A. Champneys

Publications303
h-index46
Citations9,980
Highly Influential Citations470
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AUTO 2000 : CONTINUATION AND BIFURCATION SOFTWARE FOR ORDINARY DIFFERENTIAL EQUATIONS (with HomCont)
TLDR
This is a guide to the software package AUTO for continuation and bifurcation problems in ordinary differential equations and the development of HomCont has much benefitted from various pieces of help and advice from, among others, W. W. Norton.
Piecewise-smooth Dynamical Systems: Theory and Applications
Qualitative theory of non-smooth dynamical systems.- Border-collision in piecewise-linear continuous maps.- Bifurcations in general piecewise-smooth maps.- Boundary equilibrium bifurcations in…
Bifurcations in Nonsmooth Dynamical Systems
TLDR
A review is presented of the one-parameter, nonsmooth bifurcations that occur in a variety of continuous-time piecewise-smooth dynamical systems, to explain dynamics that may be observed in simulations of systems which include friction oscillators, impact oscillator, DC-DC converters, and problems in control theory.
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Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian-Hopft bifurcation
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A global investigation of solitary-wave solutions to a two-parameter model for water waves
The model equation formula here arises as the equation for solitary-wave solutions to a fifth-order long-wave equation for gravity–capillary water waves. Being Hamiltonian, reversible and depending…
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A numerical toolbox for homoclinic bifurcation analysis
This paper presents extensions and improvements of recently developed algorithms for the numerical analysis of orbits homoclinic to equilibria in ODEs and describes the implementation of these…
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Piecewise smooth dynamical systems
TLDR
One of the books that can be recommended for new readers is piecewise smooth dynamical systems, which is not kind of difficult book to read.
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Homoclinic orbits in reversible systems and their applications in mechanics
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Bifurcation and coalescence of a plethora of homoclinic orbits for a Hamiltonian system
This is a further study of the set of homoclinic solutions (i.e., nonzero solutions asymptotic to 0 as ¦x¦→∞) of the reversible Hamiltonian systemuiv +Pu″ +u−u2=0. The present contribution is in…
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Chapter 4 – Numerical Continuation, and Computation of Normal Forms
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