Professor Alan R Champneys

Search results

• 2001

  The torsional buckling and writhing of a simply-supported rod hanging under gravity

  Stump, D., Champneys, A. & Van der Heijden, G., 2001, In: International Journal of Solids and Structures. 38, Issue 5, p. 795 - 813

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

• Unified Framework for the analysis of grazing and border-collisions in piecewise-smooth systems

  Di Bernardo, M., Budd, C. & Champneys, A., 2001, In: Physical Review Letters. 86(12), p. 2554 - 2556

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

• Walking cavity solitons

  Skryabin, D. & Champneys, A., 2001.

  Research output: Working paper

  File

  • Solitary Wave 100%
  • Component Model 50%
  • Oscillator 50%
  111 Downloads (Pure)

• Walking cavity solitons

  Skyrabin, D. & Champneys, A., 2001, In: Physical Review E: Statistical, Nonlinear, and Soft Matter Physics. 6306, Issue 6, Art No: 066610

  Research output: Contribution to journal › Article (Academic Journal) › peer-review
• 2000

  A global characterization of gap solitary-wave solutions to a coupled KdV system

  Champneys, A., Groves, M. & Woods, P., 2000, In: Physics Letters A. 271, Issue 3, p. 178 - 190

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  10 Citations (Scopus)

• A global characterization of gap solitary-wave solutions to a coupled KdV system

  Champneys, A., Groves, M. & Woods, P., 2000.

  Research output: Working paper

  File

  • Korteweg-De Vries Equation 100%
  • Solitary Wave 100%
  • Hopf Bifurcation 50%
  • Bifurcation 25%
  345 Downloads (Pure)

• Cascades of homoclinic orbits to a saddle-centre for reversible and perturbed Hamiltonian systems

  Champneys, A. & Harterich, J., 2000, In: Dynamics and Stability of Systems. 15(3), p. 231 - 252

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  21 Citations (Scopus)

• Cellular Buckling in Long Structures

  Hunt, G., Peletier, M., Champneys, A., Woods, P., Wadee, M., Budd, C. & Lord, G., 2000, In: Nonlinear Dynamics. 21, p. 3 - 29

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  215 Citations (Scopus)

• Corner collision implies border-collision bifurcation

  di Bernardo, M., Budd, C. & Champneys, A., 2000.

  Research output: Working paper

  File

  • Linear Map 100%
  • piecewise linear 100%
  • Ordinary Differential Equation 33%
  • Piecewise Smooth 33%
  • Periodic Solution 33%
  373 Downloads (Pure)

• Death of period-doublings: locating the homoclinic-doubling cascade

  Oldeman, B. E., Krauskopf, B. & Champneys, A. R., 15 Nov 2000, In: Physica D: Nonlinear Phenomena. 146, 1-4, p. 100-120 21 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  Open Access

  File

  • Vector Field 100%
  • Homoclinic 100%
  • Period Doubling 100%
  • Eigenvalue 50%
  • Numerical Algorithm 50%
  29 Citations (Scopus)

  316 Downloads (Pure)

• Do true elevation gravity-capillary solitary waves exist? a numerical investigation

  Champneys, A., Vanden-Broek, J.-M. & Lord, G., 2000.

  Research output: Working paper

  File

  • Korteweg-De Vries Equation 100%
  • Codimension 100%
  • Open Problem 100%
  • Parameter Plane 100%
  • Strong Conclusion 100%
  383 Downloads (Pure)

• Embedded solitons in a three-wave system

  Champneys, A. & Malomed, B., 2000, In: Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics. 61, p. 886 - 890

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  38 Citations (Scopus)

• Frequency selection by soliton excitation in nondegenerate intracavity downconversion

  Skyrabin, D., Champneys, A. & Firth, W., 2000, In: Physical Review Letters. 84, p. 463 - 466

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

• Higher-order nonlinear modes and bifurcation phenomena due to degenerate parameteric four-wave mixing.

  Kolossovski, K., Buryak, A., Steblina, V., Champneys, A. & Sammut, R., 2000.

  Research output: Working paper

  File

  • Solitary Wave 100%
  • Four-Wave Mixing 100%
  • Planar Waveguide 20%
  • Harmonics 20%
  • Volume 20%
  146 Downloads (Pure)

• Higher-order nonlinear modes and bifurcation phenomena due to degenerate parametric four-wave mixing

  Kolossovski, K., Buryak, A., Steblina, A., Champneys, A. & Sammut, R., 2000, In: Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics. 62, Issue 3, p. 4309 - 4317

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  14 Citations (Scopus)

• Normal form maps for grazing bifurcations in N-dimensional piecewise-smooth dynamical systems

  di Bernardo, M., Budd, C. & Champneys, A., 2000.

  Research output: Working paper

  File

  • Vector Field 100%
  • Piecewise Smooth 100%
  • Smooth Dynamical Systems 100%
  • Ordinary Differential Equation 50%
  • Leading Order Term 50%
  583 Downloads (Pure)

• Numerical unfoldings of codimension-three resonant homoclinic flip bifurcations

  Oldeman, B., Krauskopf, B. & Champneys, A., 2000.

  Research output: Working paper

  File

  • Codimension 100%
  • Eigenvalue 40%
  • Vector Field 20%
  • Parameter Space 20%
  • Dimensional Vector 20%
  384 Downloads (Pure)

• Origin of Multikinks in Nonlinear Dispersive Systems

  Champneys, A. & Kivshar, Y., 2000, In: Physical Review E: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics. 61, p. 2551 - 2554

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

• Resonant homoclinic flip bifurcations : a numerical investigation

  Krauskopf, B., Oldeman, B. & Champneys, A., 2000, Proc of Equadiff '99. World Scientific Publishing Co., Vol. 1. p. 55 - 57

  Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

• Solitary waves in nonlinear beam equations : stability, fission and fusion

  Champneys, A., McKenna, P. & Zegeling, P., 2000, In: Nonlinear Dynamics. 21, p. 31 - 53

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  26 Citations (Scopus)

• The `Indian rope trick' for a parametrically excited flexible rod : nonlinear and subharmonic analysis

  Fraser, W. & Champneys, A., 2000.

  Research output: Working paper

  File

  • Rod 100%
  • Dimensionless Parameter 50%
  • Bending Stiffness 50%
  • Dimensionality 50%
  • Critical Length 50%
  344 Downloads (Pure)

• The 'Indian rope trick' for a parametrically excited flexible rod : I linearised analysis

  Champneys, A. & Fraser, W., 2000, In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 456, p. 553 - 570

  Research output: Contribution to journal › Article (Academic Journal) › peer-review
• 1999

  A non-transverse Shilnikov-Hopf bifurcation; the uncoupling of homoclinic orbits and homoclinic tangencies

  Champneys, A. & Rodriguez-Luis, A., 1999, In: Physica D: Nonlinear Phenomena. 128, p. 130 - 158

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

• Codimension-one persistence beyond all orders of homoclinic orbits to singular saddle centres in reversible systems

  Champneys, A., 1999.

  Research output: Working paper

  File

  • Codimension 100%
  • Nonlinear Term 100%
  • Melnikov Function 100%
  • Approximates 50%
  • Asymptotics 50%
  339 Downloads (Pure)

• Computation of homoclinic orbits in partial differential equations : an application to cylindrical shell buckling

  Lord, G., Champneys, A. & Hunt, G., 1999, In: SIAM Journal on Scientific Computing. 21, p. 591 - 619

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  30 Citations (Scopus)

• Embedded solitons in a three-wave system

  Champneys, A. & Malomed, B., 1999.

  Research output: Working paper

  File

  • Solitary Wave 100%
  • Photonics 16%
  • Optical Waveguides 16%
  • Harmonics 16%
  • Bragg Gratings 16%
  312 Downloads (Pure)

• Frequency selection by soliton excitation in nondegenerate intracavity downconversion

  Skryabin, D., Champneys, A. & Firth, W., 1999.

  Research output: Working paper

  File

  • Solitary Wave 100%
  • Downconversion 100%
  264 Downloads (Pure)

• Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian Hopf bifurcation

  Woods, P. & Champneys, A., 1999, In: Physica D: Nonlinear Phenomena. 129, p. 147 - 170

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  232 Citations (Scopus)

• Homoclinic and heteroclinic orbits underlying the post-buckling of axially-compressed cylindrical shells

  Hunt, G., Lord, G. & Champneys, A., 1999, In: Computer Methods in Applied Mechanics and Engineering. 170, p. 239 - 251

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  67 Citations (Scopus)

• Homoclinic orbits in reversible systems II : Multi-bumps and saddle-centres

  Champneys, A., 1999, In: CWI Quarterly. 12, p. 185 - 212

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

• Localised solutions of a coupled first and second harmonic nonlinear Shrodinger system

  Yew, A., Champneys, A. & McKenna, P., 1999, In: Journal of Nonlinear Science. 9, p. 33 - 52

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

• Localization and solitary waves in solid mechanics

  Champneys, A., Hunt, G. & Thompson, J., 1999, World Scientific Advanced Series in Nonlinear Dynamics. 388 p.

  Research output: Book/Report › Edited book

• Moving embedded solitons

  Champneys, A. & Malomed, B., 1999, In: Journal of Physics A: Mathematical and General. 32 L, p. 547 - 553

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  35 Citations (Scopus)

• Moving embedded solitons

  Champneys, A. & Malomed, B., 1999.

  Research output: Working paper

  File

  • Codimension 100%
  • Parameter Space 100%
  • Linear Approximation 100%
  • Continuous Spectra 100%
  • Nonlinearity 100%
  266 Downloads (Pure)

• Numerical investigation of resonant homoclinic flip bifurcations I : the single homoclinic-doubling case

  Oldeman, B., Krauskopf, B. & Champneys, A., 1999, (Unpublished).

  Research output: Working paper

  File

  • Homoclinic 100%
  • Flip 93%
  • Doubling 92%
  • Bifurcation Curve 22%
  • Homoclinic Bifurcation 22%
  76 Downloads (Pure)

• On twisted elastic rods constrained to lie in the plane

  Van der Heijden, G., Champneys, A. & Thompson, J., 1999, In: Journal of the Mechanics and Physics of Solids. 47, p. 59 - 79

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

• Origin of multikinks in nonlinear dispersive systems

  Champneys, A. & Kivshar, Y., 1999.

  Research output: Working paper

  File

  • Dispersive 100%
  • Parabolic 50%
  • Discrete Set 50%
  • Nonlinear System 50%
  • Computer Simulation 50%
  95 Downloads (Pure)

• Resonant homoclinic flip bifurcations: a numerical investigation

  Krauskopf, B., Oldeman, B. & Champneys, A., 1999.

  Research output: Working paper

  File

  • Codimension 100%
  • Numerical Analysis 100%
  299 Downloads (Pure)

• Sliding Orbits and Double Spiral Bifurcation Diagrams in DC/DC converters

  Di Bernardo, M., Champneys, A., Budd, C. & Vasca, F., 1999, Proc. ISCAS99 (IEEE Conf on Circuits and Systems) Orlando, USA. p. 262 - 266

  Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

• The `Indian rope trick' for a parametrically excited flexible rod : linearised analysis

  Champneys, A. & Fraser, W., 1999.

  Research output: Working paper

  File

  • Asymptotics 100%
  • PDE 100%
  • Rod 100%
  • Critical Length 100%
  • Partial Differential Equation 66%
  113 Downloads (Pure)

• The torsional buckling and writhing of a simply-supported rod hanging under gravity

  Stump, D., Champneys, A. & van der Heijden, G., 1999.

  Research output: Working paper

  File

  • Approximates 100%
  • Asymptotics 100%
  • Parabolic 100%
  • Perturbation Theory 100%
  • Spiral 100%
  356 Downloads (Pure)
• 1998

  An adaptive Newton-Picard algorithm with subspace iteration for computing periodic solutions

  Lust, K., Roose, D., Spence, A. & Champneys, A., 1998, In: SIAM Journal on Scientific Computing. 19, p. 1188 - 1209

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  115 Citations (Scopus)

• Analysis of non-smooth dynamics of the DC/DC Buck Converter

  Di Bernardo, M., Budd, C. J. & Champneys, A., 1998, In: Nonlinearity. 11, p. 859 - 890 31 p.

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  • Piecewise Smooth 100%
  • Wide Class 100%
  • Turning Point 100%
  • Orbit 100%
  • Computer Simulation 100%

• Cascades of homoclinic orbits to a saddle-centre for reversible and perturbed Hamiltonian systems

  Champneys, A. & Haerterich, J., 1998, (Unpublished).

  Research output: Working paper

  File

  • Eigenvalue 100%
  • Hamiltonian Systems 100%
  • Reversibility 100%
  • Nondegeneracy 50%
  • Infinite Sequence 50%
  331 Downloads (Pure)

• Cellular buckling in long structures

  Peletier, M., Champneys, A., Woods, P., Wadee, M., Budd, C., Lord, G. & Hunt, G., 1998.

  Research output: Working paper

  File

  • Energy Engineering 100%
  • Homoclinic 100%
  • Structural System 100%
  • End Shortening 100%
  • Practical Significance 100%
  126 Downloads (Pure)

• Grazing, skipping and sliding : analysis of the non-smooth dynamics of the DC/DC buck converter

  Di Bernardo, M., Budd, C. & Champneys, A., 1998, In: Nonlinearity. 11, p. 859 - 890

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  141 Citations (Scopus)

• Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian Hopf bifurcation

  Champneys, A. & Woods, P., 1998.

  Research output: Working paper

  File

  • Hopf Bifurcation 100%
  • Ordinary Differential Equation 50%
  • Eigenvalue 50%
  • Dimensional System 50%
  • Orbit 50%
  442 Downloads (Pure)

• Homoclinic and heteroclinic orbits underlying the post-buckling of axially-compressed cylindrical shells

  Hunt, G., Lord, G. & Champneys, A., 1998, (Unpublished).

  Research output: Working paper

  File

  • Homoclinic 100%
  • Equilibrium State 100%
  • Non-Linear Dynamics 100%
  • Cylindrical Shell 100%
  • Asymptotics 100%
  423 Downloads (Pure)

• Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics

  Champneys, A., 1998, In: Physica D: Nonlinear Phenomena. 112, p. 158 - 186

  Research output: Contribution to journal › Article (Academic Journal) › peer-review

  237 Citations (Scopus)

• Homoclinic orbits in reversible systems II : multi-bumps and saddle-centres

  Champneys, A., 1998, (Unpublished).

  Research output: Working paper

  File

  • Ordinary Differential Equation 100%
  • Codimension 100%
  • Eigenvalue 100%
  • Hopf Bifurcation 100%
  • Time Order 100%
  98 Downloads (Pure)