title: Control of collective network chaos.
abstract: Under certain conditions, the collective behavior of a large globally-coupled heterogeneous network of coupled oscillators, as quantified by the macroscopic mean field or order parameter, can exhibit low-dimensional chaotic behavior. Recent advances describe how a small set of "reduced" ordinary differential equations can be derived that captures this mean field behavior. Here, we show that chaos control algorithms designed using the reduced equations can be successfully applied to imperfect realizations of the full network. To systematically study the effectiveness of this technique, we measure the quality of control as we relax conditions that are required for the strict accuracy of the reduced equations, and hence, the controller. Although the effects are network-dependent, we show that the method is effective for surprisingly small networks, for modest departures from global coupling, and even with mild inaccuracy in the estimate of network heterogeneity.
authors.affiliation: Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain.
authors.forename: Alexandre
authors.initials: A
authors.lastname: Wagemakers
authors.affiliation: School of Physics, Astronomy, and Computational Sciences and The Krasnow Institute for Advanced Study, George Mason University, Fairfax, Virginia 22030, USA.
authors.forename: Ernest
authors.initials: E
authors.lastname: Barreto
authors.affiliation: Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain.
authors.forename: Miguel A F
authors.initials: MA
authors.lastname: Sanjuán
authors.affiliation: School of Physics, Astronomy, and Computational Sciences and The Krasnow Institute for Advanced Study, George Mason University, Fairfax, Virginia 22030, USA.
authors.forename: Paul
authors.initials: P
authors.lastname: So
mesh_terms: D000465:Algorithms; D004581:Electronics; D009415:Nerve Net / Q000502:physiology; D009474:Neurons / Q000502:physiology; D017711:Nonlinear Dynamics