Physical Aging in Oscillatory and Excitable Systems
Final Report Abstract
Based on the existence of frustrated bonds, multistability is induced in oscillatory and excitable systems, similarly to spin glasses, whereas the attractor space here is much more versatile than in spin glasses. The three characteristic features of physical aging have been identified in repulsively coupled classical oscillators when the rich attractor space is explored via noise. If the source of disorder is replaced by a distribution in the natural frequencies, the attractor space is traversed by deterministic periodic orbits, whose periods range from the order of the natural frequencies to orders of magnitude longer ones. For these so-called long-period orbits, visible in the Kuramoto order parameter, we identified a striking self-similarity in the periodically repeating sequence of temporary patterns of phase-locked motion. This phenomenon of self-similarity of a whole dynamical sequence deserves further exploration in future work. Although time-translation invariance of autocorrelation functions is broken due to the occurrence of long transients, which usually precede the approach of the stationary long-period orbits, universal scaling could not be identified. Differently from spin glasses or other materials that show physical aging, it seems not to be an accumulation of “obstacles” that prevents the fast return to the original state and leads to slow relaxation times after a strong perturbation. Instead, the system can more or less rapidly approach other attractors when the perturbation is turned off. In spite of these differences, it seems worthwhile to further pursue the impact of long transients, long periods, and more general glasslike features on the biological properties of systems like the circadian clock or the cytoskeleton. These systems are suitable candidates for studying this impact, as both are known to display glasslike properties in common with physical aging and to play an important role in biological aging. In systems of large coupled so-called bistable frustrated units we identified a simple mechanism to control the duration of collective oscillations, starting and ending in phases that are characterized by collective approaches to fixed point(s). The control is possible via the tuning of a single bifurcation parameter. This is so simple that it may have a counterpart in the morphogenesis of the zebra fish, where temporary genetic oscillations generate such patterns. The temporary patterns depend on the variation speed of the bifurcation parameter. Due to this external tuning, the system becomes non-autonomous and inherently challenging in view of an analytic understanding of these features. So far they were established in the numerical integration of the differential equations. While tuning the single bifurcation parameter from the phase of collective oscillations to the phase of collective fixed points, we zoomed into the arrest of the synchronized oscillations. This arrest can proceed via the formation of bubbles as in nucleation processes, or via ordered and extended structures like the arms of spirals, depending on the seeds of arrest. We identified the seeds of arrest as the sites with the smallest amplitudes of oscillations. In the absence of concepts such as the bulk free energy, the interface tension and their mutual competition, we explained these phenomena in terms of the longest time that phase trajectories spend in the vicinity of the future attractor in the new phase. The work on six-species games with predation reproduced the numerically observed sequence of events in terms of a bifurcation analysis: Starting from six randomly distributed species, two domains with three species each form with rock-paper-scissors played inside the domains, followed by the subsequent extinction of one of the domains and a single species surviving in the end. The interface between the domains is unstable, because the corresponding 6-species coexistence-fixed point is unstable. This work gave first hints on how to design games of winnerless competition via a suitable choice of the eigenvalues of the Jacobian in a linear stability analysis.
Publications
- Long-range response to transmission line disturbances in DC electricity grids, Eur. Phys. J. Special Topics (EPJ ST) on “Resilient power grids and extreme events”, 223, 2517-2525 (2014)
D. Labavic, R. Suciu, H. Meyer-Ortmanns and S. Kettemann
(See online at https://doi.org/10.1140/epjst/e2014-02273-0) - Networks of coupled circuits: From a versatile toggle switch to collective coherent behavior, Chaos 24, 043118 1-14 (2014)
D. Labavic and H. Meyer-Ortmanns
(See online at https://doi.org/10.1063/1.4898795) - Physical Aging of Classical Oscillators, Phys. Rev. Lett.112, 094101 (2014)
F. Ionita and H. Meyer-Ortmanns
(See online at https://doi.org/10.1103/PhysRevLett.112.094101) - On the arrest of synchronized oscillations, Europhys.Lett. 109, 10 001-p1-p6 (2015)
D. Labavic and H. Meyer-Ortmanns
(See online at https://doi.org/10.1209/0295-5075/109/10001) - Rock-paper-scissors played within competing domains in predator-prey games, J. Stat. Mech., 113402~1-21 (2016)
D. Labavic and H. Meyer-Ortmanns
(See online at https://doi.org/10.1088/1742-5468/2016/11/113402) - A hierarchical heteroclinic network: Controlling the time evolution along its paths
M. Voit and H. Meyer-Ortmanns
- Breaking of time-translation invariance in Kuramoto dynamics with multiple time scales, Europhys. Lett.118, 40006 (2017)
S. Esmaeili, D. Labavic, M. Pleimling and H. Meyer-Ortmanns
(See online at https://doi.org/10.1209/0295-5075/118/40006) - Long-period clocks from short-period oscillators, Chaos 27, 083103 (2017)
D. Labavic and H. Meyer-Ortmanns
(See online at https://doi.org/10.1063/1.4997181) - Temporal self-similar synchronization patterns and scaling in repulsively coupled oscillators, Indian Academy of Sciences Conference Proceedings 1(1), 101-108 (2017)
D. Labavic and H. Meyer-Ortmanns
(See online at https://dx.doi.org/10.29195/iascs.01.01.0019)
