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 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.
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
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.
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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.
Siam Review (2008)
Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics
A. R. Champneys.
Physica D: Nonlinear Phenomena (1998)
Cellular Buckling in Long Structures
GW Hunt;MA Mark Peletier;AR Champneys;PD Woods.
Nonlinear Dynamics (2000)
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)
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)
Piecewise smooth dynamical systems
Alan R. Champneys;Mario di Bernardo.
Bifurcation and coalescence of a plethora of homoclinic orbits for a Hamiltonian system
B Buffoni;Alan R Champneys;JF Toland.
Journal of Dynamics and Differential Equations (1996)
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