Papers

Papers

Google Scholar / ResearchGate / ORCID / researchmap

Submitted, in preparation, etc.

• Yuka Hashimoto, Masahiro Ikeda, Hiroya Nakao, and Yoshinobu Kawahara, "Data-driven operator-theoretic analysis of weak interactions in synchronized network dynamics", submitted.

• Wataru Kurebayashi, Takuto Yamamoto, Sho Shirasaka, and Hiroya Nakao, "Phase Reduction of Strongly Coupled Limit-Cycle Oscillators", submitted.

• Yuzuru Kato and Hiroya Nakao, "Turing instability in quantum activator-inhibitor systems", in press.

• Yuzuru Kato and Hiroya Nakao, "Quatum asymptotic phase reveals signatures of quantum synchronization", submitted (preprint).

Journal papers

• Jinjie Zhu and Hiroya Nakao,
  "Noise-tuned bursting in a Hedgehog burster",
  Front. Comput. Neurosci. 16:970643 [12 pages] (2022) (Journal).

• Norihisa Namura, Shohei Takata, Katsunori Yamaguchi, Ryota Kobayashi, and Hiroya Nakao,
  "Estimating asymptotic phase and amplitude functions of limit-cycle oscillators from time series data",
  Phys. Rev. E 106, 014204 [12 pages] (2022) (Journal).

• Yuzuru Kato and Hiroya Nakao,
  "A definition of the asymptotic phase for quantum nonlinear oscillators from the Koopman operator viewpoint",
  Chaos 32, 063133 [12 pages] (2022) (Journal).

• Jinjie Zhu, Yuzuru Kato, and Hiroya Nakao,
  "Phase dynamics of noise-induced coherent oscillations in excitable systems",
  Phys. Rev. Research 4, L022041 [6 pages] (2022) (Journal).

• Keisuke Taga, Yuzuru Kato, Yoshinobu Kawahara, Yoshihiro Yamazaki, and Hiroya Nakao,
  "Koopman spectral analysis of elementary cellular automata",
  Chaos 31, 103121 [15 pages] (2021) (Journal).

• Shohei Takata, Yuzuru Kato, and Hiroya Nakao,
  "Fast optimal entrainment of limit-cycle oscillators by strong periodic inputs via phase-amplitude reduction and Floquet theory",
  Chaos 31, 093124 [18 pages] (2021) (Journal).

• Yuzuru Kato, Jinjie Zhu, Wataru Kurebayashi, and Hiroya Nakao,
  “Asymptotic Phase and Amplitude for Classical and Semiclassical Stochastic Oscillators via Koopman Operator Theory”,
  Mathematics 2021, 9, 2188 [18 pages] (2021) (Journal).

• Yuzuru Kato, Anatoly Zlotnik, Jr-Shin Li, and Hiroya Nakao,
  “Optimization of periodic input waveforms for global entrainment of weakly forced limit-cycle oscillators”,
  Nonlinear Dynamics 105, 2247-2263 (2021). (Journal).

• Jinjie Zhu and Hiroya Nakao,
  “Stochastic periodic orbits in fast-slow systems with self-induced stochastic resonance”,
  Physical Review Research 3, 033070 [11 pages] (2021) (Journal).

• Hiroya Nakao, Katsunori Yamaguchi, Shingo Katayama, and Tatsuo Yanagita,
  "Sparse optimization of mutual synchronization in collectively oscillating networks",
  Chaos 31, 063113 [19 pages] (2021) (Journal).

• H. Nakao, "Phase and Amplitude Description of Complex Oscillatory Patterns in Reaction-Diffusion Systems", In: Stefanovska A., McClintock P.V.E. (eds) Physics of Biological Oscillators. Understanding Complex Systems. Springer, Cham, 2021. (Book).

• Yuzuru Kato and Hiroya Nakao,
  "Quantum coherence resonance",
  New J. Phys. 23, 043018 (2021) (Journal, PDF).

• Innocentio A. Loe, Hiroya Nakao, Yasuhiko Jimbo, and Kiyoshi Kotani,
  "Phase-reduction for synchronization of oscillating flow by perturbation on surrounding structure",
  J. Fluid Mech. 911, R2 (2021). (Journal, PDF).

• Yuzuru Kato and Hiroya Nakao,
  "Instantaneous phase synchronization of two decoupled quantum limit-cycle oscillators induced by conditional photon detection",
  Phys. Rev. Research 3, 013085 (2021). (Journal, PDF).

• Yuzuru Kato and Hiroya Nakao,
  "Enhancement of quantum synchronization via continuous measurement and feedback control",
  New J. Phys. 23, 013007 (2021). (Journal, PDF).

• Hiroya Nakao and Igor Mezic,
  "Spectral Analysis of the Koopman Operator for Partial Differential Equations",
  Chaos 30, 113131 (2020). (Journal, PDF)

• Kiyoshi Kotani, Yutaro Ogawa, Sho Shirasaka, Akihiko Akao, Yasuhiko Jimbo, and Hiroya Nakao,
  “Nonlinear phase-amplitude reduction of delay-induced oscillations”,
  Phys. Rev. Research 2, 033106 (2020). (Journal, PDF)

• Sho Shirasaka, Wataru Kurebayashi and Hiroya Nakao,
  "Phase-amplitude reduction of limit-cycling systems",
  In: Mauroy A., Mezic I., Susuki Y. (eds) The Koopman Operator in Systems and Control. Lecture Notes in Control and Information Sciences, vol 484. Springer, Cham [35 pages] (2020). (Book)

• Timoteo Carletti and Hiroya Nakao,
  "Turing patterns in a network-reduced FitzHugh-Nagumo model",
  Phys. Rev. E 101, 022203 [12 pages] (2020). (Journal, PDF)

• Yuzuru Kato and Hiroya Nakao,
  "Semiclassical optimization of entrainment stability and phase coherence in weakly forced quantum limit-cycle oscillators",
  Phys. Rev. E 101, 012210 [9 pages] (2020). (Journal, PDF)

• Yoshiki Kuramoto and Hiroya Nakao,
  "On the Concept of Dynamical Reduction - The Case of Coupled Oscillators-",
  Philosophical Transactions of the Royal Society A 377: 20190041 (2019). (Journal)

• Yuzuru Kato, Naoki Yamamoto, Hiroya Nakao,
  "Semiclassical phase reduction theory for quantum synchronization",
  Phys. Rev. Research 1, 033012 [15 pages] (2019). (Journal, PDF)

• Nobuhiro Watanabe, Yuzuru Kato, Sho Shirasaka, Hiroya Nakao,
  "Optimization of linear and nonlinear interaction schemes for stable synchronization of weakly coupled limit-cycle oscillators",
  Physical Review E 100, 042205 [15 pages] (2019). (Journal, PDF)

• Ikuhiro Yamaguchi, Takuya Isomura, Hiroya Nakao, Yutaro Ogawa, Yasuhiko Jimbo, Kiyoshi Kotani,
  "Suppression of Macroscopic Oscillations in Mixed Populations of Active and Inactive Oscillators Coupled through Lattice Laplacian",
  Journal of the Physical Society of Japan, Vol. 88, 054004[8 Pages] (2019). (Journal)

• Masanori Ouchi and Hiroya Nakao,
  “Modeling cochlear two-tone suppression using a system of nonlinear oscillators with feed-forward coupling”,
  Nonlinear Theory and Its Applications, IEICE, Vol. 10, pp. 90-99 (2019). (Journal, PDF)

• Kunihiko Taira and Hiroya Nakao,
  "Phase-response analysis of synchronization for periodic flows",
  Journal of Fluid Mechanics, 846, R2 (2018). (Journal)

• Hiroya Nakao, Sho Yasui, Masashi Ota, Kensuke Arai, and Yoji Kawamura,
  "Phase reduction and synchronization of a network of coupled dynamical elements exhibiting collective oscillations",
  Chaos 28, 045103 (2018) (J. L. Hudson focus issue). (Journal, PDF)

• Yoji Kawamura, Sho Shirasaka, Tatsuo Yanagita, and Hiroya Nakao,
  "Optimizing mutual synchronization of rhythmic spatiotemporal patterns in reaction-diffusion systems",
  Physical Review E 96, 012224 (2017). (Journal, PDF)

• Sho Shirasaka, Nobuhiro Watanabe, Yoji Kawamura, and Hiroya Nakao,
  "Optimizing stability of mutual synchronization between a pair of limit-cycle oscillators with weak cross coupling",
  Physical Review E 96, 012223 (2017). (Journal, PDF)

• Shigeumi Hata and Hiroya Nakao,
  "Localization of Laplacian eigenvectors in random networks",
  Scientific Reports 7, 1121 (2017). (Journal, PDF)

• Sho Shirasaka, Wataru Kurebayashi, and Hiroya Nakao,
  "Phase-amplitude reduction of transient dynamics far from attractors for limit-cycling systems",
  Chaos 27, 023119 (2017). (Journal, PDF)

• Sho Shirasaka, Wataru Kurebayashi, and Hiroya Nakao,
  "Phase reduction theory for hybrid nonlinear oscillators",
  Phys. Rev. E 95, 012212 (2017). (Journal, PDF)

• Yoji Kawamura and Hiroya Nakao,
  "Optimization of noise-induced synchronization of oscillator networks",
  Phys. Rev. E 94, 032201 (2016). (Journal, PDF)

• Hiroya Nakao,
  "Phase reduction approach to synchronization of nonlinear oscillators" (review),
  Contemporary Physics 57, 188-214 (2016). (Journal)

• Wataru Kurebayashi, Sho Shirasaka, and Hiroya Nakao,
  "A criterion for timescale decomposition of external inputs for generalized phase reduction of limit-cycle oscillators",
  Nonlinear Theory and Its Applications (IEICE) 6, 171-180 (2015). (Journal)

• Yoji Kawamura and Hiroya Nakao,
  "Phase description of oscillatory convection with a spatially translational mode",
  Physica D 295-296, 11-29 (2015). (Journal)

• Wataru Kurebayashi, Tsubasa Ishii, Mikio Hasegawa and Hiroya Nakao,
  "Design and control of noise-induced synchronization patterns",
  EPL 107, 10009 (2014). (Journal)

• Hiroya Nakao,
  "Complex Ginzburg-Landau equation on networks and its non-uniform dynamics",
  Eur. Phys. J. Special Topics 223, 2411-2421 (2014). (Journal)

• Ikuhiro Yamaguchi, Yutaro Ogawa, Hiroya Nakao, Yasuhiko Jimbo, Kiyoshi Kotani,
  "Linear Analysis of the Corticothalamic Model with Time Delay",
  Electronics and Communications in Japan 97, 32-44 (2014). (Journal)

• Hiroya Nakao, Tatsuo Yanagita, and Yoji Kawamura,
  "Phase reduction approach to synchronization of spatiotemporal rhythms in reaction-diffusion systems",
  Physical Review X 4, 021032 (2014). (Journal, PDF)

• Masahiro Kazama, Wataru Kurebayashi, Takahiro Tsuchida, Yuta Minoshima, Mikio Hasegawa, Koji Kimura, and Hiroya Nakao,
  "Enhancement of noise correlation for noise-induced synchronization of limit-cycle oscillators by threshold filtering",
  Nonlinear Theory and Its Applications (IEICE) 5 157-171 (2014). (Journal, PDF)

• Shigefumi Hata, Hiroya Nakao, and Alexander S. Mikhailov,
  "Advection of passive particles over flow networks",
  Physical Review E 89, 020801(R) (2014). (Journal, PDF)

• Yoji Kawamura and Hiroya Nakao,
  "Noise-induced synchronization of oscillatory convection and its optimization",
  Physical Review E 89, 012912 (2014). (Journal, PDF)

• Shigefumi Hata, Hiroya Nakao, and Alexander S. Mikhailov,
  "Dispersal-induced destabilization of metapopulations and oscillatory Turing patterns in ecological networks",
  Scientific Reports 4, 3585 (2014). (Journal)

• Shigefumi Hata, Hiroya Nakao, and Alexander S. Mikhailov,
  "Sufficient conditions for wave instability in three-component reaction-diffusion systems",
  Progress of Theoretical and Experimental Physics, 013A01 (2014). (Journal)

• Yoji Kawamura and Hiroya Nakao,
  "Collective phase description of oscillatory convection",
  Chaos 23, 043129 (2013). (Journal, PDF)

• Wataru Kurebayashi, Sho Shirasaka, and Hiroya Nakao,
  "Phase reduction method for strongly perturbed limit cycle oscillators",
  Physical Review Letters 111, 214101 (2013). (Journal, PDF)

• Y. A., S. H., and H. N.,
  "Phase ordering in coupled noisy bistable systems on scale-free networks",
  Physical Review E 88, 052806 (2013) (Journal, PDF)

• Kiyoshi Kotani, Ikuhiro Yamaguchi, Yutaro Ogawa, Yasuhiko Jimbo, Hiroya Nakao, G. Bard Ermentrout,
  "Adjoint method provides phase response functions for delay-induced oscillations",
  Physical Review Letters 109, 044101 (2012). (Journal, PDF)

• Shigefumi Hata, Hiroya Nakao, and Alexander S. Mikhailov,
  "Global feedback control of Turing patterns in network-organized activator-inhibitor systems",
  EPL 98, 64004 (2012). (Journal)

• Y. A and H. N,
  "Persistent fluctuations in the synchronization rate in globally coupled oscillators with periodic external forcing",
  Physical Review E 85, 056207 (2012). (Journal, PDF)

• Ikuhiro Yamaguchi, Yutaro Ogawa, Yasuhiko Jimbo, Hiroya Nakao, and Kiyoshi Kotani,
  "Reduction Theories Elucidate the Origins of Complex Biological Rhythms Generated by Interacting Delay-Induced Oscillations",
  PLoS ONE 6, e26497 (2011). (Journal)

• Yoji Kawamura, Hiroya Nakao, and Yoshiki Kuramoto,
  "Collective phase description of globally coupled excitable elements",
  Physical Review E 84, 046211 (2011). (Journal, PDF)

• Shigefumi Hata, Kensuke Arai, Roberto F. Galán, and Hiroya Nakao,
  "Optimal phase response curves for stochastic synchronization of limit-cycle oscillators by common Poisson noise",
  Physical Review E 84, 016229 (2011). (Journal, PDF)

• Yoji Kawamura, Hiroya Nakao, Kensuke Arai, Hiroshi Kori, and Yoshiki Kuramoto,
  "Phase synchronization between collective rhythms of globally coupled oscillator groups: Noisy identical case",
  Chaos 20, 043109 (2010). (Journal, PDF)

• Yoji Kawamura, Hiroya Nakao, Kensuke Arai, Hiroshi Kori, and Yoshiki Kuramoto,
  "Phase synchronization between collective rhythms of globally coupled oscillator groups: Noiseless non-identical case",
  Chaos 20, 043110 (2010). (Journal, PDF)

• Denis S. Goldobin. Jun-nosuke Teramae, Hiroya Nakao, and G. Bard Ermentrout,
  "Dynamics of limit cycle oscillators subject to general noise",
  Physical Review Letters 105, 154101 (2010). (Journal, PDF)

• Hiroya Nakao, Jun-nosuke Teramae, Denis S. Goldobin, and Yoshiki Kuramoto,
  "Effective long-time phase dynamics of limit-cycle oscillators driven by weak colored noise",
  Chaos 20, 03312 (2010). (Journal, PDF)

• Shigefumi Hata, Takeaki Shimokawa, Kensuke Arai, and Hiroya Nakao,
  "Synchronization of uncoupled oscillators by common gamma impulses: from phase locking to noise-induced synchronization",
  Physical Review E 82, 036206 (2010). (Journal, PDF)

• Hiroya Nakao and Alexander S. Mikhailov,
  "Turing patterns in network-organized activator-inhibitor systems",
  Nature Physics 6, 544-550 (2010). (Journal)

• Hisa-aki Tanaka, Hiroya Nakao, and Kenta Shinohara,
  "Self-organizing timing allocation mechanism in distributed wireless sensor networks",
  IEICE Electronic Express (ELEX) 6, 1562-1568 (2009). (Journal, PDF)

• Hiroshi Kori, Yoji Kawamura, Hiroya Nakao, Kensuke Arai, and Yoshiki Kuramoto,
  "Collective dynamical response of coupled oscillators with general network structure",
  Physical Review E 80, 036207 (2009). (Journal, PDF)

• Jun-nosuke Teramae, Hiroya Nakao, and G. Bard Ermentrout,
  "Stochastic phase reduction for a general class of noisy limit cycle oscillators",
  Physical Review Letters 102, 194102 (2009). (Journal, PDF)

• Hiroya Nakao and Alexander S. Mikhailov,
  "Diffusion-induced instability and chaos in random oscillator networks",
  Physical Review E 79, 036214 (2009). (Journal, PDF)

• Ken Nagai and Hiroya Nakao,
  "Experimental synchronization of circuit oscillations induced by common telegraph noise",
  Physical Review E 79, 036205 (2009). (Journal, PDF)

• Kensuke Arai and Hiroya Nakao,
  "Averaging approach to phase coherence of uncoupled limit-cycle oscillators receiving common random impulses",
  Physical Review E 78, 066220 (2008). (Journal, PDF)

• Yoji Kawamura, Hiroya Nakao, Kensuke Arai, Hiroshi Kori, and Yoshiki Kuramoto,
  "Collective phase sensitivity",
  Physical Review Letters 101, 024101 (2008). (Journal, PDF)

• Kensuke Arai and Hiroya Nakao,
  "Phase coherence in an ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses",
  Physical Review E 77, 036218 (2008). (Journal, PDF)

• Hiroya Nakao, Kensuke Arai, and Yoji Kawamura,
  "Noise-induced synchronization and clustering in ensembles of uncoupled limit-cycle oscillators",
  Physical Review Letters 98, 184101 (2007). (Journal, PDF)

• Yoji Kawamura, Hiroya Nakao, and Yoshiki Kuramoto,
  "Noise-induced turbulence in nonlocally coupled oscillators",
  Physical Review E 75, 036209 (2007). (Journal, PDF)

• Hiroya Nakao, Shuya Kitada, and Alexander S. Mikhailov,
  "Universal finite-sample effect on the perturbation growth in chaotic dynamical systems",
  Physical Review E 74, 026213 (2006). (Journal, PDF)

• Hiroya Nakao, Ken Nagai, and Kensuke Arai,
  "Reproducibility of a noisy limit-cycle oscillator induced by a fluctuating input",
  Progress of Theoretical Physics Supplement (OCNN2004 proceedings) 161, 294-297 (2006). (Journal)

• Hiroya Nakao,
  "Population coding by globally coupled phase oscillators",
  Journal of the Physical Society of Japan 75, 034001 (2006). (Journal)

• Hiroya Nakao, Ken-suke Arai, Ken Nagai, Yasuhiro Tsubo, and Yoshiki Kuramoto,
  "Synchrony of limit-cycle oscillators induced by random external impulses",
  Physical Review E 72, 026220 (2005). (Journal, PDF)

• Hirokazu Asano and Hiroya Nakao,
  "Independent component analysis of spatiotemporal chaos",
  Journal of the Physical Society of Japan 74, 1661-1665 (2005). (Journal)

• Ken Nagai, Hiroya Nakao, and Yasuhiro Tsubo,
  "Synchrony of neural oscillators induced by random telegraphic currents",
  Physical Review E 71, 036217 (2005). (Journal, PDF)

• Hiroya Nakao and Alexander S. Mikhailov,
  "Statistics of rare strong bursts in autocatalytic stochastic growth with diffusion",
  Chaos 13, 953-961 (2003). (Journal, PDF)

• Hiroya Nakao, Tsuyoshi Mishiro, and Michio Yamada,
  "Visualization of correlation cascade in spatio-temporal chaos using wavelets",
  International Journal of Bifurcation and Chaos 11, 1483-1493 (2001). (Journal)

• Hiroya Nakao,
  "Multi-scaling properties of truncated Levy flights",
  Physics Letters A 266, 282-289 (2000). (Journal)

• Yoshiki Kuramoto, Hiroya Nakao, and Dorjsuren Battogtokh,
  "Multi-scaled turbulence in large populations of oscillators in a diffusive medium",
  Physica A 288, 244-264 (2000). (Journal)

• Hiroya Nakao,
  "Anomalous spatio-temporal chaos in a two-dimensional system of non-locally coupled oscillators",
  Chaos 9, 902-909 (1999). (Journal, PDF)

• Hiroya Nakao and Yoshiki Kuramoto,
  "Multi-affinity and multi-fractality in systems of chaotic elements with long-wave forcing",
  European Physical Journal B 11, 345-360 (1999). (Journal)

• Yoshiki Kuramoto, Dorjsuren Battogtokh, and Hiroya Nakao,
  "Multiaffine Chemical Turbulence",
  Physical Review Letters 81, 3543-3546 (1998). (Journal, PDF)

• Hiroya Nakao,
  "Asymptotic power law of moments in a random multiplicative process with weak additive noise",
  Physical Review E 58, 1591-1600 (1998). (Journal, PDF)

• Yoshiki Kuramoto and Hiroya Nakao,
  "Power-Law Spatial Correlations and the Onset of Individual Motions in Self-Oscillatory Media with Non-Local Coupling",
  Physica D 103, 294-313 (1997). (Journal)

• Yoshiki Kuramoto and Hiroya Nakao,
  "Scaling Properties in Large Assemblies of Simple Dynamical Units Driven by Long-Wave Random Forcing",
  Physical Review Letters 78, 4039-4042 (1997). (Journal, PDF)

• Yoshiki Kuramoto and Hiroya Nakao,
  "Origin of Power-Law Spatial Correlations in Distributed Oscillators and Maps with Nonlocal Coupling",
  Physical Review Letters 76, 4352-4355 (1996). (Journal, PDF)

Conference proceedings

• Hiroya Nakao and Igor Mezic,
  "Koopman eigenfunctionals and phase-amplitude reduction of rhythmic reaction-diffusion systems",
  Proceedings of the SICE Annual Conference 2018 September 11-14, 2018, Nara, Japan, p.74-77 (2018).
  

• Wataru Kurebayashi, Sho Shirasaka and Hiroya Nakao,
  "Optimal Model Selection for Estimating Stochastic Koopman Modes",
  Proceedings of 2017 International Symposium on Nonlinear Theory and its Applications (NOLTA2017), p. 12 (2017).

• Wataru Kurebayashi, Sho Shirasaka and Hiroya Nakao,
  "Phase Reduction Theory for Strongly Coupled Limit-Cycle Oscillators",
  Proceedings of 2017 International Symposium on Nonlinear Theory and its Applications (NOLTA2017), p. 342 (2017).

• Wataru Kurebayashi, Sho Shirasaka and Hiroya Nakao,
  "Optimal Parameter Selection for Kernel Dynamic Mode Decomposition",
  Proceedings of 2016 International Symposium on Nonlinear Theory and Its Applications, NOLTA2016, Yugawara, Japan, November 27th-30th, 2016, 370-373.

• Masashi Ota, Sho Yasui, Sho Shirasaka, and Hiroya Nakao,
  "Stability and sensitivity of synchronized states in a network of symmetrically coupled nonlinear oscillators for generating gait patterns",
  Proceedings of 2015 International Symposium on Nonlinear Theory and its Applications NOLTA2015, Kowloon, Hong Kong, China, December 1-4, 2015, 664-667.

• Sho Shirasaka, Wataru Kurebayashi, and Hiroya Nakao,
  "Uncontrolled manifold analysis of oscillatory motions in dynamical models of body movement based on the Floquet theory",
  Proceedings of 2015 International Symposium on Nonlinear Theory and its Applications NOLTA2015, Kowloon, Hong Kong, China, December 1-4, 2015, 668-671.

• Ken Nishikawa, Wataru Kurebayashi, and Hiroya Nakao,
  "Bayesian Parameter Estimation of Non-stationary Collective Dynamics in Moving Animal Groups",
  Proceedings of 2014 International Symposium on Nonlinear Theory and its Applications, Luzern, Switzerland, 882-885 (2014).

• Wataru Kurebayashi, Sho Shirasaka, and Hiroya Nakao,
  "Synchronization Analysis of Nonlinear Oscillators by a Quadratic Phase Model",
  Proceedings of 2014 International Symposium on Nonlinear Theory and its Applications, Luzern, Switzerland, 874-877 (2014).

• Wataru Kurebayashi, Kantaro Fujiwara, Hiroya Nakao, and Tohru Ikeguchi,
  "A Theory on Noise-Induced Synchronization of Chaotic Oscillators",
  Proceedings of 2012 International Symposium on Nonlinear Theory and its Applications, Palma, Majorca, Spain, 344-347 (2012).

• Ikuhiro Yamaguchi, Yutaro Ogawa, Hiroya Nakao, Yasuhiko Jimbo, and Kiyoshi Kotani,
  "Ginzburg-Landau Equations Reduced from Coupled Delay Differential Equations",
  Proceedings of 2012 International Symposium on Nonlinear Theory and its Applications, Palma, Majorca, Spain, 915-918 (2012).

• Hiroya Nakao, Tatsuo Yanagita, and Yoji Kawamura,
  "Phase description of stable limit-cycle solutions in reaction-diffusion systems",
  Procedia IUTAM, vol. 5, 227-233 (2012). (PDF)

• Shigefumi Hata and Hiroya Nakao,
  "Optimal phase response curves for stochastic synchronization and desynchronization of limit-cycle oscillators",
  Proceedings of 2011 International Symposium on Nonlinear Theory and its Applications, Kobe, Japan, 100-103 (2011).

• Kensuke Arai and Hiroya Nakao,
  "The analysis of phase coherence of an ensemble of uncoupled limit-cycle oscillators via averaging of a jump-diffusion Kolmogorov equation",
  Proceedings of 2007 International Symposium on Nonlinear Theory and its Applications, Vancouver, Canada, 100-103 (2007). (PDF)

• Kensuke Arai and Hiroya Nakao,
  "Reproducibility of limit-cycle oscillators induced by random impulses",
  Proceedings of 2006 International Symposium on Nonlinear Theory and its Applications, Bologna, Italy, 295-298 (2006). (PDF)

Unpublished, etc.

• "Comment on 'Phase Reduction of Stochastic Limit Cycle Oscillators'",
  Hiroya Nakao, Jun-nosuke Teramae, and G. Bard Ermentrout, (arXiv preprint, PDF)
  Unpublished, but see Physical Review Letters 102, 194102(1-4) (2009). (Journal, PDF)

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