Kukillaya, Raghavendra P.; Holmes, Philip J. A hexapedal jointed-leg model for insect locomotion in the horizontal plane. (English) Zbl 1248.92003 Biol. Cybern. 97, No. 5-6, 379-395 (2007). MSC: 92C10 PDFBibTeX XMLCite \textit{R. P. Kukillaya} and \textit{P. J. Holmes}, Biol. Cybern. 97, No. 5--6, 379--395 (2007; Zbl 1248.92003) Full Text: DOI
Holmes, Philip; Full, Robert J.; Koditschek, Dan; Guckenheimer, John The dynamics of legged locomotion: Models, analyses, and challenges. (English) Zbl 1100.34002 SIAM Rev. 48, No. 2, 207-304 (2006). Reviewer: R. Kodnar (Bratislava) MSC: 34-02 34C60 34C15 34C25 34C29 34E10 92C10 92C20 93C85 PDFBibTeX XMLCite \textit{P. Holmes} et al., SIAM Rev. 48, No. 2, 207--304 (2006; Zbl 1100.34002) Full Text: DOI
Smith, T. R.; Moehlis, J.; Holmes, P. Heteroclinic cycles and periodic orbits for the O(2)-equivariant 0:1:2 mode interaction. (English) Zbl 1099.37044 Physica D 211, No. 3-4, 347-376 (2005). MSC: 37G40 34C37 34C20 34C25 34C28 PDFBibTeX XMLCite \textit{T. R. Smith} et al., Physica D 211, No. 3--4, 347--376 (2005; Zbl 1099.37044) Full Text: DOI
Ghigliazza, R. M.; Holmes, P. Towards a neuromechanical model for insect locomotion: hybrid dynamical systems. (English) Zbl 1084.34050 Regul. Chaotic Dyn. 10, No. 2, 193-225 (2005). MSC: 34C60 34C25 34C23 92C10 PDFBibTeX XMLCite \textit{R. M. Ghigliazza} and \textit{P. Holmes}, Regul. Chaotic Dyn. 10, No. 2, 193--225 (2005; Zbl 1084.34050)
Ghigliazza, R. M.; Altendorfer, R.; Holmes, P.; Koditschek, D. A simply stabilized running model. (English) Zbl 1074.70005 SIAM Rev. 47, No. 3, 519-549 (2005). MSC: 70E55 70E50 70K50 92C10 PDFBibTeX XMLCite \textit{R. M. Ghigliazza} et al., SIAM Rev. 47, No. 3, 519--549 (2005; Zbl 1074.70005) Full Text: DOI Link
Ghigliazza, R. M.; Holmes, P. A minimal model of a central pattern generator and motoneurons for insect locomotion. (English) Zbl 1090.34040 SIAM J. Appl. Dyn. Syst. 3, No. 4, 671-700 (2004). MSC: 34C60 34C15 34C25 34C29 92C20 37N25 34C23 PDFBibTeX XMLCite \textit{R. M. Ghigliazza} and \textit{P. Holmes}, SIAM J. Appl. Dyn. Syst. 3, No. 4, 671--700 (2004; Zbl 1090.34040) Full Text: DOI Link
Ghigliazza, R. M.; Holmes, P. Minimal models of bursting neurons: How multiple currents, conductances, and timescales affect bifurcation diagrams. (English) Zbl 1090.34039 SIAM J. Appl. Dyn. Syst. 3, No. 4, 636-670 (2004). MSC: 34C60 34C15 34C25 34C29 92C20 37N25 34E15 34C23 PDFBibTeX XMLCite \textit{R. M. Ghigliazza} and \textit{P. Holmes}, SIAM J. Appl. Dyn. Syst. 3, No. 4, 636--670 (2004; Zbl 1090.34039) Full Text: DOI
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
Ghigliazza, R. M.; Altendorfer, R.; Holmes, P.; Koditschek, D. A simply stabilized running model. (English) Zbl 1088.34517 SIAM J. Appl. Dyn. Syst. 2, No. 2, 187-218 (2003). MSC: 34C23 37J20 37J25 37J60 70Hxx 70K42 70K50 PDFBibTeX XMLCite \textit{R. M. Ghigliazza} et al., SIAM J. Appl. Dyn. Syst. 2, No. 2, 187--218 (2003; Zbl 1088.34517) 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
Holmes, Philip; Doelman, Arjen; Hek, Geertje; Domokos, Gábor Homoclinic orbits and chaos in three- and four-dimensional flows. (English) Zbl 1004.37013 Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 359, No. 1784, 1429-1438 (2001). Reviewer: Messoud Efendiev (Berlin) MSC: 37C29 34C37 37D45 37G40 37J45 PDFBibTeX XMLCite \textit{P. Holmes} et al., Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 359, No. 1784, 1429--1438 (2001; Zbl 1004.37013) Full Text: DOI
Schmitt, John; Holmes, Philip Mechanical models for insect locomotion: Stability and parameter studies. (English) Zbl 1059.70006 Physica D 156, No. 1-2, 139-168 (2001). MSC: 70E55 70E50 92C10 PDFBibTeX XMLCite \textit{J. Schmitt} and \textit{P. Holmes}, Physica D 156, No. 1--2, 139--168 (2001; Zbl 1059.70006) Full Text: DOI
Moser, Jürgen [Holmes, Philip J.] Stable and random motions in dynamical systems. With special emphasis on celestial mechanics. With a new foreword by Philip J. Holmes. 3rd pbk-ed. 3rd pbk-ed. (English) Zbl 0991.70002 Princeton, NJ: Prineton University Press. 198 p. (2001). Reviewer: David Martin de Diego (Madrid) MSC: 70-02 70F15 37N05 37Cxx PDFBibTeX XMLCite \textit{J. Moser}, Stable and random motions in dynamical systems. With special emphasis on celestial mechanics. With a new foreword by Philip J. Holmes. 3rd pbk-ed. Princeton, NJ: Prineton University Press (2001; Zbl 0991.70002)
Holmes, P.; Domokos, G.; Hek, G. Euler buckling in a potential field. (English) Zbl 1139.74415 J. Nonlinear Sci. 10, No. 4, 477-505 (2000). MSC: 74G60 34C37 37J45 74K10 37N15 PDFBibTeX XMLCite \textit{P. Holmes} et al., J. Nonlinear Sci. 10, No. 4, 477--505 (2000; Zbl 1139.74415) Full Text: DOI
Wittenberg, Ralf W.; Holmes, Philip The limited effectiveness of normal forms: A critical review and extension of local bifurcation studies of the Brusselator PDE. (English) Zbl 0893.34027 Physica D 100, No. 1-4, 1-40 (1997). MSC: 34C20 34C23 34C25 34C37 PDFBibTeX XMLCite \textit{R. W. Wittenberg} and \textit{P. Holmes}, Physica D 100, No. 1--4, 1--40 (1997; Zbl 0893.34027) Full Text: DOI
Ghrist, Robert W.; Holmes, Philip J.; Sullivan, Michael C. Knots and links in three-dimensional flows. (English) Zbl 0869.58044 Lecture Notes in Mathematics. 1654. Berlin: Springer. x, 208 p. (1997). Reviewer: K.Resende (Campinas) MSC: 37C10 57M25 34C25 37-02 57-02 PDFBibTeX XMLCite \textit{R. W. Ghrist} et al., Knots and links in three-dimensional flows. Berlin: Springer (1997; Zbl 0869.58044) Full Text: DOI
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
Ghrist, Robert W.; Holmes, Philip J. An ODE whose solutions contain all knots and links. (English) Zbl 0878.34038 Int. J. Bifurcation Chaos Appl. Sci. Eng. 6, No. 5, 779-800 (1996). MSC: 34C25 94C05 PDFBibTeX XMLCite \textit{R. W. Ghrist} and \textit{P. J. Holmes}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 6, No. 5, 779--800 (1996; Zbl 0878.34038) 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
Ghrist, Robert; Holmes, Philip Knots and orbit genealogies in three dimensional flows. (English) Zbl 0803.58047 Schlomiuk, Dana (ed.), Bifurcations and periodic orbits of vector fields. Proceedings of the NATO Advanced Study Institute and Séminaire de Mathématiques Supérieures, Montréal, Canada, July 13-24, 1992. Dordrecht: Kluwer Academic Publishers. NATO ASI Ser., Ser. C, Math. Phys. Sci. 408, 185-239 (1993). Reviewer: W.Kryszewski (Torún) MSC: 37C10 57M25 37G99 PDFBibTeX XMLCite \textit{R. Ghrist} and \textit{P. Holmes}, NATO ASI Ser., Ser. C, Math. Phys. Sci. 408, 185--239 (1993; Zbl 0803.58047)
Holmes, P. J.; Stuart, C. A. Homoclinic orbits for eventually autonomous planar flows. (English) Zbl 0757.34038 Z. Angew. Math. Phys. 43, No. 4, 598-625 (1992). Reviewer: Yu.N.Bibikov (St.Petersburg) MSC: 34C37 37G15 PDFBibTeX XMLCite \textit{P. J. Holmes} and \textit{C. A. Stuart}, Z. Angew. Math. Phys. 43, No. 4, 598--625 (1992; Zbl 0757.34038) 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
Mielke, A.; Holmes, P.; O’Reilly, O. Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle- center. (English) Zbl 0749.58022 J. Dyn. Differ. Equations 4, No. 1, 95-126 (1992). Reviewer: W.Sarlet (Gent) MSC: 37J99 37G99 34C25 PDFBibTeX XMLCite \textit{A. Mielke} et al., J. Dyn. Differ. Equations 4, No. 1, 95--126 (1992; Zbl 0749.58022) Full Text: DOI
Campbell, Sue Ann; Holmes, Philip Heteroclinic cycles and modulated travelling waves in a system with \(D_ 4\) symmetry. (English) Zbl 0774.34031 Physica D 59, No. 1-3, 52-78 (1992). MSC: 34C37 34C23 34C25 34C27 PDFBibTeX XMLCite \textit{S. A. Campbell} and \textit{P. Holmes}, Physica D 59, No. 1--3, 52--78 (1992; Zbl 0774.34031) Full Text: DOI
Devaney, Robert L. (ed.); Keen, Linda (ed.) [Devaney, R. L.; Holmes, P. J.; Alligood, K. T.; Yorke, J. A.; Keen, Linda; Branner, B.; Harrison, J.; Barnsley, M. F.] Chaos and fractals. The mathematics behind the computer graphics. (Lectures delivered in the AMS short course on August 6-7, 1988, given in conjunction with the AMS centennial meeting in Procidence, RI). (English) Zbl 0677.58004 Proceedings of Symposia in Applied Mathematics, 39; AMS Short Course Lecture Notes; Introductory Survey Lectures. Providence, RI: American Mathematical Society (AMS). ix, 148 p. $ 31.00 (1989). Reviewer: G.Ehrig MSC: 37-06 37D45 37-02 37G99 37B10 00B25 68U05 37F50 30D05 28A80 PDFBibTeX XMLCite \textit{R. L. Devaney} (ed.) and \textit{L. Keen} (ed.), Chaos and fractals. The mathematics behind the computer graphics. (Lectures delivered in the AMS short course on August 6-7, 1988, given in conjunction with the AMS centennial meeting in Procidence, RI). Providence, RI: American Mathematical Society (1989; Zbl 0677.58004)
Holmes, Philip Knotted periodic orbits in suspensions of Smale’s horseshoe: Extended families and bifurcation sequences. (English) Zbl 0825.58035 Physica D 40, No. 1, 42-64 (1989). MSC: 37D99 37G99 57M25 37D45 PDFBibTeX XMLCite \textit{P. Holmes}, Physica D 40, No. 1, 42--64 (1989; Zbl 0825.58035) Full Text: DOI
Wiggins, Stephen; Holmes, Philip Errata: Homoclinic orbits in slowly varying oscillators. (English) Zbl 0649.34043 SIAM J. Math. Anal. 19, No. 5, 1245-1255 (1988). MSC: 34C25 34D10 37J99 PDFBibTeX XMLCite \textit{S. Wiggins} and \textit{P. Holmes}, SIAM J. Math. Anal. 19, No. 5, 1245--1255 (1988; Zbl 0649.34043) Full Text: DOI
Holmes, Philip Knots and orbit genealogies in nonlinear oscillators. (English) Zbl 0646.34041 New directions in dynamical systems, London Math. Soc. Lect. Note Ser. 127, 150-191 (1988). Reviewer: P.Holmes MSC: 34C15 57M25 34C25 PDFBibTeX XML
Guckenheimer, John; Holmes, Philip Structurally stable heteroclinic cycles. (English) Zbl 0645.58022 Math. Proc. Camb. Philos. Soc. 103, No. 1, 189-192 (1988). Reviewer: J.Andres MSC: 37J99 37G15 PDFBibTeX XMLCite \textit{J. Guckenheimer} and \textit{P. Holmes}, Math. Proc. Camb. Philos. Soc. 103, No. 1, 189--192 (1988; Zbl 0645.58022) Full Text: DOI
Hockett, Kevin; Holmes, Philip Bifurcation to badly ordered orbits in one-parameter families of circle maps or angels fallen from the devil’s staircase. (English) Zbl 0644.58006 Proc. Am. Math. Soc. 102, No. 4, 1031-1051 (1988). MSC: 37B99 37G99 26A18 PDFBibTeX XMLCite \textit{K. Hockett} and \textit{P. Holmes}, Proc. Am. Math. Soc. 102, No. 4, 1031--1051 (1988; Zbl 0644.58006) Full Text: DOI
Armbruster, Dieter; Guckenheimer, John; Holmes, Philip Heteroclinic cycles and modulated travelling waves in systems with 0(2) symmetry. (English) Zbl 0634.34027 Physica D 29, No. 3, 257-282 (1988). MSC: 34C25 37G99 PDFBibTeX XMLCite \textit{D. Armbruster} et al., Physica D 29, No. 3, 257--282 (1988; Zbl 0634.34027) Full Text: DOI
Holmes, P. J. Knotted periodic orbits in suspensions of annulus maps. (English) Zbl 0642.58039 Proc. R. Soc. Lond., Ser. A 411, 351-378 (1987). Reviewer: Ding Tongren MSC: 37G99 34C25 PDFBibTeX XMLCite \textit{P. J. Holmes}, Proc. R. Soc. Lond., Ser. A 411, 351--378 (1987; Zbl 0642.58039) Full Text: DOI
Kiemel, Tim; Holmes, Philip A model for the periodic synaptic inhibition of a neuronal oscillator. (English) Zbl 0629.92004 IMA J. Math. Appl. Med. Biol. 4, 145-169 (1987). Reviewer: B.D.Sleeman MSC: 92Cxx 34C05 PDFBibTeX XMLCite \textit{T. Kiemel} and \textit{P. Holmes}, IMA J. Math. Appl. Med. Biol. 4, 145--169 (1987; Zbl 0629.92004)
Wiggins, Stephen; Holmes, Philip Homoclinic orbits in slowly varying oscillators. (English) Zbl 0622.34041 SIAM J. Math. Anal. 18, 612-629 (1987). Reviewer: Charles A.Swanson (Vancouver) MSC: 34C25 34D10 37J99 37G99 70H05 34A12 PDFBibTeX XMLCite \textit{S. Wiggins} and \textit{P. Holmes}, SIAM J. Math. Anal. 18, 612--629 (1987; Zbl 0622.34041) Full Text: DOI Link
Wiggins, Stephen; Holmes, Philip Periodic orbits in slowly varying oscillators. (English) Zbl 0619.34041 SIAM J. Math. Anal. 18, 592-611 (1987). MSC: 34C25 34C10 37G99 PDFBibTeX XMLCite \textit{S. Wiggins} and \textit{P. Holmes}, SIAM J. Math. Anal. 18, 592--611 (1987; Zbl 0619.34041) Full Text: DOI
Holmes, Philip Knotted periodic orbits in suspensions of Smale’s horseshoe: period multiplying and cabled knots. (English) Zbl 0623.58014 Physica D 21, 7-41 (1986). MSC: 37G99 37J40 PDFBibTeX XMLCite \textit{P. Holmes}, Physica D 21, 7--41 (1986; Zbl 0623.58014) 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 Chaotic motions in a weakly nonlinear model for surface waves. (English) Zbl 0602.76015 J. Fluid Mech. 162, 365-388 (1986). Reviewer: P.Smith MSC: 76B15 37G99 70K20 PDFBibTeX XMLCite \textit{P. Holmes}, J. Fluid Mech. 162, 365--388 (1986; Zbl 0602.76015) Full Text: DOI
Veerman, Peter; Holmes, Philip The existence of arbitrarily many distinct periodic orbits in a two degree of freedom Hamiltonian system. (English) Zbl 0595.58036 Physica D 14, No. 2-3, 177-192 (1985). MSC: 37G99 PDFBibTeX XMLCite \textit{P. Veerman} and \textit{P. Holmes}, Physica D 14, No. 2--3, 177--192 (1985; Zbl 0595.58036) Full Text: DOI
Holmes, P. Dynamics of a nonlinear oscillator with feedback control. I: Local analysis. (English) Zbl 0581.93028 J. Dyn. Syst. Meas. Control 107, 159-165 (1985). Reviewer: G.Leonov MSC: 93C10 37G99 70K05 34C15 70K20 37C75 37G15 93C15 93D99 PDFBibTeX XMLCite \textit{P. Holmes}, J. Dyn. Syst. Meas. Control 107, 159--165 (1985; Zbl 0581.93028) Full Text: DOI
Bélair, Jacques; Holmes, Philip On linearly coupled relaxation oscillations. (English) Zbl 0565.70025 Q. Appl. Math. 42, 193-219 (1984). Reviewer: H.J.Bangen MSC: 70K05 PDFBibTeX XMLCite \textit{J. Bélair} and \textit{P. Holmes}, Q. Appl. Math. 42, 193--219 (1984; Zbl 0565.70025) Full Text: DOI
Holmes, P.; Whitley, D. Bifurcations of one- and two-dimensional maps. (English) Zbl 0556.58023 Philos. Trans. R. Soc. Lond., A 311, 43-102 (1984). Reviewer: J.Czyz MSC: 37D99 34C25 PDFBibTeX XMLCite \textit{P. Holmes} and \textit{D. Whitley}, Philos. Trans. R. Soc. Lond., Ser. A 311, 43--102 (1984; Zbl 0556.58023) Full Text: DOI
Greenspan, Bernie; Holmes, Philip Repeated resonance and homoclinic bifurcation in a periodically forced family of oscillators. (English) Zbl 0547.34028 SIAM J. Math. Anal. 15, 69-97 (1984). Reviewer: V.Răsvan MSC: 34C15 34C25 70H05 34C05 34C29 PDFBibTeX XMLCite \textit{B. Greenspan} and \textit{P. Holmes}, SIAM J. Math. Anal. 15, 69--97 (1984; Zbl 0547.34028) Full Text: DOI
Holmes, Philip Some remarks on chaotic particle paths in time-periodic, three- dimensional swirling flows. (English) Zbl 0521.76049 Contemp. Math. 28, 393-404 (1984). MSC: 76F99 PDFBibTeX XMLCite \textit{P. Holmes}, Contemp. Math. 28, 393--404 (1984; Zbl 0521.76049) Full Text: DOI
Shaw, S. W.; Holmes, P. J. A periodically forced impact oscillator with large dissipation. (English) Zbl 0539.70032 J. Appl. Mech. 50, 849-857 (1983). MSC: 70K40 70K50 PDFBibTeX XMLCite \textit{S. W. Shaw} and \textit{P. J. Holmes}, J. Appl. Mech. 50, 849--857 (1983; Zbl 0539.70032) Full Text: DOI
Guckenheimer, John; Holmes, Philip Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. (English) Zbl 0515.34001 Applied Mathematical Sciences, 42. New York etc.: Springer-Verlag. XVI, 453 p., 206 figs. (1983). MSC: 34-02 34C15 37-XX 70H05 34C25 34D20 34C29 PDFBibTeX XML Full Text: DOI
Holmes, P. J. The dynamics of repeated impacts with a sinusoidally vibrating table. (English) Zbl 0518.73015 J. Sound Vib. 84, 173-189 (1982). MSC: 74M20 70F99 74K20 74H45 PDFBibTeX XMLCite \textit{P. J. Holmes}, J. Sound Vib. 84, 173--189 (1982; Zbl 0518.73015) Full Text: DOI
Holmes, Philip J.; Marsden, Jerrold E. Horseshoes in perturbations of Hamiltonian systems with two degrees of freedom. (English) Zbl 0489.58013 Commun. Math. Phys. 82, 523-544 (1982). MSC: 37J99 37D99 70H05 PDFBibTeX XMLCite \textit{P. J. Holmes} and \textit{J. E. Marsden}, Commun. Math. Phys. 82, 523--544 (1982; Zbl 0489.58013) Full Text: DOI
Holmes, Philip J. Errata and addenda: Averaging and chaotic motions in forced oscillations. (English) Zbl 0518.70023 SIAM J. Appl. Math. 40, 167-168 (1981). MSC: 70K20 37D45 34C25 70K99 70L05 70K40 PDFBibTeX XMLCite \textit{P. J. Holmes}, SIAM J. Appl. Math. 40, 167--168 (1981; Zbl 0518.70023) 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; Lewis, Donald A periodically forced scalar ordinary differential equation. (English) Zbl 0486.34029 Int. J. Non-Linear Mech. 16, 233-246 (1981). MSC: 37G99 PDFBibTeX XMLCite \textit{P. Holmes} and \textit{D. Lewis}, Int. J. Non-Linear Mech. 16, 233--246 (1981; Zbl 0486.34029) Full Text: DOI
Holmes, C.; Holmes, P. Second order averaging and bifurcations to subharmonics in Duffing’s equation. (English) Zbl 0478.73028 J. Sound Vib. 78, 161-174 (1981). MSC: 74G60 34C29 74S30 34E10 74J99 PDFBibTeX XMLCite \textit{C. Holmes} and \textit{P. Holmes}, J. Sound Vib. 78, 161--174 (1981; Zbl 0478.73028) Full Text: DOI
Holmes, Philip J. Averaging and chaotic motions in forced oscillations. (English) Zbl 0472.70024 SIAM J. Appl. Math. 38, 65-80 (1980). MSC: 70K20 37D45 34C25 70K99 70L05 PDFBibTeX XMLCite \textit{P. J. Holmes}, SIAM J. Appl. Math. 38, 65--80 (1980; Zbl 0472.70024) Full Text: DOI
Rand, R. H.; Holmes, P. J. Bifurcation of periodic motions in two weakly coupled van der Pol oscillators. (English) Zbl 0447.70028 Int. J. Non-Linear Mech. 15, 387-399 (1980). MSC: 70K05 70G10 PDFBibTeX XMLCite \textit{R. H. Rand} and \textit{P. J. Holmes}, Int. J. Non-Linear Mech. 15, 387--399 (1980; Zbl 0447.70028) Full Text: DOI
Holmes, Philip Periodic, nonperiodic and irregular motions in a Hamiltonian system. (English) Zbl 0427.70026 Rocky Mt. J. Math. 10, 679-693 (1980). MSC: 70H05 PDFBibTeX XMLCite \textit{P. Holmes}, Rocky Mt. J. Math. 10, 679--693 (1980; Zbl 0427.70026) Full Text: DOI
Holmes, Philip J. A strange family of three-dimensional vector fields near a degenerate singularity. (English) Zbl 0421.58016 J. Differ. Equations 37, 382-403 (1980). MSC: 37D45 37G99 PDFBibTeX XMLCite \textit{P. J. Holmes}, J. Differ. Equations 37, 382--403 (1980; Zbl 0421.58016) Full Text: DOI
Holmes, Philip; Marsden, Jerrold E. Qualitative techniques for bifurcation analysis of complex systems. (English) Zbl 0437.34039 Bifurcation theory and applications in scientific disciplines, Pap. Conf., New York 1977, Ann. New York Acad. Sci., Vol. 316, 608-622 (1979). MSC: 37-XX 34C25 34C10 PDFBibTeX XML
Moon, F. C.; Holmes, P. J. A magnetoelastic strange attractor. (English) Zbl 0405.73082 J. Sound Vib. 65, 275-296 (1979). MSC: 74F15 74H55 PDFBibTeX XMLCite \textit{F. C. Moon} and \textit{P. J. Holmes}, J. Sound Vib. 65, 275--296 (1979; Zbl 0405.73082) Full Text: DOI
Holmes, P. J.; Rand, D. A. The bifurcations of Duffing’s equation: An application of catastrophe theory. (English) Zbl 0337.34049 J. Sound Vibration 44, 237-253 (1976). MSC: 34D30 34C25 37D99 70K20 93C10 PDFBibTeX XMLCite \textit{P. J. Holmes} and \textit{D. A. Rand}, J. Sound Vib. 44, 237--253 (1976; Zbl 0337.34049) Full Text: DOI