A nonconstant trajectory approaching a <stable focus> winds around it infinitely often. Its $a$ coordinate therefore changes sign repeatedly near zero. Since the <biological population> profile must remain nonnegative, such a trajectory cannot represent the wave. The only nonnegative trajectory avoiding that winding at the origin would be the equilibrium itself, which cannot join the populated state. Thus $\boxed{\text{no nonnegative front for }0<c<2\eta}$.

Solution

Past exam of the topics in applied mathematics course of the University of Oxford / 2007 / A / 3 / i / c / Solution

 Solution (source code)