title: Dynamical robustness of coupled heterogeneous oscillators.
abstract: We study tolerance of dynamic behavior in networks of coupled heterogeneous oscillators to deterioration of the individual oscillator components. As the deterioration proceeds with reduction in dynamic behavior of the oscillators, an order parameter evaluating the level of global oscillation decreases and then vanishes at a certain critical point. We present a method to analytically derive a general formula for this critical point and an approximate formula for the order parameter in the vicinity of the critical point in networks of coupled Stuart-Landau oscillators. Using the critical point as a measure for dynamical robustness of oscillator networks, we show that the more heterogeneous the oscillator components are, the more robust the oscillatory behavior of the network is to the component deterioration. This property is confirmed also in networks of Morris-Lecar neuron models coupled through electrical synapses. Our approach could provide a useful framework for theoretically understanding the role of population heterogeneity in robustness of biological networks.
authors.affiliation: Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan and Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan and Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan.
authors.forename: Gouhei
authors.initials: G
authors.lastname: Tanaka
authors.affiliation: Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan.
authors.forename: Kai
authors.initials: K
authors.lastname: Morino
authors.affiliation: Graduate School of Engineering, Osaka Prefecture University, Sakai 599-8531, Japan.
authors.forename: Hiroaki
authors.initials: H
authors.lastname: Daido
authors.affiliation: Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan and Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 113-8656, Japan and Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan.
authors.forename: Kazuyuki
authors.initials: K
authors.lastname: Aihara
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000818:Animals; D001683:Biological Clocks / Q000502:physiology*; D003198:Computer Simulation; D025461:Feedback, Physiological / Q000502:physiology; D006801:Humans; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D009991:Oscillometry / Q000379:methods*; D009435:Synaptic Transmission / Q000502:physiology*