Showing papers by "Hiroya Nakao published in 2012"

Global feedback control of Turing patterns in network-organized activator-inhibitor systems

Abstract: Results of the first systematic study on feedback control of nonequilibrium pattern formation in networks are reported. Effects of global feedback control on Turing patterns in network-organized activator-inhibitor system have been investigated. The feedback signal was introduced into one of the parameters of the system and was proportional to the amplitude of the developing Turing pattern. Without the control, the Turing instability corresponded to a subcritical bifurcation and hysteresis effects were observed. Sufficiently strong feedback control rendered, however, the bifurcation supercritical and eliminated the hysteresis effects.

Adjoint method provides phase response functions for delay-induced oscillations

Abstract: Limit-cycle oscillations induced by time delay are widely observed in various systems, but a systematic phase-reduction theory for them has yet to be developed. Here we present a practical theoretical framework to calculate the phase response function Z(θ), a fundamental quantity for the theory, of delay-induced limit cycles with infinite-dimensional phase space. We show that Z(θ) can be obtained as a zero eigenfunction of the adjoint equation associated with an appropriate bilinear form for the delay differential equations. We confirm the validity of the proposed framework for two biological oscillators and demonstrate that the derived phase equation predicts intriguing multimodal locking behavior.

Persistent fluctuations in synchronization rate in globally coupled oscillators with periodic external forcing.

Abstract: A system of phase oscillators with repulsive global coupling and periodic external forcing undergoing asynchronous rotation is considered. The synchronization rate of the system can exhibit persistent fluctuations depending on parameters and initial phase distributions, and the amplitude of the fluctuations scales with the system size for uniformly random initial phase distributions. Using the Watanabe-Strogatz transformation that reduces the original system to low-dimensional macroscopic equations, we show that the fluctuations are collective dynamics of the system corresponding to low-dimensional trajectories of the reduced equations. It is argued that the amplitude of the fluctuations is determined by the inhomogeneity of the initial phase distribution, resulting in system-size scaling for the random case.

Linear Analysis of the Corticothalamic Model with Time Delay

Abstract: Summary The corticothalamic Compact Model with time delay proposed by Kim and Robinson is analyzed focusing on the resting EEG, which can be described by the linear version of the model with white-noise input, under the assumption of spatial homogeneity and temporal steadiness. After discussing the availability and restriction of the model by comparing to the original Pre-Compact Model, a data analysis method for the resting EEG using the model is presented. The experimental results analyzed by the method suggest that the eye-closed state compared to the eye-open state would be characterized by enhanced corticothalamic feedback and depressed cortical excitation. The validity of the Reduced Equations derived in our previous paper is also investigated for the resting EEG, concluding that the Reduced Equations would be available with some restriction for the resting EEG, although the center manifold theory on which the Reduced Equations are based is justified at the edge of linear stability in principle.