Mode locking in systems of globally-coupled phase oscillators [article]

Richard Sebastian Eydam, Technische Universität Berlin, Technische Universität Berlin, Matthias Wolfrum
In systems of globally coupled phase oscillators with sufficiently structured natural frequencies, a new type of collective behavior is discovered that exists below the synchronization threshold. The solution type is distinguished by the appearance of sharp pulses in the mean field amplitude which imply a temporary high coherence among the phases. This is similar to a process known in lasers called mode locking that refers to the formation of optical pulsed by the interaction through a
more » ... optical medium. General features of mode-locked solutions of coupled phase oscillators are identified and a classification of the different solution types is provided. The ability of phase oscillator systems to perform mode locking is investigated with respect to the interaction function, the system size and the realization of the natural frequencies. It was found that higher harmonics in the Fourier series of the interaction function play an influential role in the self-organization of mode-locked solutions. For the simple sinusoidal coupling of the Kuramoto model, self-organized mode locking could not be observed, though, mode- locked solutions are found that coexist with phase turbulence. The chaotic transients that precede mode locking are examined with respect to the interaction function and the system size revealing a supertransient behavior of type-II, i.e. average transient length grows exponentially with the system size. The stability and bifurcation scenarios of mode-locked solutions are studied, displaying an involved picture of the local stability and revealing intermittency as the typical route from mode locking to phase turbulence. Close to the stability boundaries of mode-locked solutions, low-dimensional chaotic attractors can be found that maintain the pulsed behavior with a jittering of the inter-pulse intervals and pulse heights. In large oscillator ensembles with a modal structure in the natural frequencies, mode-locked solutions generally arise in a two-stage process of inner-modal synchronization and [...]
doi:10.14279/depositonce-8576 fatcat:n2c4uxqgtren3ocsdol7inygdi