BIFURCATION PHENOMENA IN THE 1:1 RESONANT HORN FOR THE FORCED VAN DER POL—DUFFING EQUATION

1 March 1992

journal article
Published by World Scientific Pub Co Pte Ltd in International Journal of Bifurcation and Chaos

Vol. 2 (1) , 93-100
https://doi.org/10.1142/s0218127492000094

Abstract

This paper presents the 1:1 resonant horn bifurcation phenomena for the forced van der Pol—Duffing equation. It is shown that the transition to chaos in the case of small dissipation evolves in two parallel processes: a sequence of period-doubling bifurcations and the birth, growth and merging of homoclinic structures.

Keywords

BIFURCATIONS
RESONANT HORN
PARALLEL PROCESSES
BIFURCATION PHENOMENA
CHAOS
DER POL
FORCED VAN
DUFFING

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