Article Contents
Article Contents

# Hopf bifurcation for some analytic differential systems in $\R^3$ via averaging theory

• We study the Hopf bifurcation from the singular point with eigenvalues $a$ε$\ \pm\ bi$ and $c$ε located at the origen of an analytic differential system of the form $\dot x= f( x)$, where $x \in \R^3$. Under convenient assumptions we prove that the Hopf bifurcation can produce $1$, $2$ or $3$ limit cycles. We also characterize the stability of these limit cycles. The main tool for proving these results is the averaging theory of first and second order.
Mathematics Subject Classification: Primary: 37G15, 37D45.

 Citation:

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