| Abstract: |
| The concepts of isochrons and asymptotic phase, originally introduced in the context of mathematical biology, refer to the timing properties of robust self-sustained oscillations (limit cycles) occurring in any physical or man-made system. In the context of a tunable photonic oscillator, specifically an optically injected semiconductor laser where two semiconductor lasers are coupled in a controller-follower configuration, these notions can be mathematically established through the Fourier averages of an observable quantity such as the intensity of the system. The introduction of these concepts into the study of the original system when subject to periodic external perturbation yields an efficient reduction of the three-dimensional, or in general the multidimensional, system to a one-dimensional circle map. This reduction in dimensionality enables easier analysis and interpretation of the system`s behavior. In this work, the dynamical behavior of the circle map---determined by the phase response of the limit-cycle oscillation---corresponding to different kinds of input stimuli is numerically investigated. Thus, conditions for resonant synchronization resulting in desirable outputs of the original nonlinear system of ordinary differential equations can be obtained towards potential practical applications related to photonic signal-processing units. |
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