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Stochastic heat equations with cubic nonlinearity and additive spacetime noise in 2D
Control of attractors in nonlinear dynamical systems using external noise: Effects of noise on synchronization phenomena
1.  Department of Applied Physics, Faculty of Science, Tokyo Institute of Technology, 2121 Ohokayama, Meguroku, Tokyo 1520033, Japan 
2.  FIRST, Aihara Innovative Mathematical Modelling Project, Japan Science and Technology Agency, 461 Komaba, Meguroku, Tokyo 1538505, Japan 
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R. C. Desai and R. Zwanzig, Statistical mechanics of a nonlinear stochastic model, J. Stat. Phys., 19 (1978), 124. Google Scholar 
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D. A. Dawson, Critical dynamics and fluctuations for a meanfield model of cooperative behavior, J. Stat. Phys., 31 (1983), 2985. Google Scholar 
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M. Shiino, Htheorem and stability analysis for meanfield models of nonequilibrium phase transitions in stochastic systems, Phys. Lett. A, 112 (1985), 302306. Google Scholar 
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M. Shiino, Dynamical behavior of stochastic systems of infinitely many coupled nonlinear oscillators exhibiting phase transitions of meanfield type: H theorem on asymptotic approach to equilibrium and critical slowing down of orderparameter fluctuations, Phys. Rev. A, 36 (1987), 23932412. Google Scholar 
[5] 
T. D. Frank, "Nonlinear FokkerPlanck Equations," Fundamentals and applications. Springer Series in Synergetics. SpringerVerlag, Berlin, 2005. Google Scholar 
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L. Gammaitoni, P. Hänggi, P. Jung and F. Marchesoni, Stochastic resonance, Rev. Mod. Phys., 70 (1998), 223287. Google Scholar 
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B. Lindner, J. GarcíaOjalvo, A. Neiman and L. SchimanskyGeier, Effects of noise in excitable systems, Phys. Rep., 392 (2004), 321424. Google Scholar 
[8] 
M. A. Zaks, X. Sailer, L. SchimanskyGeier and A. B. Neiman, Noise induced complexity: From subthreshold oscillations to spiking in coupled excitable systems, Chaos, 15 (2005), 026117102611713. Google Scholar 
[9] 
H. Hasegawa, Generalized ratecode model for neuron ensembles with finite populations, Phys. Rev. E, 75 (2007), 051904105190411. Google Scholar 
[10] 
T. Kanamaru and K. Aihara, Stochastic synchrony of chaos in a pulsecoupled neural network with both chemical and electrical synapses among inhibitory neurons, Neural Comp., 20 (2008), 19511972. Google Scholar 
[11] 
M. Shiino and K. Yoshida, Chaosnonchaos phase transitions induced by external noise in ensembles of nonlinearly coupled oscillators, Phys. Rev. E, 63 (2001), 02621010262106. Google Scholar 
[12] 
A. Ichiki, H. Ito and M. Shiino, Chaosnonchaos phase transitions induced by multiplicative noise in ensembles of coupled twodimensional oscillators, Physica E, 40 (2007), 402405. Google Scholar 
[13] 
M. Shiino and K. Doi, Nonequilibrium phase transitions in stochastic systems with and without time delay: Controlling various attractors with noise, Proceedings of the 2007 IEEE Symposium on Foundations of Computational Intelligence (2007), 100105. Google Scholar 
[14] 
K. Okumura and M. Shiino, Analytical approach to noise effects on synchronization in a system of coupled excitable elements, Lecture Notes in Computer Science, 6443 (2010), 486493. Google Scholar 
[15] 
K. Okumura, A. Ichiki and M. Shiino, Effects of noise on synchronization phenomena exhibited by meanfield coupled limit cycle oscillators with two natural frequencies, Physica E, 43 (2011), 794797. Google Scholar 
[16] 
K. Okumura, A. Ichiki and M. Shiino, Stochastic phenomena of synchronization in ensembles of meanfield coupled limit cycle oscillators with two native frequencies, Europhys. Lett., 92 (2010), 50009p150009p6. Google Scholar 
show all references
References:
[1] 
R. C. Desai and R. Zwanzig, Statistical mechanics of a nonlinear stochastic model, J. Stat. Phys., 19 (1978), 124. Google Scholar 
[2] 
D. A. Dawson, Critical dynamics and fluctuations for a meanfield model of cooperative behavior, J. Stat. Phys., 31 (1983), 2985. Google Scholar 
[3] 
M. Shiino, Htheorem and stability analysis for meanfield models of nonequilibrium phase transitions in stochastic systems, Phys. Lett. A, 112 (1985), 302306. Google Scholar 
[4] 
M. Shiino, Dynamical behavior of stochastic systems of infinitely many coupled nonlinear oscillators exhibiting phase transitions of meanfield type: H theorem on asymptotic approach to equilibrium and critical slowing down of orderparameter fluctuations, Phys. Rev. A, 36 (1987), 23932412. Google Scholar 
[5] 
T. D. Frank, "Nonlinear FokkerPlanck Equations," Fundamentals and applications. Springer Series in Synergetics. SpringerVerlag, Berlin, 2005. Google Scholar 
[6] 
L. Gammaitoni, P. Hänggi, P. Jung and F. Marchesoni, Stochastic resonance, Rev. Mod. Phys., 70 (1998), 223287. Google Scholar 
[7] 
B. Lindner, J. GarcíaOjalvo, A. Neiman and L. SchimanskyGeier, Effects of noise in excitable systems, Phys. Rep., 392 (2004), 321424. Google Scholar 
[8] 
M. A. Zaks, X. Sailer, L. SchimanskyGeier and A. B. Neiman, Noise induced complexity: From subthreshold oscillations to spiking in coupled excitable systems, Chaos, 15 (2005), 026117102611713. Google Scholar 
[9] 
H. Hasegawa, Generalized ratecode model for neuron ensembles with finite populations, Phys. Rev. E, 75 (2007), 051904105190411. Google Scholar 
[10] 
T. Kanamaru and K. Aihara, Stochastic synchrony of chaos in a pulsecoupled neural network with both chemical and electrical synapses among inhibitory neurons, Neural Comp., 20 (2008), 19511972. Google Scholar 
[11] 
M. Shiino and K. Yoshida, Chaosnonchaos phase transitions induced by external noise in ensembles of nonlinearly coupled oscillators, Phys. Rev. E, 63 (2001), 02621010262106. Google Scholar 
[12] 
A. Ichiki, H. Ito and M. Shiino, Chaosnonchaos phase transitions induced by multiplicative noise in ensembles of coupled twodimensional oscillators, Physica E, 40 (2007), 402405. Google Scholar 
[13] 
M. Shiino and K. Doi, Nonequilibrium phase transitions in stochastic systems with and without time delay: Controlling various attractors with noise, Proceedings of the 2007 IEEE Symposium on Foundations of Computational Intelligence (2007), 100105. Google Scholar 
[14] 
K. Okumura and M. Shiino, Analytical approach to noise effects on synchronization in a system of coupled excitable elements, Lecture Notes in Computer Science, 6443 (2010), 486493. Google Scholar 
[15] 
K. Okumura, A. Ichiki and M. Shiino, Effects of noise on synchronization phenomena exhibited by meanfield coupled limit cycle oscillators with two natural frequencies, Physica E, 43 (2011), 794797. Google Scholar 
[16] 
K. Okumura, A. Ichiki and M. Shiino, Stochastic phenomena of synchronization in ensembles of meanfield coupled limit cycle oscillators with two native frequencies, Europhys. Lett., 92 (2010), 50009p150009p6. Google Scholar 
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