Showing papers by "Hiroya Nakao published in 2015"
TL;DR: The original analysis by Turing to networks is extended and applied to ecological metapopulations with dispersal connections between habitats, finding such oscillatory instabilities for all possible food webs with three predator or prey species.
Abstract: As shown by Alan Turing in 1952, differential diffusion may destabilize uniform distributions of reacting species and lead to emergence of patterns. While stationary Turing patterns are broadly known, the oscillatory instability, leading to traveling waves in continuous media and sometimes called the wave bifurcation, remains less investigated. Here, we extend the original analysis by Turing to networks and apply it to ecological metapopulations with dispersal connections between habitats. Remarkably, the oscillatory Turing instability does not lead to wave patterns in networks, but to spontaneous development of heterogeneous oscillations and possible extinction of species. We find such oscillatory instabilities for all possible food webs with three predator or prey species, under various assumptions about the mobility of individual species and nonlinear interactions between them. Hence, the oscillatory Turing instability should be generic and must play a fundamental role in metapopulation dynamics, providing a common mechanism for dispersal-induced destabilization of ecosystems.
42 citations
TL;DR: In this paper, the phase description of oscillatory convection in a cylindrical Hele-Shaw cell is formulated as a phase reduction method for limit-torus solutions in infinite-dimensional dynamical systems.
26 citations
TL;DR: Kurebayashi et al. as discussed by the authors proposed a generalized phase reduction method for weakly driven limit-cycle oscillators, which has played an important role in theoretical analysis of synchro-nization phenomena.
Abstract: The phase reduction method is a dimension reduction method for weakly driven limit-cycle oscillators, which has played an important role in the theoretical analysis of synchro- nization phenomena. Recently, we proposed a generalization of the phase reduction method [W. Kurebayashi et al., Phys. Rev. Lett. 111, 2013]. This generalized phase reduction method can robustly predict the dynamics of strongly driven oscillators, for which the conventional phase reduction method fails. In this generalized method, the external input to the oscillator should be properly decomposed into a slowly varying component and remaining weak fluctua- tions. In this paper, we propose a simple criterion for timescale decomposition of the external input, which gives accurate prediction of the phase dynamics and enables us to systematically apply the generalized phase reduction method to a general class of limit-cycle oscillators. The validity of the criterion is confirmed by numerical simulations.
12 citations
TL;DR: Kurebayashi et al. as mentioned in this paper proposed a generalized phase reduction method for weakly driven limit-cycle oscillators, which has played an important role in theoretical analysis of synchro-nization phenomena.
Abstract: The phase reduction method is a dimension reduction method for weakly driven limit-cycle oscillators, which has played an important role in the theoretical analysis of synchro- nization phenomena. Recently, we proposed a generalization of the phase reduction method [W. Kurebayashi et al., Phys. Rev. Lett. 111, 2013]. This generalized phase reduction method can robustly predict the dynamics of strongly driven oscillators, for which the conventional phase reduction method fails. In this generalized method, the external input to the oscillator should be properly decomposed into a slowly varying component and remaining weak fluctua- tions. In this paper, we propose a simple criterion for timescale decomposition of the external input, which gives accurate prediction of the phase dynamics and enables us to systematically apply the generalized phase reduction method to a general class of limit-cycle oscillators. The validity of the criterion is confirmed by numerical simulations.
7 citations
TL;DR: A method for controlling synchronization patterns of limit-cycle oscillators by common noisy inputs, i.e., by utilizing noise-induced synchronization, is proposed and confirmed by numerical simulations.
Abstract: We propose a method for controlling synchronization patterns of limit-cycle oscillators by common noisy inputs, i.e., by utilizing noise-induced synchronization. Various synchronization patterns, including fully synchronized and clustered states, can be realized by using linear filters that generate appropriate common noisy signals from given noise. The optimal linear filter can be determined from the linear phase response property of the oscillators and the power spectrum of the given noise. The validity of the proposed method is confirmed by numerical simulations.