Abstract
In this paper, we study dynamical Bifurcation of the Burgers-Fisher equation. We show that the equation bifurcates an invariant set $\mathcal{A}_n (\beta)$ as the control parameter $\beta$ crosses over $n^2$ with $n \in \mathbb{N}$. It turns out that $\mathcal{A}_n (\beta)$ is homeomorphic to $S^1$, the unit circle.
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