Eckhoff, Philip; Wong-Lin, Kongfatt; Holmes, Philip Dimension reduction and dynamics of a spiking neural network model for decision making under neuromodulation. (English) Zbl 1217.34079 SIAM J. Appl. Dyn. Syst. 10, No. 1, 148-188 (2011). MSC: 34C60 34C23 34C29 60H10 35F05 92B20 92C20 PDFBibTeX XMLCite \textit{P. Eckhoff} et al., SIAM J. Appl. Dyn. Syst. 10, No. 1, 148--188 (2011; Zbl 1217.34079) Full Text: DOI Link
Goodman, Roy H.; Holmes, Philip J.; Weinstein, Michael I. Strong NLS soliton-defect interactions. (English) Zbl 1061.35132 Physica D 192, No. 3-4, 215-248 (2004). MSC: 35Q55 37K40 37K05 PDFBibTeX XMLCite \textit{R. H. Goodman} et al., Physica D 192, No. 3--4, 215--248 (2004; Zbl 1061.35132) Full Text: DOI arXiv
Medvedev, G. S.; Ono, K.; Holmes, P. J. Travelling wave solutions of the degenerate Kolmogorov-Petrovski-Piskunov equation. (English) Zbl 1060.35052 Eur. J. Appl. Math. 14, No. 3, 343-367 (2003). Reviewer: Messoud A. Efendiev (Berlin) MSC: 35K57 35K65 35B40 35K15 PDFBibTeX XMLCite \textit{G. S. Medvedev} et al., Eur. J. Appl. Math. 14, No. 3, 343--367 (2003; Zbl 1060.35052) Full Text: DOI
Goodman, Roy H.; Holmes, Philip J.; Weinstein, Michael I. Interaction of sine-Gordon kinks with defects: Phase space transport in a two-mode model. (English) Zbl 0985.35074 Physica D 161, No. 1-2, 21-44 (2002). MSC: 35Q53 37J45 82C21 PDFBibTeX XMLCite \textit{R. H. Goodman} et al., Physica D 161, No. 1--2, 21--44 (2002; Zbl 0985.35074) Full Text: DOI
Wittenberg, Ralf W.; Holmes, Philip Spatially localized models of extended systems. (English) Zbl 0985.76037 Nonlinear Dyn. 25, No. 1-3, 111-132 (2001). MSC: 76F20 65T60 35Q35 PDFBibTeX XMLCite \textit{R. W. Wittenberg} and \textit{P. Holmes}, Nonlinear Dyn. 25, No. 1--3, 111--132 (2001; Zbl 0985.76037) Full Text: DOI
Holmes, P. J.; Mattingly, J. C.; Wittenberg, R. W. Low-dimensional models of turbulence or, the dynamics of coherent structures. (English) Zbl 1007.35059 Robinson, James C. (ed.) et al., From finite to infinite dimensional dynamical systems. Proceedings of the NATO advanced study institute, Cambridge, UK, August 21-September 1, 1995. Dordrecht: Kluwer Academic Publishers. NATO Sci. Ser. II, Math. Phys. Chem. 19, 177-215 (2001). Reviewer: Oleg Titow (Berlin) MSC: 35Q30 76F20 76D05 37N10 PDFBibTeX XMLCite \textit{P. J. Holmes} et al., NATO Sci. Ser. II, Math. Phys. Chem. 19, 177--215 (2001; Zbl 1007.35059)
Goodman, R. H.; Weinstein, M. I.; Holmes, P. J. Nonlinear propagation of light in one-dimensional periodic structures. (English) Zbl 1005.78011 J. Nonlinear Sci. 11, No. 2, 123-168 (2001). MSC: 78A60 78A10 35Q60 PDFBibTeX XMLCite \textit{R. H. Goodman} et al., J. Nonlinear Sci. 11, No. 2, 123--168 (2001; Zbl 1005.78011) Full Text: DOI arXiv
Holmes, Philip; Kutz, J. Nathan Dynamics and bifurcations of a planar map modeling dispersion managed breathers. (English) Zbl 0936.34030 SIAM J. Appl. Math. 59, No. 4, 1288-1302 (1999). Reviewer: A.Steindl (Wien) MSC: 34C23 78A60 35B20 35Q55 41A60 35B32 34A45 PDFBibTeX XMLCite \textit{P. Holmes} and \textit{J. N. Kutz}, SIAM J. Appl. Math. 59, No. 4, 1288--1302 (1999; Zbl 0936.34030) Full Text: DOI
Mielke, Alexander; Holmes, Philip; Kutz, J. Nathan Global existence and uniqueness for an optical fibre laser model. (English) Zbl 0913.35018 Nonlinearity 11, No. 6, 1489-1504 (1998). MSC: 35B32 35Q55 78A60 41A60 PDFBibTeX XMLCite \textit{A. Mielke} et al., Nonlinearity 11, No. 6, 1489--1504 (1998; Zbl 0913.35018) Full Text: DOI
Kalies, W. D.; Holmes, P. J. On a dynamical model for phase transformation in nonlinear elasticity. (English) Zbl 0876.73015 Chadam, John (ed.) et al., Pattern formation: symmetry methods and applications. Proceedings of two related workshops held at the Fields Institute for Research in Mathematical Sciences, Waterloo, Canada, ‘Pattern formation and symmetry breaking in PDEs’, Feb. 22-28, 1993 and ‘Applications of pattern formation’, March 24-28, 1993. Providence, RI: American Mathematical Society. Fields Inst. Commun. 5, 255-269 (1996). Reviewer: P.Puri (New Orleans) MSC: 74B20 74A15 37G99 35R35 PDFBibTeX XMLCite \textit{W. D. Kalies} and \textit{P. J. Holmes}, Fields Inst. Commun. 5, 255--269 (1996; Zbl 0876.73015)
Dankowicz, Harry; Holmes, Philip; Berkooz, Gal; Elezgaray, Juan Local models of spatio-temporally complex fields. (English) Zbl 0885.35115 Physica D 90, No. 3-4, 387-407 (1996). MSC: 35Q53 76F05 PDFBibTeX XMLCite \textit{H. Dankowicz} et al., Physica D 90, No. 3--4, 387--407 (1996; Zbl 0885.35115) Full Text: DOI
Doelman, Arjen; Holmes, Philip On the creation of multi-pulse traveling waves by global bifurcations. (English) Zbl 0867.35042 Mielke, A. (ed.) et al., Structure and dynamics of nonlinear waves in fluids. Proceedings of the IUTAM/ ISIMM symposium, Hannover, Germany, August 17–20, 1994. Singapore: World Scientific. Adv. Ser. Nonlinear Dyn. 7, 201-208 (1995). MSC: 35K55 34C37 34C23 PDFBibTeX XMLCite \textit{A. Doelman} and \textit{P. Holmes}, Adv. Ser. Nonlinear Dyn. 7, 201--208 (1995; Zbl 0867.35042)
Myers, Mark; Holmes, Philip; Elezgaray, Juan; Berkooz, Gal Wavelet projections of the Kuramoto-Sivashinsky equation. I: Heteroclinic cycles and modulated traveling waves for short systems. (English) Zbl 0890.58086 Physica D 86, No. 3, 396-427 (1995). MSC: 35K55 35Q53 82B44 37C80 PDFBibTeX XMLCite \textit{M. Myers} et al., Physica D 86, No. 3, 396--427 (1995; Zbl 0890.58086) Full Text: DOI
Duan, Jinqiao; Holmes, Philip Fronts, domain walls and pulses in a generalized Ginzburg-Landau equation. (English) Zbl 0820.58053 Proc. Edinb. Math. Soc., II. Ser. 38, No. 1, 77-97 (1995). Reviewer: P.Holmes (Princeton) MSC: 34C27 35Q55 34C37 37-XX PDFBibTeX XMLCite \textit{J. Duan} and \textit{P. Holmes}, Proc. Edinb. Math. Soc., II. Ser. 38, No. 1, 77--97 (1995; Zbl 0820.58053) Full Text: DOI
Duan, Jinqiao; Holmes, Philip On the Cauchy problem of a generalized Ginzburg-Landau equation. (English) Zbl 0833.35067 Nonlinear Anal., Theory Methods Appl. 22, No. 8, 1033-1040 (1994). MSC: 35K55 35K15 35B65 PDFBibTeX XMLCite \textit{J. Duan} and \textit{P. Holmes}, Nonlinear Anal., Theory Methods Appl. 22, No. 8, 1033--1040 (1994; Zbl 0833.35067) Full Text: DOI
Duan, Jinqiao; Titi, Edriss S.; Holmes, Philip Regularity, approximation and asymptotic dynamics for a generalized Ginzburg-Landau equation. (English) Zbl 0808.35133 Nonlinearity 6, No. 6, 915-933 (1993). Reviewer: L.Vazquez (Madrid) MSC: 35Q55 35G10 35K25 35B65 37C70 65M70 PDFBibTeX XMLCite \textit{J. Duan} et al., Nonlinearity 6, No. 6, 915--933 (1993; Zbl 0808.35133) Full Text: DOI
Duan, Jinqiao; Holmes, Philip; Titi, Edriss S. Global existence theory for a generalized Ginzburg-Landau equation. (English) Zbl 0783.35070 Nonlinearity 5, No. 6, 1303-1314 (1992). Reviewer: B.A.Malomed (Ramat Aviv) MSC: 35Q55 35K55 35K60 PDFBibTeX XMLCite \textit{J. Duan} et al., Nonlinearity 5, No. 6, 1303--1314 (1992; Zbl 0783.35070) Full Text: DOI
Holmes, Philip; Berkooz, Gal; Lumley, John L. Turbulence, dynamical systems and the unreasonable effectiveness of empirical eigenfunctions. (English) Zbl 0744.58066 Proc. Int. Congr. Math., Kyoto/Japan 1990, Vol. II, 1607-1617 (1991). Reviewer: I.Oprea (Bucureşti) MSC: 76F20 35Q30 37G99 PDFBibTeX XMLCite \textit{P. Holmes} et al., in: Proceedings of the international congress of mathematicians (ICM), August 21--29, 1990, Kyoto, Japan. Volume II. Tokyo etc.: Springer-Verlag. 1607--1617 (1991; Zbl 0744.58066)
Ball, J. M.; Holmes, P. J.; James, R. D.; Pego, R. L.; Swart, P. J. On the dynamics of fine structure. (English) Zbl 0791.35030 J. Nonlinear Sci. 1, No. 1, 17-70 (1991). MSC: 35J20 74Hxx PDFBibTeX XMLCite \textit{J. M. Ball} et al., J. Nonlinear Sci. 1, No. 1, 17--70 (1991; Zbl 0791.35030) Full Text: DOI
Berkooz, Gal; Holmes, Philip; Lumley, J. L. Intermittent dynamics in simple models of the turbulent wall layer. (English) Zbl 0729.76040 J. Fluid Mech. 230, 75-95 (1991). MSC: 76F10 35Q35 PDFBibTeX XMLCite \textit{G. Berkooz} et al., J. Fluid Mech. 230, 75--95 (1991; Zbl 0729.76040) Full Text: DOI
Holmes, Philip J.; Swart, Pieter J. A mathematical cartoon for the dynamics of fine structure. (English) Zbl 0737.35006 Applied mathematics and computing, Trans. 8th Army Conf., Ithaca/NY (USA) 1990, ARO Rep. 91-1, 11-21 (1991). Reviewer: P.Holmes MSC: 35B40 35Q72 35B30 PDFBibTeX XMLCite \textit{P. J. Holmes} and \textit{P. J. Swart}, in: Global existence, regularity, and boundedness for the Kuramoto- Sivashinsky equation in thin 2D domains. . 11--21 (1991; Zbl 0737.35006)
Szeri, Andrew; Holmes, Philip Nonlinear stability and bifurcation in Hamiltonian systems with symmetry. (English) Zbl 0702.76054 Mathematics of nonlinear science, Proc. AMS Spec. Sess. Annu. Meet., Phoenix/AZ (USA) 1989, Contemp. Math. 108, 33-62 (1990). MSC: 76E30 35B35 35B32 PDFBibTeX XML
Armbruster, Dieter; Guckenheimer, John; Holmes, Philip Kuramoto-Sivashinsky dynamics on the center-unstable manifold. (English) Zbl 0687.34036 SIAM J. Appl. Math. 49, No. 3, 676-691 (1989). Reviewer: B.Aulbach MSC: 34C30 34C40 35B32 37G99 PDFBibTeX XMLCite \textit{D. Armbruster} et al., SIAM J. Appl. Math. 49, No. 3, 676--691 (1989; Zbl 0687.34036) Full Text: DOI
Holmes, Philip Spatial structure of time-periodic solutions of the Ginzburg-Landau equation. (English) Zbl 0618.35003 Physica D 23, 84-90 (1986). MSC: 35B10 35Q99 37D45 PDFBibTeX XMLCite \textit{P. Holmes}, Physica D 23, 84--90 (1986; Zbl 0618.35003) Full Text: DOI
Holmes, Philip; Marsden, Jerrold A partial differential equation with infinitely many periodic orbits: Chaotic oscillations of a forced beam. (English) Zbl 0507.58031 Arch. Ration. Mech. Anal. 76, 135-165 (1981). MSC: 37D45 35B10 37G99 35B05 PDFBibTeX XMLCite \textit{P. Holmes} and \textit{J. Marsden}, Arch. Ration. Mech. Anal. 76, 135--165 (1981; Zbl 0507.58031) Full Text: DOI
Holmes, Philip Space- and time-periodic perturbations of the Sine-Gordon equation. (English) Zbl 0499.58030 Dynamical systems and turbulence, Proc. Symp., Coventry 1980, Lect. Notes Math. 898, 164-191 (1981). MSC: 58J65 58J70 35B20 35B32 35B35 35B10 PDFBibTeX XML
Holmes, Philip Global bifurcations and chaos in the forced oscillations of buckled structures. (English) Zbl 0429.73044 Proc. 1978 IEEE Conf. on decision and control, incl. 17th Symp. on adaptive processes, San Diego/Calif. 1979, 181-185 (1979). MSC: 74G60 74H45 46E35 74K10 35B32 PDFBibTeX XML
Holmes, Philip; Marsden, Jerrold Bifurcations to divergence and flutter in flow-induced oscillations: an infinite dimensional analysis. (English) Zbl 0406.58024 Control of distributed parameter systems, Proc. 2nd IFAC Symp., Conventry 1977, 133-145 (1978). MSC: 37G99 58C25 58K99 35K60 93C20 PDFBibTeX XML
Holmes, Philip; Marsden, Jerrold Bifurcation to divergence and flutter in flow-induced oscillations: An infinite dimensional analysis. (English) Zbl 0385.93028 Automatica 14, 367-384 (1978). MSC: 93C20 93C10 35B32 35B05 37G99 PDFBibTeX XMLCite \textit{P. Holmes} and \textit{J. Marsden}, Automatica 14, 367--384 (1978; Zbl 0385.93028) Full Text: DOI
Holmes, Philip J.; Marsden, Jerrold E. Bifurcations of dynamical systems and nonlinear oscillations in engineering systems. (English) Zbl 0379.35009 Nonlin. partial Differ. Equat. Appl., Proc. Semin., Indiana Univ. 1976/77, Lect. Notes Math. 648, 163-206 (1978). MSC: 35B99 35G20 PDFBibTeX XML