Electron. J. Diff. Eqns.,
Vol. 2005(2005), No. 83, pp. 116.
Bifurcation diagram of a cubic threeparameter
autonomous system
Lenka Barakova, Evgenii P. Volokitin
Abstract:
In this paper, we study the cubic threeparameter autonomous planar system
where
. Our goal is to obtain a
bifurcation diagram; i.e., to divide the parameter space into
regions within which the system has topologically equivalent phase
portraits and to describe how these portraits are transformed at
the bifurcation boundaries. Results may be applied to the
macroeconomical model ISLM with Kaldor's assumptions. In this
model existence of a stable limit cycles has already been studied
(AndronovHopf bifurcation). We present the whole bifurcation
diagram and among others, we prove existence of more difficult
bifurcations and existence of unstable cycles.
Submitted February 9, 2005. Published July 19, 2005.
Math Subject Classifications: 34C05, 34D45, 34C23.
Key Words: Phase portrait; bifurcation; central manifold;
topological equivalence; structural stability;
bifurcation diagram;limit cycle.
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Lenka Baráková
Mendel University, Dept. of Math.
Zemedelska 1, 613 00 Brno, Czech Rep.
email: barakova@mendelu.cz 

Evgenii P. Volokitin
Sobolev Institute of Mathematics
Novosibirsk, 630090, Russia
email: volok@math.nsc.ru 
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