, for example. I know this is probably a trivial question, but I have to ask.

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