3 papers
math.DS2009
Limit Cycle Bifurcations in a Quartic Ecological Model
Henk W. Broer, Valery A. Gaiko
In this paper we complete the global qualitative analysis of a quartic ecological model. In particular, studying global bifurcations of singular points and limit cycles, we prove t…
math.DS2006
Liénard's system and Smale's problem
Valery A. Gaiko
In this paper, using geometric properties of the field rotation parameters, we present a solution of Smale's Thirteenth Problem on the maximum number of limit cycles for Liénard's…
math.DS2006
Geometry of planar quadratic systems
Valery A. Gaiko
In this paper, the global qualitative analysis of planar quadratic dynamical systems is established and a new geometric approach to solving Hilbert's Sixteenth Problem in this spec…