3,275 research outputs found
Zero-Hopf bifurcation in the FitzHugh-Nagumo system
We characterize the values of the parameters for which a zero--Hopf
equilibrium point takes place at the singular points, namely, (the origin),
and in the FitzHugh-Nagumo system. Thus we find two --parameter
families of the FitzHugh-Nagumo system for which the equilibrium point at the
origin is a zero-Hopf equilibrium. For these two families we prove the
existence of a periodic orbit bifurcating from the zero--Hopf equilibrium point
. We prove that exist three --parameter families of the FitzHugh-Nagumo
system for which the equilibrium point at and is a zero-Hopf
equilibrium point. For one of these families we prove the existence of , or
, or periodic orbits borning at and
Periods, Lefschetz numbers and entropy for a class of maps on a bouquet of circles
We consider some smooth maps on a bouquet of circles. For these maps we can
compute the number of fixed points, the existence of periodic points and an
exact formula for topological entropy. We use Lefschetz fixed point theory and
actions of our maps on both the fundamental group and the first homology group.Comment: 19 pages, 2 figure
On the birth of limit cycles for non-smooth dynamical systems
The main objective of this work is to develop, via Brower degree theory and
regularization theory, a variation of the classical averaging method for
detecting limit cycles of certain piecewise continuous dynamical systems. In
fact, overall results are presented to ensure the existence of limit cycles of
such systems. These results may represent new insights in averaging, in
particular its relation with non smooth dynamical systems theory. An
application is presented in careful detail
Period sets of linear toral endomorphisms on
The period set of a dynamical system is defined as the subset of all integers
such that the system has a periodic orbit of length . Based on known
results on the intersection of period sets of torus maps within a homotopy
class, we give a complete classification of the period sets of (not necessarily
invertible) toral endomorphisms on the --dimensional torus .Comment: 10 page
On the Integrability of Liénard systems with a strong saddle
We study the local analytic integrability for real Li\'{e}nard systems, , with but which implies that it has a strong saddle at the origin. First we prove that this problem is equivalent to study the local analytic integrability of the resonant saddles. This result implies that the local analytic integrability of a strong saddle is a hard problem and only partial results can be obtained. Nevertheless this equivalence gives a new method to compute the so-called resonant saddle quantities transforming the resonant saddle into a strong saddle.The first author is partially supported by a MINECO/FEDER grant number MTM2014-
53703-P and an AGAUR (Generalitat de Catalunya) grant number 2014SGR-1204. The
second author is partially supported by a FEDER-MINECO grant MTM2016-77278-P, a
MINEC0 grant MTM2013-40998-P, and an AGAUR grant number 2014SGR-568
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