Collective dynamics of a network of ratchets coupled via a stochastic dynamical environment

Abstract

We investigate the collective dynamics of a network of inertia particles diffusing in a ratchet potential and interacting indirectly through their stochastic dynamical environment. We obtain analytically the condition for the existence of a stable collective state, and we show that the number N of particles in the network, and the strength k of their interaction with the environment, play key roles in synchronization and transport processes. Synchronization is preceded by symmetry-breaking associated with double-resonance oscillations and is shown to be strongly dependent on the network size: convergence to the synchronization manifold occurs much faster with a large network. For small networks, increasing the noise level enhances synchronization in the weakly coupled regime, while particles in a large network are weakly synchronized. Similarly, in the strongly coupled regime, particles in a small network are weakly synchronized; whereas the synchronization is strong and robust against noise when the network-size is large. Small and moderate networks maximize and stabilize efficient transport. Although the dynamics for larger networks is highly correlated, the transport current is erratic.

Temperature-induced activation and reversal of the relativistic ratchet currents on a graphene chip model

“…Not much has been done concerning the ratchet transport of interacting particles, where the collective dynamics may arise. We acknowledge the elastically coupled particles in a periodically fashing ratchet [49], the optimal transport of two elastically interacting particles in the parameter space [50], the hydrodynamic interactions between Brownian particles influencing the performance of a fluctuating ratchet [51] and, finally, the collective transient ratchet transport induced by many elastically interacting particles [52] and the collective dynamics of a network of ratchets coupled via a stochastic dynamical environment [53].…”

Dynamical Response of Particles in Asymmetric Ratchet Potential

“…For instance, Nana-Nbendjo et al [24] carried out an analytical study of its stability, examined resonance oscillations for two indirectly-coupled ratchets and reported the existence of multi-resonance. In a very recent and related work, Vincent et al [25] considered the collective dynamics of a network of particles in a ratchet potential and observed collective resonance. Remarkably, these works were mainly concerned with numerical results, with no recourse to the analytical treatment of the frequency response.…”