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Shilnikov chaos, Filippov sliding and boundary equilibrium bifurcations

Published online by Cambridge University Press:  13 June 2018

P. A. GLENDINNING
P. A. GLENDINNING*
Affiliation:
School of Mathematics, University of Manchester, Manchester M13 9PL, UK email: p.a.glendinning@manchester.ac.uk
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Abstract

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In the 1960s, L.P. Shilnikov showed that certain homoclinic orbits for smooth families of differential equations imply the existence of chaos, and there are complicated sequences of bifurcations near the parameter value at which the homoclinic orbit exists. We describe how this analysis is modified if the differential equations are piecewise smooth and the homoclinic orbit has a sliding segment. Moreover, we show that the Shilnikov mechanism appears naturally in the unfolding of boundary equilibrium bifurcations in $\mathbb{R}^3$.

Keywords

Bifurcation theoryhomoclinic orbitspiecewise smooth dynamics

Information

Type
Papers
Information
European Journal of Applied Mathematics , Volume 29 , Special Issue 5: Theory and applications of nonsmooth dynamical systems , October 2018 , pp. 757 - 777
Copyright
Copyright © Cambridge University Press 2018 

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