= Phase locking
Phase locking is the maintenance of a fixed phase relation (possibly an integer combination of phases) between coupled oscillations, or between a pattern and imposed forcing. The following spatial-forcing example occurs in an <amplitude equation>. For a real-coefficient conjugately forced <amplitude equation>, $A=\rho e^{i\phi}$ obeys $\rho_T=(\mu+\beta\cos2\phi-\lambda\rho^2)\rho$ and $\phi_T=-\beta\sin2\phi$. Thus forcing selects stable phases $0,\pi$ for $\beta>0$ and $\pi/2,3\pi/2$ for $\beta<0$, when a nonzero amplitude exists. At $\beta=0$ this pinning disappears and the phase is neutral.
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