ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

discrete models

Bogdanov–Takens bifurcation: from flows to discrete systems

The methodically important bifurcation – Bogdanov–Takens bifurcation – is discussed. For the primary model its bifurcations and evolution of phase portraits are described. The examples of nonlinear systems with such bifurcation are presented. The method of discrete models of construction that is founded on semi-explicit Euler scheme is discussed. On the base of the continuous prototype the discrete model of Bogdanov– Takens oscillator is constructed. The analytical analysis of bifurcations of a codimension one and two for discrete model is realized.