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Volumn , Issue , 2012, Pages 7184-7192

Synchronization and pattern formation in diffusively coupled systems

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS;

EID: 84874238292     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2012.6425824     Document Type: Conference Paper
Times cited : (12)

References (40)
  • 1
    • 0002298523 scopus 로고    scopus 로고
    • Diffusive coupling, dissipation, and synchronization
    • J.K. Hale. Diffusive coupling, dissipation, and synchronization. Journal of Dynamics and Differential Equations, 9(1):1-52, 1997.
    • (1997) Journal of Dynamics and Differential Equations , vol.9 , Issue.1 , pp. 1-52
    • Hale, J.K.1
  • 6
    • 79956192798 scopus 로고    scopus 로고
    • Certifying spatially uniform behavior in reactiondiffusion PDE and compartmental ODE systems
    • M. Arcak. Certifying spatially uniform behavior in reactiondiffusion PDE and compartmental ODE systems. Automatica, 47(6):1219-1229, 2011.
    • (2011) Automatica , vol.47 , Issue.6 , pp. 1219-1229
    • Arcak, M.1
  • 7
    • 84857476795 scopus 로고    scopus 로고
    • A feedback quenched oscillator produces turing patterning with one diffuser
    • 01
    • Justin Hsia, William J. Holtz, Daniel C. Huang, Murat Arcak, and Michel M. Maharbiz. A feedback quenched oscillator produces turing patterning with one diffuser. PLoS Computational Biology, 8(1):e1002331, 01 2012.
    • (2012) PLoS Computational Biology , vol.8 , Issue.1
    • Hsia, J.1    Holtz, W.J.2    Huang, D.C.3    Arcak, M.4    Maharbiz, M.M.5
  • 10
    • 0039592729 scopus 로고    scopus 로고
    • From kuramoto to crawford: Exploring the onset of synchronization in populations of coupled oscillators
    • S.H. Strogatz. From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators. Physica D, 143:1-20, 2000.
    • (2000) Physica D , vol.143 , pp. 1-20
    • Strogatz, S.H.1
  • 12
    • 33846885260 scopus 로고    scopus 로고
    • Self-organized quasiperiodicity in oscillator ensembles with global nonlinear coupling
    • M. Rosenblum and A. Pikovsky. Self-organized quasiperiodicity in oscillator ensembles with global nonlinear coupling. Physical Review Letters, 98(6), 2007.
    • (2007) Physical Review Letters , vol.98 , Issue.6
    • Rosenblum, M.1    Pikovsky, A.2
  • 13
    • 41349097039 scopus 로고    scopus 로고
    • The onset of synchronization in large networks of coupled oscillators
    • J.G. Restrepo, B.R. Hunt, and E. Ott. The onset of synchronization in large networks of coupled oscillators. Physical Review E, 71:036151, 2005.
    • (2005) Physical Review e , vol.71 , pp. 036151
    • Restrepo, J.G.1    Hunt, B.R.2    Ott, E.3
  • 16
    • 0000753609 scopus 로고
    • Global existence for semilinear parabolic systems
    • J. Morgan. Global existence for semilinear parabolic systems. SIAM Journal on Mathematical Analysis, 20(5):1128-1144, 1989.
    • (1989) SIAM Journal on Mathematical Analysis , vol.20 , Issue.5 , pp. 1128-1144
    • Morgan, J.1
  • 17
    • 27244462819 scopus 로고
    • The secant condition for instability in biochemical feedback control - Parts i and II
    • C.D. Thron. The secant condition for instability in biochemical feedback control - Parts I and II. Bulletin of Mathematical Biology, 53:383-424, 1991.
    • (1991) Bulletin of Mathematical Biology , vol.53 , pp. 383-424
    • Thron, C.D.1
  • 18
    • 0003448545 scopus 로고    scopus 로고
    • volume 19 of Graduate Studies in Mathematics. American Mathematical Society
    • L.C. Evans. Partial Differential Equations, volume 19 of Graduate Studies in Mathematics. American Mathematical Society, 1998.
    • (1998) Partial Differential Equations
    • Evans, L.C.1
  • 20
    • 20344362744 scopus 로고
    • A lower bound for the smallest eigenvalue of the Laplacian
    • R.C. Gunning, editor. Princeton University Press, Princeton, N.J.
    • J. Cheeger. A lower bound for the smallest eigenvalue of the Laplacian. In R.C. Gunning, editor, Problems in Analysis (A Symposium in Honor of Salomon Bochner), pages 195-199. Princeton University Press, Princeton, N.J., 1970.
    • (1970) Problems in Analysis (A Symposium in Honor of Salomon Bochner) , pp. 195-199
    • Cheeger, J.1
  • 21
    • 0003882879 scopus 로고    scopus 로고
    • American Mathematical Society, Providence, Rhode Island
    • F.R.K. Chung. Spectral Graph Theory. American Mathematical Society, Providence, Rhode Island, 1997.
    • (1997) Spectral Graph Theory
    • Chung, F.R.K.1
  • 22
    • 0004486808 scopus 로고
    • Current problems in pattern formation
    • S.A. Levin, editor. American Mathematical Society, Providence, Rhode Island
    • H.G. Othmer. Current problems in pattern formation. In S.A. Levin, editor, Lectures on Mathematics in the Life Sciences, volume 9, pages 57-85. American Mathematical Society, Providence, Rhode Island, 1977.
    • (1977) Lectures on Mathematics in the Life Sciences , vol.9 , pp. 57-85
    • Othmer, H.G.1
  • 23
  • 24
    • 0001842649 scopus 로고
    • Large time behavior of solutions of systems of nonlinear reaction-diffusion equations
    • E. Conway, D. Hoff, and J. Smoller. Large time behavior of solutions of systems of nonlinear reaction-diffusion equations. SIAM Journal on Applied Mathematics, 35(1):1-16, 1978.
    • (1978) SIAM Journal on Applied Mathematics , vol.35 , Issue.1 , pp. 1-16
    • Conway, E.1    Hoff, D.2    Smoller, J.3
  • 26
    • 0032094219 scopus 로고    scopus 로고
    • On contraction analysis for nonlinear systems
    • J.-J. Lohmiller, W. Slotine. On contraction analysis for nonlinear systems. Automatica, 34:683-696, 1998.
    • (1998) Automatica , vol.34 , pp. 683-696
    • Lohmiller, J.-J.1    Slotine, W.2
  • 30
    • 17844374314 scopus 로고    scopus 로고
    • A synthetic multicellular system for programmed pattern formation
    • S. Basu, Y. Gerchman, C.H. Collins, F.H. Arnold, and R. Weiss. A synthetic multicellular system for programmed pattern formation. Nature, 434:1130-1134, 2005.
    • (2005) Nature , vol.434 , pp. 1130-1134
    • Basu, S.1    Gerchman, Y.2    Collins, C.H.3    Arnold, F.H.4    Weiss, R.5
  • 31
    • 68349119045 scopus 로고    scopus 로고
    • Morphogen-defined patterning of Escherichia Coli enabled by an externally tunable band-pass filter
    • T. Sohka, R.A. Heins, and M. Ostermeier. Morphogen-defined patterning of Escherichia Coli enabled by an externally tunable band-pass filter. Journal of Biological Engineering, 3(10):387-401, 2009.
    • (2009) Journal of Biological Engineering , vol.3 , Issue.10 , pp. 387-401
    • Sohka, T.1    Heins, R.A.2    Ostermeier, M.3
  • 32
    • 70349436997 scopus 로고    scopus 로고
    • A modified consumer inkjet for spatiotemporal control of gene expression
    • D.J. Cohen, R.C. Morfino, and M.M. Maharbiz. A modified consumer inkjet for spatiotemporal control of gene expression. PLoS ONE, 4(9), 2009.
    • (2009) PLoS ONE , vol.4 , Issue.9
    • Cohen, D.J.1    Morfino, R.C.2    Maharbiz, M.M.3
  • 33
    • 0015454185 scopus 로고
    • A theory of biological pattern formation
    • A. Gierer and H. Meinhardt. A theory of biological pattern formation. Biological Cybernetics, 12(1):30-39, 1972.
    • (1972) Biological Cybernetics , vol.12 , Issue.1 , pp. 30-39
    • Gierer, A.1    Meinhardt, H.2
  • 35
    • 33646772012 scopus 로고
    • Synchronized and differentiated modes of cellular dynamics
    • H. Haken, editor. Springer
    • H. Othmer. Synchronized and differentiated modes of cellular dynamics. In H. Haken, editor, Dynamics of Synergetic Systems, volume 6. Springer, 1980.
    • (1980) Dynamics of Synergetic Systems , vol.6
    • Othmer, H.1
  • 36
    • 0034688173 scopus 로고    scopus 로고
    • A synthetic oscillatory network of transcriptional regulators
    • M. B. Elowitz and S. Leibler. A synthetic oscillatory network of transcriptional regulators. Nature, pages 339-342, 2000.
    • (2000) Nature , pp. 339-342
    • Elowitz, M.B.1    Leibler, S.2
  • 37
    • 0026896517 scopus 로고
    • Nonlinear control design for slightly nonminimum phase systems: Application to V/STOL aircraft
    • J. Hauser, S. Sastry, and G. Meyer. Nonlinear control design for slightly nonminimum phase systems: Application to V/STOL aircraft. Automatica, 28(4):665-679, 1992.
    • (1992) Automatica , vol.28 , Issue.4 , pp. 665-679
    • Hauser, J.1    Sastry, S.2    Meyer, G.3
  • 39
    • 0038115065 scopus 로고    scopus 로고
    • The segmentation clock: Converting embryonic time into spatial pattern
    • O. Pourquié. The segmentation clock: Converting embryonic time into spatial pattern. Science, 301:328-330, 2003.
    • (2003) Science , vol.301 , pp. 328-330
    • Pourquié, O.1
  • 40
    • 0004210529 scopus 로고    scopus 로고
    • Sinauer Associates, Inc., ninth edition
    • S.F. Gilbert. Developmental Biology. Sinauer Associates, Inc., ninth edition, 2010.
    • (2010) Developmental Biology
    • Gilbert, S.F.1


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