The link between coherence echoes and mode locking.

We investigate the appearance of sharp pulses in the mean field of Kuramoto-type globally-coupled phase oscillator systems. In systems with exactly equidistant natural frequencies, self-organized periodic pulsations of the mean field, called mode locking, have been described recently as a new collective dynamics below the synchronization threshold. We show here that mode locking can appear also for frequency combs with modes of finite width, where the natural frequencies are randomly chosen from equidistant frequency intervals.

Leap-frog patterns in systems of two coupled FitzHugh-Nagumo units.

We study a system of two identical FitzHugh-Nagumo units with a mutual linear coupling in the fast variables. While an attractive coupling always leads to synchronous behavior, a repulsive coupling can give rise to dynamical regimes with alternating spiking order, called leap-frogging. We analyze various types of periodic and chaotic leap-frogging regimes, using numerical path-following methods to investigate their emergence and stability, as well as to obtain the complex bifurcation scenario which organizes their appearance in parameter space.

Mode locking in systems of globally coupled phase oscillators.

We investigate the dynamics of a Kuramoto-type system of globally coupled phase oscillators with equidistant natural frequencies and a coupling strength below the synchronization threshold. It turns out that in such cases one can observe a stable regime of sharp pulses in the mean field amplitude with a pulsation frequency given by spacing of the natural frequencies. This resembles a process known as mode locking in lasers and relies on the emergence of a phase relation induced by the nonlinear coupling.