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Global bifurcations of limit cycles in the Kukles cubic system
Valery A. Gaiko
In this paper, using our bifurcational geometric approach, we solve the problem on the maximum number and distribution of limit cycles in the Kukles system representing a planar po…
Global bifurcations of limit cycles in a Holling-type dynamical system
Valery A. Gaiko
In this paper, we complete the global qualitative analysis of a quartic family of planar vector fields corresponding to a rational Holling-type dynamical system which models the dy…
A bifurcational geometric approach to the problem of chaos transition in the classical Lorenz system
Valery A. Gaiko
The classical Lorenz system is considered. For many years, this system has been the subject of study by numerous authors. However, until now the structure of the Lorenz attractor i…
The general Liénard polynomial system
Valery A. Gaiko
In this paper, applying a canonical system with field rotation parameters and using geometric properties of the spirals filling the interior and exterior domains of limit cycles, w…
Global bifurcations of multiple limit cycles in the FitzHugh-Nagumo system
Valery A. Gaiko
In this paper, we complete the global qualitative analysis of the well-known FitzHugh-Nagumo neuronal model. In particular, studying global limit cycle bifurcations and applying th…
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…