The breathing dynamics often change in time and cause different variations in the cardiorespiratory interaction. There exist various breathing patterns, among them one critically important is the variability of the breathing frequency. We investigated the respiratory and the coupled cardiorespiratory system under controlled time-varying breathing patterns. Four breathing scenarios were used for this: spontaneous breathing, one where the subjects changed their breathing frequency according to linear ramp law, another according to a sine law and third according to an aperiodic predefined law. We introduced a framework of variability measures to trace and quantify the effect from the time-varying breathing perturbations. In particular, we studied intra-subject time-average variability, inter-subject subject-average variability and residual variability. These variability measures were estimated from the coupling strength and the similarity of coupling functions, for which we used methods specifically able to follow the time-evolving dynamics – the time–frequency wavelet transform and the adaptive dynamical Bayesian inference. The results demonstrated that the coupling and similarity were significantly greater in controlled, compared to free spontaneous breathing in many cases (p<0.0083). There were differences also among different controlled breathing regimes, and they appear both for intra-subject and inter-subject analysis. However, when the specific breathing perturbation is taken out, the results for the residual variability and the averaged coupling functions showed that the underlying interaction mechanisms remain invariant and not significantly different from spontaneous breathing (p>0.0083). This variability framework carries implications and can be applied more generally to other coupled oscillators and networks.