Ageing in Excitable and Oscillatory Systems

We consider classical nonlinear oscillators like rotators and Kuramoto oscillators on hexagonal lattices of small or intermediate size. When the coupling between these elements is repulsive and the bonds are frustrated, we observe coexisting states, each one with its own basin of attraction. For special lattices sizes the multiplicity of stationary states gets extremely rich. When disorder is introduced into the system by additive or multiplicative noise, we observe a noise-driven migration of oscillator phases in a rather rough potential landscape. Upon this migration, a multitude of different escape times from one metastable state to the next is generated [1]. Based on these observations, it does not come as a surprise that the set of oscillators shows physical ageing. Physical ageing is more specific than biological ageing. It is characterized by non-exponential relaxation after a perturbation, breaking of time-translation invariance, and dynamical scaling. When our system of oscillators is quenched from the regime of a unique fixed point toward the regime of multistable limit-cycle solutions, the autocorrelation functions depend on the waiting time after the quench, so that time translation invariance is broken, and dynamical scaling is observed for a certain range of time scales [2]. We point to open questions concerning the relation between physical and biological ageing. At first, such a relation seems to exist only on a superficial semantic level.

[1] F.Ionita, D.Labavic, M.Zaks, and H.Meyer-Ortmanns, Eur. Phys.J.B 86(12), 511 (2013). [2] F.Ionita, H.Meyer-Ortmanns, Phys.Rev.Lett.112, 094101 (2014).