H-Index & Metrics Best Publications

H-Index & Metrics

Discipline name H-index Citations Publications World Ranking National Ranking
Mathematics D-index 39 Citations 10,179 125 World Ranking 1054 National Ranking 67

Overview

What is he best known for?

The fields of study he is best known for:

  • Quantum mechanics
  • Mathematical analysis
  • Mechanical engineering

The scientist’s investigation covers issues in Mathematical analysis, Bifurcation, Homoclinic orbit, Numerical continuation and Nonlinear system. His study in Mathematical analysis is interdisciplinary in nature, drawing from both Dynamical systems theory and Phase space. His research integrates issues of Numerical analysis, Ordinary differential equation and Complex dynamics in his study of Bifurcation.

His Homoclinic orbit research integrates issues from Pure mathematics, Orbit and Hamiltonian system, Classical mechanics. His studies deal with areas such as Dynamical system, Hopf bifurcation, Spectral method and Floquet theory as well as Numerical continuation. His Nonlinear system study combines topics in areas such as System parameters, Schrödinger's cat, Photorefractive effect, Coupling strength and Function.

His most cited work include:

  • AUTO-07p: Continuation and bifurcation software for ordinary differential equations (1445 citations)
  • Piecewise-smooth Dynamical Systems: Theory and Applications (797 citations)
  • AUTO 2000 : CONTINUATION AND BIFURCATION SOFTWARE FOR ORDINARY DIFFERENTIAL EQUATIONS (with HomCont) (364 citations)

What are the main themes of his work throughout his whole career to date?

His scientific interests lie mostly in Mathematical analysis, Homoclinic orbit, Nonlinear system, Bifurcation and Classical mechanics. The concepts of his Mathematical analysis study are interwoven with issues in Parameter space, Dynamical systems theory and Numerical continuation. His study looks at the relationship between Homoclinic orbit and fields such as Buckling, as well as how they intersect with chemical problems.

His research in Nonlinear system focuses on subjects like Mechanics, which are connected to Bifurcation diagram. His Bifurcation study integrates concerns from other disciplines, such as Geometry and Applied mathematics. His Piecewise research is multidisciplinary, incorporating elements of Discontinuity and Boundary.

He most often published in these fields:

  • Mathematical analysis (29.23%)
  • Homoclinic orbit (21.83%)
  • Nonlinear system (21.48%)

What were the highlights of his more recent work (between 2015-2021)?

  • Mechanics (17.25%)
  • Classical mechanics (17.25%)
  • Nonlinear system (21.48%)

In recent papers he was focusing on the following fields of study:

Alan R Champneys mainly investigates Mechanics, Classical mechanics, Nonlinear system, Bistability and Rotor. His Mechanics research includes themes of Inlet and Work. His studies in Classical mechanics integrate themes in fields like Conservation of mass, Dynamical systems theory and Flat surface.

His Nonlinear system study integrates concerns from other disciplines, such as Vibration, Elastic instability and Periodic function. His research on Rotor also deals with topics like

  • Stator, which have a strong connection to Degrees of freedom and Space,
  • Isotropy together with Gyroscope, Grazing bifurcation, Resonance and Limit,
  • Dynamics that intertwine with fields like Bifurcation, Point, Rigid body mechanics, Computational mathematics and Nonlinear Oscillations. Alan R Champneys specializes in Bifurcation, namely Homoclinic orbit.

Between 2015 and 2021, his most popular works were:

  • The Painlevé paradox in contact mechanics (34 citations)
  • Amazonian forest-savanna bistability and human impact. (32 citations)
  • Nonlinear dynamics of a Jeffcott rotor with torsional deformations and rotor-stator contact (30 citations)

In his most recent research, the most cited papers focused on:

  • Quantum mechanics
  • Mathematical analysis
  • Mechanical engineering

Alan R Champneys mostly deals with Mechanics, Classical mechanics, Nonlinear system, Stator and Instability. Within one scientific family, Alan R Champneys focuses on topics pertaining to Work under Mechanics, and may sometimes address concerns connected to Vibration. His work in the fields of Classical mechanics, such as Painlevé paradox, overlaps with other areas such as G protein.

His Nonlinear system research is multidisciplinary, incorporating perspectives in Elastic instability, Aeroelasticity, Rotor and Morphing. His Stator study incorporates themes from Space, Nonlinear Oscillations and Bifurcation. He undertakes multidisciplinary studies into Bifurcation and Asynchronous communication in his work.

This overview was generated by a machine learning system which analysed the scientist’s body of work. If you have any feedback, you can contact us here.

Best Publications

Piecewise-smooth Dynamical Systems: Theory and Applications

Mario Di Bernardo;C. J. Budd;Alan R. Champneys;P. Kowalczyk.
(2007)

1839 Citations

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

E. J. Doedel;A. R. Champneys;Fabio Dercole;T. F. Fairgrieve.
(2007)

1706 Citations

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

Eusebius J. Doedel;Randy C. Paenroth;Alan R. Champneys;Thomas F. Fairgrieve.
ftp://ftp.cs.concordia.ca/pub/doedel/auto. (1997)

681 Citations

Bifurcations in Nonsmooth Dynamical Systems

Mario di Bernardo;Chris J. Budd;Alan R. Champneys;Piotr Kowalczyk.
Siam Review (2008)

366 Citations

Piecewise smooth dynamical systems

Alan R. Champneys;Mario di Bernardo.
Scholarpedia (2008)

323 Citations

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

A. R. Champneys.
Physica D: Nonlinear Phenomena (1998)

269 Citations

Cellular Buckling in Long Structures

Giles W Hunt;M A Peletier;A R Champneys;P D Woods.
Nonlinear Dynamics (2000)

263 Citations

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

M. di Bernardo;C. J. Budd;A. R. Champneys.
Physica D: Nonlinear Phenomena (2001)

240 Citations

A numerical toolbox for homoclinic bifurcation analysis

A.R. Champneys;Yu. A. Kuznetsov;Yu. A. Kuznetsov;B. Sandstede.
International Journal of Bifurcation and Chaos (1996)

238 Citations

NUMERICAL DETECTION AND CONTINUATION OF CODIMENSION-TWO HOMOCLINIC BIFURCATIONS

A.R. Champneys;Yu. A. Kuznetsov.
International Journal of Bifurcation and Chaos (1994)

194 Citations

Editorial Boards

IMA Journal of Applied Mathematics
(Impact Factor: 1.146)

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