The phase response curve of a limit cycle, or PRC, is a curve, defined over the period of the cycle, that expresses, at each time of that period, the effect of a small input vector on the cycle. In experimental circumstances, this may correspond to injected current, to the addition of more chemical agents, etc. A positive value means that the current cycle is shortened in time, a negative value means that the period is prolonged.
The PRC, as it is generally computed, is exact for infinitesimally small input vectors. In practice the maximum norm of the input vector would depend on the needed accuracy and the values of the system's state variables.
The derivative phase response curve or dPRC also has some very important applications.
For the concrete use of PRC and dPRC in synchronization studies in neural modeling,
we refer to [].
We have developed a new numerical method of computing the PRC and dPRC, that is specifically
aimed at the computation during continuation of limit cycles. For the computation of one single PRC it is not less efficient than
previous methods, but the advantage is less obvious. For details on this method,
we refer to [Govaerts and Sautois 2006a]. The standard method, which uses numerical integration
of the adjoint system, was implemented in XPPAUT []. MatCont and Cl_MatCont support the computation of the PRC and dPRC of limit cycles during continuation, using this new method.
The use in MatCont is easy: before starting the actual limit cycle continuation, the user can specify whether he wants to compute the PRC, dPRC or both, and he needs to indicate the input vector used. When a scalar is given as input, then the vector has this scalar as first entry and all other entries are zero. Then in separate plotting windows, for each computed step in limit cycle continuation, the PRC and/or dPRC are computed and plotted.