Zobrazeno 1 - 10
of 60
pro vyhledávání: '"Gaiko, Valery A."'
Autor:
Gaiko, Valery A.
In this paper, we carry out a global qualitative analysis of a reduced planar quartic Topp system which models the dynamics of diabetes. In particular, studying global bifurcations, we prove that such a system can have at most two limit cycles.
Externí odkaz:
http://arxiv.org/abs/1904.05311
Autor:
Gaiko, Valery A.
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 polynomial dynamical system with arbitrary linear and cubic right-hand s
Externí odkaz:
http://arxiv.org/abs/1611.08113
Autor:
Gaiko, Valery A.
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 dynamics of the populations of predators and their prey in a given ecolo
Externí odkaz:
http://arxiv.org/abs/1504.03353
A bifurcational geometric approach to the problem of chaos transition in the classical Lorenz system
Autor:
Gaiko, Valery A.
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 is not clear completely yet, and the most important question at present
Externí odkaz:
http://arxiv.org/abs/1307.8315
Autor:
Gaiko, Valery A.
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, we solve first the problem on the maximum number of limit cycles surrou
Externí odkaz:
http://arxiv.org/abs/1202.3540
Autor:
Gaiko, Valery A.
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 the Wintner-Perko termination principle for multiple limit cycles, we pr
Externí odkaz:
http://arxiv.org/abs/1104.3019
Autor:
Broer, Henk W., Gaiko, Valery A.
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 that the corresponding dynamical system has at most two limit cycles.
Externí odkaz:
http://arxiv.org/abs/0902.2433
Autor:
Gaiko, Valery A.
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. Using the field rotation parameters of the constructed canonical system
Externí odkaz:
http://arxiv.org/abs/0803.3055
Autor:
Gaiko, Valery A., van Horssen, Wim T.
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 continuous nonlinear function. Studying all possible local and global bifurc
Externí odkaz:
http://arxiv.org/abs/0803.0490
Autor:
Gaiko, Valery A.
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 Li\'{e}nard's polynomial system. We also generalize the obtained result and pres
Externí odkaz:
http://arxiv.org/abs/math/0611143