title: Superlinearly scalable noise robustness of redundant coupled dynamical systems.
abstract: We illustrate through theory and numerical simulations that redundant coupled dynamical systems can be extremely robust against local noise in comparison to uncoupled dynamical systems evolving in the same noisy environment. Previous studies have shown that the noise robustness of redundant coupled dynamical systems is linearly scalable and deviations due to noise can be minimized by increasing the number of coupled units. Here, we demonstrate that the noise robustness can actually be scaled superlinearly if some conditions are met and very high noise robustness can be realized with very few coupled units. We discuss these conditions and show that this superlinear scalability depends on the nonlinearity of the individual dynamical units. The phenomenon is demonstrated in discrete as well as continuous dynamical systems. This superlinear scalability not only provides us an opportunity to exploit the nonlinearity of physical systems without being bogged down by noise but may also help us in understanding the functional role of coupled redundancy found in many biological systems. Moreover, engineers can exploit superlinear noise suppression by starting a coupled system near (not necessarily at) the appropriate initial condition.
authors.affiliation: Department of Physics, North Carolina State University, Raleigh, North Carolina 27695-8202, USA.
authors.forename: Vivek
authors.initials: V
authors.lastname: Kohar
authors.affiliation: Department of Physics, North Carolina State University, Raleigh, North Carolina 27695-8202, USA.
authors.forename: Behnam
authors.initials: B
authors.lastname: Kia
authors.affiliation: Physics Department, The College of Wooster, Wooster, Ohio 44691, USA.
authors.forename: John F
authors.initials: JF
authors.lastname: Lindner
authors.affiliation: Department of Physics, North Carolina State University, Raleigh, North Carolina 27695-8202, USA.
authors.forename: William L
authors.initials: WL
authors.lastname: Ditto