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Volumn 8, Issue , 2014, Pages

Exploring equilibria in stochastic delay differential equations using persistent homology

Author keywords

[No Author keywords available]

Indexed keywords

ADDITIVE NOISE; DATA HANDLING; DESIGN; DIFFERENTIAL EQUATIONS; DYNAMICAL SYSTEMS; INFORMATION ANALYSIS; NORMAL DISTRIBUTION; VIBRATION ANALYSIS; VIBRATIONS (MECHANICAL);

EID: 84930190795     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/DETC201435655     Document Type: Conference Paper
Times cited : (8)

References (46)
  • 1
    • 33749336242 scopus 로고    scopus 로고
    • Oscillatory regulation of hes1: Discrete stochastic delay modelling and simulation
    • p. e117
    • Barrio, M., Burrage, K., Leier, A., and Tian, T., 2006. "Oscillatory regulation of hes1: Discrete stochastic delay modelling and simulation". PLoS Comput Biol, 2(9), 09, p. e117.
    • (2006) PLoS Comput Biol , vol.2 , Issue.9 , pp. 09
    • Barrio, M.1    Burrage, K.2    Leier, A.3    Tian, T.4
  • 2
    • 34248147513 scopus 로고    scopus 로고
    • Stochastic delay differential equations for genetic regulatory networks
    • Special issue on evolutionary problems
    • Tian, T., Burrage, K., Burrage, P. M., and Carletti, M., 2007. "Stochastic delay differential equations for genetic regulatory networks". Journal of Computational and Applied Mathematics, 205(2), pp. 696 - 707. Special issue on evolutionary problems.
    • (2007) Journal of Computational and Applied Mathematics , vol.205 , Issue.2 , pp. 696-707
    • Tian, T.1    Burrage, K.2    Burrage, P.M.3    Carletti, M.4
  • 5
    • 5544262166 scopus 로고
    • Solution moment stability in stochastic differential delay equations
    • Oct
    • Mackey, M. C., and Nechaeva, I. G., 1995. "Solution moment stability in stochastic differential delay equations". Phys. Rev. E, 52(4), Oct, pp. 3366-3376.
    • (1995) Phys. Rev. e , vol.52 , Issue.4 , pp. 3366-3376
    • Mackey, M.C.1    Nechaeva, I.G.2
  • 6
    • 0000680355 scopus 로고    scopus 로고
    • Small delay approximation of stochastic delay differential equations
    • Apr
    • Guillouzic, S., L'Heureux, I., and Longtin, A., 1999. "Small delay approximation of stochastic delay differential equations". Phys. Rev. E, 59, Apr, pp. 3970-3982.
    • (1999) Phys. Rev. e , vol.59 , pp. 3970-3982
    • Guillouzic, S.1    L'heureux, I.2    Longtin, A.3
  • 8
    • 0035420558 scopus 로고    scopus 로고
    • Stationary solutions of linear stochastic delay differential equations: Applications to biological systems
    • Jul
    • Frank, T. D., and Beek, P. J., 2001. "Stationary solutions of linear stochastic delay differential equations: Applications to biological systems". Phys. Rev. E, 64, Jul, p. 021917.
    • (2001) Phys. Rev. e , vol.64 , pp. 021917
    • Frank, T.D.1    Beek, P.J.2
  • 9
    • 0034509078 scopus 로고    scopus 로고
    • Introduction to the numerical analysis of stochastic delay differential equations
    • Numerical Analysis 2000. Vol. VI: Ordinary Differential Equations and Integral Equations
    • Buckwar, E., 2000. "Introduction to the numerical analysis of stochastic delay differential equations". Journal of Computational and Applied Mathematics, 125(1-2), pp. 297 -307. Numerical Analysis 2000. Vol. VI: Ordinary Differential Equations and Integral Equations.
    • (2000) Journal of Computational and Applied Mathematics , vol.125 , Issue.1-2 , pp. 297-307
    • Buckwar, E.1
  • 10
    • 0037293686 scopus 로고    scopus 로고
    • Numerical solutions of stochastic differential delay equations under local lipschitz condition
    • Mao, X., and Sabanis, S., 2003. "Numerical solutions of stochastic differential delay equations under local lipschitz condition". Journal of Computational and Applied Mathematics, 151(1), pp. 215 - 227.
    • (2003) Journal of Computational and Applied Mathematics , vol.151 , Issue.1 , pp. 215-227
    • Mao, X.1    Sabanis, S.2
  • 11
    • 33646534005 scopus 로고    scopus 로고
    • Approximate solutions of stochastic differential delay equations with markovian switching
    • Yuan, C., and Glover, W., 2006. "Approximate solutions of stochastic differential delay equations with markovian switching". Journal of Computational and Applied Mathematics, 194(2), pp. 207 - 226.
    • (2006) Journal of Computational and Applied Mathematics , vol.194 , Issue.2 , pp. 207-226
    • Yuan, C.1    Glover, W.2
  • 12
    • 34548450855 scopus 로고    scopus 로고
    • Multi-step maruyama methods for stochastic delay differential equations
    • Buckwar, E., and Winkler, R., 2007. "Multi-step maruyama methods for stochastic delay differential equations". Stochastic Analysis and Applications, 25(5), pp. 933-959.
    • (2007) Stochastic Analysis and Applications , vol.25 , Issue.5 , pp. 933-959
    • Buckwar, E.1    Winkler, R.2
  • 13
    • 2142818234 scopus 로고    scopus 로고
    • Discretetime approximations of stochastic delay equations: The milstein scheme
    • Hu, Y., Mohammed, S.-E. A., and Yan, F., 2004. "Discretetime approximations of stochastic delay equations: The milstein scheme". Annals of Probability, 32(1A), pp. 265-314.
    • (2004) Annals of Probability , vol.32 , Issue.1 A , pp. 265-314
    • Hu, Y.1    Mohammed, S.-E.A.2    Yan, F.3
  • 14
    • 23844491182 scopus 로고    scopus 로고
    • Exponential stability in p-th mean of solutions, and of convergent eulertype solutions, of stochastic delay differential equations
    • Baker, C. T. H., and Buckwar, E., Dec.
    • Baker, C. T. H., and Buckwar, E., 2005. "Exponential stability in p-th mean of solutions, and of convergent eulertype solutions, of stochastic delay differential equations". J. Comput. Appl. Math., 184(2), Dec., pp. 404-427.
    • (2005) J. Comput. Appl. Math. , vol.184 , Issue.2 , pp. 404-427
  • 15
    • 33748434648 scopus 로고    scopus 로고
    • A note on exponential stability in pth mean of solutions of stochastic delay differential equations
    • Luo, J., 2007. "A note on exponential stability in pth mean of solutions of stochastic delay differential equations". Journal of Computational and Applied Mathematics, 198(1), pp. 143 - 148.
    • (2007) Journal of Computational and Applied Mathematics , vol.198 , Issue.1 , pp. 143-148
    • Luo, J.1
  • 16
    • 33750933459 scopus 로고    scopus 로고
    • Exponential stability of equidistant eulermaruyama approximations of stochastic differential delay equations
    • Mao, X., 2007. "Exponential stability of equidistant eulermaruyama approximations of stochastic differential delay equations". Journal of Computational and Applied Mathematics, 200(1), pp. 297 - 316.
    • (2007) Journal of Computational and Applied Mathematics , vol.200 , Issue.1 , pp. 297-316
    • Mao, X.1
  • 20
    • 0034704222 scopus 로고    scopus 로고
    • Nonlinear dimensionality reduction by locally linear embedding
    • Roweis, S., and Saul, L., 2000. "Nonlinear dimensionality reduction by locally linear embedding". Science, 290(5500), p. 23232326.
    • (2000) Science , vol.290 , Issue.5500 , pp. 23232326
    • Roweis, S.1    Saul, L.2
  • 21
    • 0042378381 scopus 로고    scopus 로고
    • Laplacian eigenmaps for dimensionality reduction and data representation
    • Belkin, M., and Niyogi, P., 2003. "Laplacian eigenmaps for dimensionality reduction and data representation". Neural Computation, 15(6), pp. 1373-1396.
    • (2003) Neural Computation , vol.15 , Issue.6 , pp. 1373-1396
    • Belkin, M.1    Niyogi, P.2
  • 22
    • 0037948870 scopus 로고    scopus 로고
    • Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data
    • Donoho, D. L., and Grimes, C., 2003. "Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data". Proceedings of the National Academy of Sciences, 100(10), pp. 5591-5596.
    • (2003) Proceedings of the National Academy of Sciences , vol.100 , Issue.10 , pp. 5591-5596
    • Donoho, D.L.1    Grimes, C.2
  • 23
    • 14544307975 scopus 로고    scopus 로고
    • Principal manifolds and nonlinear dimension reduction via local tangent space alignment
    • Zhang, Z., and Zha, H., 2002. "Principal manifolds and nonlinear dimension reduction via local tangent space alignment". SIAM Journal of Scientific Computing, 26, pp. 313-338.
    • (2002) SIAM Journal of Scientific Computing , vol.26 , pp. 313-338
    • Zhang, Z.1    Zha, H.2
  • 24
    • 33745431702 scopus 로고    scopus 로고
    • Diffusion maps
    • Special Issue: Diffusion Maps and Wavelets
    • Coifman, R. R., and Lafon, S., 2006. "Diffusion maps". Applied and Computational Harmonic Analysis, 21(1), pp. 5 - 30. Special Issue: Diffusion Maps and Wavelets.
    • (2006) Applied and Computational Harmonic Analysis , vol.21 , Issue.1 , pp. 5-30
    • Coifman, R.R.1    Lafon, S.2
  • 25
    • 33745342032 scopus 로고    scopus 로고
    • Diffusion maps, spectral clustering and reaction coordinates of dynamical systems
    • Special Issue: Diffusion Maps and Wavelets
    • Nadler, B., Lafon, S., Coifman, R. R., and Kevrekidis, I. G., 2006. "Diffusion maps, spectral clustering and reaction coordinates of dynamical systems". Applied and Computational Harmonic Analysis, 21(1), pp. 113 - 127. Special Issue: Diffusion Maps and Wavelets.
    • (2006) Applied and Computational Harmonic Analysis , vol.21 , Issue.1 , pp. 113-127
    • Nadler, B.1    Lafon, S.2    Coifman, R.R.3    Kevrekidis, I.G.4
  • 26
    • 48349109325 scopus 로고    scopus 로고
    • Non-linear independent component analysis with diffusion maps
    • Singer, A., and Coifman, R. R., 2008. "Non-linear independent component analysis with diffusion maps". Applied and Computational Harmonic Analysis, 25(2), pp. 226 -239.
    • (2008) Applied and Computational Harmonic Analysis , vol.25 , Issue.2 , pp. 226-239
    • Singer, A.1    Coifman, R.R.2
  • 27
    • 24644511779 scopus 로고    scopus 로고
    • Multiscale analysis of stochastic delay differential equations
    • Klosek, M., and Kuske, R., 2005. "Multiscale analysis of stochastic delay differential equations". Multiscale Modeling & Simulation, 3(3), pp. 706-729.
    • (2005) Multiscale Modeling & Simulation , vol.3 , Issue.3 , pp. 706-729
    • Klosek, M.1    Kuske, R.2
  • 28
    • 5244342270 scopus 로고    scopus 로고
    • Stochastic resonance in coupled oscillator systems with time delay
    • Feb
    • Kim, S., Park, S. H., and Pyo, H.-B., 1999. "Stochastic resonance in coupled oscillator systems with time delay". Phys. Rev. Lett., 82, Feb, pp. 1620-1623.
    • (1999) Phys. Rev. Lett. , vol.82 , pp. 1620-1623
    • Kim, S.1    Park, S.H.2    Pyo, H.-B.3
  • 29
    • 0001676780 scopus 로고    scopus 로고
    • Resonance with noise and delay
    • Apr
    • Ohira, T., and Sato, Y., 1999. "Resonance with noise and delay". Phys. Rev. Lett., 82, Apr, pp. 2811-2815.
    • (1999) Phys. Rev. Lett. , vol.82 , pp. 2811-2815
    • Ohira, T.1    Sato, Y.2
  • 30
    • 0037148346 scopus 로고    scopus 로고
    • Noise-induced resonance in delayed feedback systems
    • Masoller, C., 2002. "Noise-induced resonance in delayed feedback systems". Phys. Rev. Lett., 88(3), p. 34102.
    • (2002) Phys. Rev. Lett. , vol.88 , Issue.3 , pp. 34102
    • Masoller, C.1
  • 31
    • 33646409330 scopus 로고    scopus 로고
    • Multiple-scales approximation of a coherence resonance route to chatter
    • Kuske, R., 2006. "Multiple-scales approximation of a coherence resonance route to chatter". Computing in Science Engineering, 8(3), pp. 35-43.
    • (2006) Computing in Science Engineering , vol.8 , Issue.3 , pp. 35-43
    • Kuske, R.1
  • 32
    • 77954346089 scopus 로고    scopus 로고
    • Competition of noise sources in systems with delay: The role of multiple time scales
    • Kuske, R., 2010. "Competition of noise sources in systems with delay: The role of multiple time scales". Journal of Vibration and Control, 16(7-8), pp. 983-1003.
    • (2010) Journal of Vibration and Control , vol.16 , Issue.7-8 , pp. 983-1003
    • Kuske, R.1
  • 33
    • 84867079606 scopus 로고    scopus 로고
    • Stochastic resonance in a time-delayed bistable system with colored coupling between noise terms
    • Luo, X., Wu, D., and Zhu, S., 2012. "Stochastic resonance in a time-delayed bistable system with colored coupling between noise terms". International Journal of Modern Physics B, 26(30), p. 1250149.
    • (2012) International Journal of Modern Physics B , vol.26 , Issue.30 , pp. 1250149
    • Luo, X.1    Wu, D.2    Zhu, S.3
  • 34
    • 84861412710 scopus 로고    scopus 로고
    • Structure of the afferent terminals in terminal ganglion of a cricket and persistent homology
    • p. e37278
    • Brown, J., and Gedeon, T., 2012. "Structure of the afferent terminals in terminal ganglion of a cricket and persistent homology". PLoS ONE, 7(5), 05, p. e37278.
    • (2012) PLoS ONE , vol.7 , Issue.5 , pp. 05
    • Brown, J.1    Gedeon, T.2
  • 35
    • 79955561607 scopus 로고    scopus 로고
    • Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival
    • Nicolau, M., Levine, A. J., and Carlsson, G., 2011. "Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival". Proceedings of the National Academy of Sciences, 108(17), pp. 7265-7270.
    • (2011) Proceedings of the National Academy of Sciences , vol.108 , Issue.17 , pp. 7265-7270
    • Nicolau, M.1    Levine, A.J.2    Carlsson, G.3
  • 36
    • 41849094721 scopus 로고    scopus 로고
    • Coverage in sensor networks via persistent homology
    • Apr.
    • de Silva, V., and Ghrist, R., 2007. "Coverage in sensor networks via persistent homology". Algebraic&Geometric Topology, 7, Apr., pp. 339-358.
    • (2007) Algebraic&Geometric Topology , vol.7 , pp. 339-358
    • De Silva, V.1    Ghrist, R.2
  • 45
    • 0035439412 scopus 로고    scopus 로고
    • An algorithmic introduction to numerical simulation of stochastic differential equations
    • Higham, D., 2001. "An algorithmic introduction to numerical simulation of stochastic differential equations". SIAM Review, 43(3), pp. 525-546.
    • (2001) SIAM Review , vol.43 , Issue.3 , pp. 525-546
    • Higham, D.1


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