Transients in multivariable dynamical systems depend on which parameter is switched as illustrated in lasers

Canard resonance: on noise-induced ordering of trajectories in heterogeneous networks of slow-fast systems

We analyse the dynamics of a network of semiconductor lasers coupled via their mean intensity through a non-linear optoelectronic feedback loop. We establish experimentally the excitable character of a single node, which stems from the slow-fast nature of the system, adequately described by a set of rate equations with three well separated time scales. Beyond the excitable regime, the system undergoes relaxation oscillations where the nodes display canard dynamics. We show numerically that, without noise, the coupled system follows an intricate canard trajectory, with the nodes switching on one by one. While incorporating noise leads to a better correspondence between numerical simulations and experimental data, it also has an unexpected ordering effect on the canard orbit, causing the nodes to switch on closer together in time. We find that the dispersion of the trajectories of the network nodes in phase space is minimized for a non-zero noise strength, and call this phenomenon canard resonance.

Identifying physical properties of a CO2 laser by dynamical modeling of measured time series

We estimate internal parameters of a Q-switched CO2 laser by fitting trajectories of the four-level model to measured scalar time series. The four-level model is a five-dimensional nonlinear system of ordinary differential equations. A multiple shooting technique is used to construct the unobserved time courses of the population densities and to reveal the dependence of the parameters on the excitation current. For excitations barely above the laser threshold large pulse variations are identified as an effect of small variations of the pump parameter.