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Mathematics

D-Index
57
Citations
14782
World Ranking
683
National Ranking
50

Overview

Alan R Champneys is affiliated with the University of Bristol in the United Kingdom. Their research primarily focuses on the field of Engineering, with extensive work in related subfields such as Computer Networks and Communications, Public Health, Environmental and Occupational Health, Statistical and Nonlinear Physics, Biomedical Engineering, and Control and Systems Engineering.

The scientist's primary topics of research include:

  • Nonlinear Dynamics and Pattern Formation
  • Mathematical and Theoretical Epidemiology and Ecology Models
  • Sports Dynamics and Biomechanics
  • Ecosystem dynamics and resilience
  • Stochastic dynamics and bifurcation
  • COVID-19 epidemiological studies
  • Evolution and Genetic Dynamics

Several recent papers illustrate their research contributions and thematic focus:

  • "Bistability, wave pinning and localisation in natural reaction-diffusion systems", 2020, Physica D Nonlinear Phenomena
  • "Emergence of the London Millennium Bridge instability without synchronisation", 2021, Nature Communications
  • "Localized patterns and semi-strong interaction, a unifying framework for reaction-diffusion systems", 2021, IMA Journal of Applied Mathematics
  • "Dissecting the snake: Transition from localized patterns to spike solutions", 2021, Physica D Nonlinear Phenomena
  • "Unified framework for localized patterns in reaction-diffusion systems; the Gray-Scott and Gierer-Meinhardt cases", 2021, Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences

The venues where the scientist frequently publishes include:

  • arXiv (Cornell University)
  • SIAM Journal on Applied Dynamical Systems
  • IMA Journal of Applied Mathematics
  • Journal of Mathematical Biology
  • Scientific Reports

Alan R Champneys often collaborates with other researchers. Their frequent co-authors include:

  • Edgardo Villar-Sepúlveda
  • Fahad Al Saadi
  • Róbert Szalai
  • Alexander D. Shaw
  • Michael I. Friswell

Best Publications

  • Piecewise-smooth Dynamical Systems: Theory and Applications

    Mario Di Bernardo;C. J. Budd;Alan R. Champneys;P. Kowalczyk

  • AUTO-07p: Continuation and bifurcation software for ordinary differential equations

    E. J. Doedel;A. R. Champneys;Fabio Dercole;T. F. Fairgrieve

  • AUTO 2000 : CONTINUATION AND BIFURCATION SOFTWARE FOR ORDINARY DIFFERENTIAL EQUATIONS (with HomCont)

    Eusebius J. Doedel;Randy C. Paenroth;Alan R. Champneys;Thomas F. Fairgrieve

  • Bifurcations in Nonsmooth Dynamical Systems

    Mario di Bernardo;Chris J. Budd;Alan R. Champneys;Piotr Kowalczyk

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

    A. R. Champneys

  • Cellular Buckling in Long Structures

    GW Hunt;MA Mark Peletier;AR Champneys;PD Woods

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

    Unknown

  • A numerical toolbox for homoclinic bifurcation analysis

    A.R. Champneys;Yu. A. Kuznetsov;Yu. A. Kuznetsov;B. Sandstede

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

    M. di Bernardo;C. J. Budd;A. R. Champneys

  • Piecewise smooth dynamical systems

    Alan R. Champneys;Mario di Bernardo

  • Localized Hexagon Patterns of the Planar Swift–Hohenberg Equation

    David J. B. Lloyd;Björn Sandstede;Daniele Avitabile;Alan R. Champneys

  • Bifurcation and coalescence of a plethora of homoclinic orbits for a Hamiltonian system

    B Buffoni;Alan R Champneys;JF Toland

  • NUMERICAL DETECTION AND CONTINUATION OF CODIMENSION-TWO HOMOCLINIC BIFURCATIONS

    A.R. Champneys;Yu. A. Kuznetsov

  • Chapter 4 – Numerical Continuation, and Computation of Normal Forms

    Wolf-Jürgen Beyn;Alan Champneys;Eusebius Doedel;Willy Govaerts

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

    Mario di Bernardo;Chris Budd;Alan Champneys

  • Grazing and border-collision in piecewise-smooth systems: a unified analytical framework.

    M. di Bernardo;C. J. Budd;A. R. Champneys

  • From Helix to Localized Writhing in the Torsional Post-Buckling of Elastic Rods

    John Michael Tutill Thompson;A. R. Champneys

  • Bifurcation of a plethora of multi-modal homoclinic orbits for autonomous Hamiltonian systems

    A R Champneys;J F Toland

  • Embedded solitons : solitary waves in resonance with the linear spectrum

    Alan R Champneys;BA Malomed;J Yang;DJ Kaup

  • TWO-PARAMETER DISCONTINUITY-INDUCED BIFURCATIONS OF LIMIT CYCLES: CLASSIFICATION AND OPEN PROBLEMS

    P. Kowalczyk;M. Di Bernardo;A. R. Champneys;S. J. Hogan

  • Corner collision implies border-collision bifurcation

    M. di Bernardo;C. J. Budd;A. R. Champneys

  • Nonlinear Dynamics and Chaos : Where do we go from here?

    John Hogan;Alan Champneys;Bernd Krauskopf;Mario di Bernardo

Frequent Co-Authors

Mario di Bernardo
Mario di Bernardo University of Naples Federico II
Chris Budd
Chris Budd University of Bath
Boris A. Malomed
Boris A. Malomed Tel Aviv University
Bernd Krauskopf
Bernd Krauskopf University of Auckland
Björn Sandstede
Björn Sandstede Brown University
Mervyn J Miles
Mervyn J Miles University of Bristol
Julian F. R. Paton
Julian F. R. Paton University of Auckland
Dmitry V. Skryabin
Dmitry V. Skryabin University of Bath
John Toland
John Toland University of Bath
Iain D. Gilchrist
Iain D. Gilchrist University of Bristol

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