Description:
<jats:p>We examine the effect of periodic and discrete perturbations on the phase of an oscillatory chemical reaction system near a Hopf bifurcation. Discrete perturbations reset the phase of the oscillation and periodic perturbations entrain the frequency of the oscillation for perturbation frequencies in a small range about each rational multiple of the natural frequency. These phase responses may be determined from time series of a single essential species. The new phase resulting from discrete perturbations and the relative phase between the oscillation and the forcing of an entrained oscillation are described by the same response function, which is a simple sinusoid. We show that for single species perturbations, the amplitude and phase offset of this response function equal the magnitude and the argument, respectively, of the corresponding component of the adjoint eigenvector of the Jacobi matrix (that corresponds to a pure imaginary eigenvalue). These phase response methods are simpler than quenching studies for determining the adjoint eigenvectors, and in addition yield the local isochrons of the periodic orbit.</jats:p>