Št. zadetkov: 26
Objavljeni znanstveni prispevek na konferenci
Oznake:
polynomial systems of ODE`s;isochronicity;linearizability;normal forms;
We propose a generalization of the notion of isochronicity for real polynomial autonomous systems to the case of complex two dimensional systems of ODEs. We study the generalized problem in the case of a quadratic system and a system with homogeneous cubic nonlinearities. Main tools of the study are ...
Leto:
2012
Vir:
Fakulteta za naravoslovje in matematiko (UM FNM)
Izvirni znanstveni članek
Oznake:
matematika;limitni cikli;bifurkacija;problem centra;mathematic;limit cycles;bifurcation;center problem;
We study analytic properties of the Poincaré return map and generalized focal values of analytic planar systems with a nilpotent focus or center. We use the focal values and the map to study the number of limit cycles of this kind of systems and obtain some new results on the lower and upper bounds ...
Leto:
2012
Vir:
Fakulteta za naravoslovje in matematiko (UM FNM)
Izvirni znanstveni članek
Oznake:
matematika;polinomi;dekompozicija;mathematics;polynomials;decomposition;
The objective of this paper is twofold. First, we describe a method to solve large systems of polynomial equations using modular arithmetics. Then, we apply the approach to the study of the problem of linearizability for a quadratic system of ordinary differential equations.
Leto:
2011
Vir:
Fakulteta za naravoslovje in matematiko (UM FNM)
Izvirni znanstveni članek
Oznake:
matematika;mathematics;
In this paper we present the necessary and sufficient conditions for linearizability of the planar time-reversible cubic complex system ▫$\dot{x}=x+P(x,y)$▫, ▫$\dot{y}=-y+Q(x,y)$▫. From these conditions, the necessary and sufficient conditions for the origin to be an isochronous center of the time-r ...
Leto:
2010
Vir:
Fakulteta za naravoslovje in matematiko (UM FNM)
Izvirni znanstveni članek
Oznake:
matematika;Lotka-Volterra;polinomi;mathematics;polynoms;
Integrability conditions for Lotka-Volterra planar complex quintic systems
Leto:
2010
Vir:
Fakulteta za naravoslovje in matematiko (UM FNM)
Izvirni znanstveni članek
Oznake:
matematika;limitni cikli;bifurkacija;mathematics;limit cycles;bifurcation;
We describe a method based on algorithms of computational algebra for obtaining an upper bound for the number of limit cycles bifurcating from a center or a focus of polynomial vector field. We apply it to a cubic system depending on six parameters and prove that in the generic case at most six limi ...
Leto:
2010
Vir:
Fakulteta za naravoslovje in matematiko (UM FNM)
Objavljeni znanstveni prispevek na konferenci (vabljeno predavanje)
Oznake:
fizika;kvantna mehanika;harmonski oscilatorji;
Exact analysis of adiabatic invariants in time dependent harmonic oscillator
Leto:
2009
Vir:
Fakulteta za naravoslovje in matematiko (UM FNM)
Izvirni znanstveni članek
Oznake:
second-order impulsive differential equations;antiperiodic boundary value conditions;Green's function;
We prove existence results for second-order impulsive differential equations with antiperiodic boundary value conditions in the presence of classical fixed point theorems. We also obtain the expression of Green's function of related linear operator in the space of piecewise continuous functions.
Leto:
2008
Vir:
Digitalna knjižnica Univerze v Mariboru (DKUM)
Izvirni znanstveni članek
Oznake:
integrabilnost;fokusne količine;stanje centra;integrability;focus quantities;center conditions;
Fix a collection of polynomial vector fields on $R^3$ with a singularity at the origin, for every one of which the linear part at the origin has two pure imaginary and one non-zero eigenvalue. Some such systems admit a local analytic first integral, which then defines a local center manifold of the ...
Leto:
2014
Vir:
Fakulteta za naravoslovje in matematiko (UM FNM)
Doktorska disertacija
Oznake:
disertacije;sistemi navadnih diferencialnih enačb;integrabilnost;linearizabilnost;limitni cikli;reverzibilnost;Hamiltonski sistemi;
Krovna tema pričujoče doktorske disertacije je kvalitativna obravnava nekaterih družin navadnih diferencialnih enačb (NDE). Osrednja pozornost je namenjena ravninskim in tridimenzionalnim polinomskim sistemom ter preiskovanju pogojev, pri katerih se sistemi ponašajo s katero od naslovnih lastnosti: ...
Leto:
2023
Vir:
Fakulteta za naravoslovje in matematiko (UM FNM)