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

Vincent, U. E. and Nana-Nbendjo, B. R. and McClintock, P. V. E. (2013) Collective dynamics of a network of ratchets coupled via a stochastic dynamical environment. Physical Review E, 87 (2). ISSN 1539-3755

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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. DOI: 10.1103/PhysRevE.87.022913

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Journal Article
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Physical Review E
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22 Mar 2013 09:00
Last Modified:
21 Nov 2022 23:29