We consider the dynamical behavior of coupled oscillators with robust heteroclinic cycles between saddles that may be periodic or chaotic. We differentiate attracting cycles into types that we call phase resetting and free running depending on whether the cycle approaches a given saddle along one or many trajectories. At loss of stability of attracting cycling, we show in a phase-resetting exam...

There are two opposing hypotheses about the brain mechanisms underlying sensory event-related potentials (ERPs). One holds that sensory ERPs are generated by phase resetting of ongoing electroencephalographic (EEG) activity, and the other that they result fiom signal averaging of stimulus-evoked neural responses. We tested several contrasting predictions of these hypotheses by direct intracorti...

One of the characteristic features a stochastic process under resetting is that probability density converges to nonequilibrium stationary state (NESS). In addition, approach exhibits dynamical phase transition, which can be interpreted as traveling front separating spatial regions for has relaxed NESS from those where it not. establish existence transition by carrying out an asymptotic expansi...