title: 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.
authors.affiliation: Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom. u.vincent@lancaster.ac.uk
authors.forename: U E
authors.initials: UE
authors.lastname: Vincent
authors.forename: B R
authors.initials: BR
authors.lastname: Nana-Nbendjo
authors.forename: P V E
authors.initials: PV
authors.lastname: McClintock
mesh_terms: D003198:Computer Simulation; D004735:Energy Transfer; D015233:Models, Statistical; D017711:Nonlinear Dynamics; D013269:Stochastic Processes