5 papers
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…
Limit Cycles of a Quadratic System with Two Parallel Straight Line-Isoclines
Valery A. Gaiko
In this paper, a quadratic system with two parallel straight line-isoclines is considered. This system corresponds to the system of class II in the classification of Ye Yanqian. Us…
Towards Theory of Piecewise Linear Dynamical Systems
Valery A. Gaiko, Wim T. van Horssen
In this paper, we consider a planar dynamical system with a piecewise linear function containing an arbitrary number (but finite) of dropping sections and approximating some contin…
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…
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…