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Displaying 81 – 100 of 240

Limit cycles in the equation of whirling pendulum with autonomous perturbation

Hana Lichardová (1999)

Applications of Mathematics

The two-parameter Hamiltonian system with the autonomous perturbation is considered. Via the Mel’nikov method, existence and uniqueness of a limit cycle of the system in a certain region of a two-dimensional space of parameters is proved.

Limit cycles in the Holling-Tanner model.

Armengol Gasull, Robert E. Koolj, Joan Torregrosa (1997)

Publicacions Matemàtiques

This paper deals with the following question: does the asymptotic stability of the positive equilibrium of the Holling-Tanner model imply it is also globally stable? We will show that the answer to this question is negative. The main tool we use is the computation of Poincaré-Lyapunov constants in case a weak focus occurs. In this way we are able to construct an example with two limit cycles.

Limit cycles of a class of Hilbert's sixteenth problem presented by fractional differential equations.

Erjaee, G.H., Zangeneh, H.R.Z., Nyamoradi, N. (2010)

Advances in Difference Equations [electronic only]

Limit Cycles of Perturbations of a Class of Quadratic Hamiltonian Vector Fields

Markov, Yavor (1996)

Serdica Mathematical Journal

We prove that in quadratic perturbations of generic Hamiltonian vector fields with two saddle points and one center there can appear at most two limit cycles. This bound is exact.

Local Bifurcations in a Nonlinear Model of a Bioreactor

Dimitrova, Neli (2009)

Serdica Journal of Computing

This paper is partially supported by the Bulgarian Science Fund under grant Nr. DO 02– 359/2008.We consider a nonlinear model of a continuously stirred bioreactor and study the stability of the equilibrium points with respect to practically important model parameters. We determine regions in the parameter space where the steady states undergo transcritical and Hopf bifurcations. In the latter case, the stability of the emerged limit cycles is also studied. Numerical simulations in the computer algebra...

Local integrating factors.

Walcher, Sebastian (2003)

Journal of Lie Theory

Melnikov deviations and limit cycles for Lienard equations

J. Billeke, H., Wallace, M. Burgos (1992)

Revista colombiana de matematicas

Monotonicity of the period map of a non-Hamiltonian center.

Jorge Billeke, Eduardo Sáez (1994)

Collectanea Mathematica

New examples of holomorphic foliations without algebraic leaves

Henryk Żołądek (1998)

Studia Mathematica

We present a series of polynomial planar vector fields without algebraic invariant curves in $C P^{2}$ .

New sufficient conditions for a center and global phase portraits for polynomial systems.

Hector Giacomini, Malick Ndiaye (1996)

Publicacions Matemàtiques

In this paper we consider cubic polynomial systems of the form: x' = y + P(x, y), y' = −x + Q(x, y), where P and Q are polynomials of degree 3 without linear part. If M(x, y) is an integrating factor of the system, we propose its reciprocal V (x, y) = 1 / M(x,y) as a linear function of certain coefficients of the system. We find in this way several new sets of sufficient conditions for a center. The resulting integrating factors are of Darboux type and the first integrals are in the Liouville form.By...

Non oscillating solutions of analytic gradient vector fields

Fernando Sanz (1998)

Annales de l'institut Fourier

Let $γ$ be an integral solution of an analytic real vector field $ξ$ defined in a neighbordhood of $0 \in ℝ^{3}$ . Suppose that $γ$ has a single limit point, $ω (γ) = {0}$ . We say that $γ$ is non oscillating if, for any analytic surface $H$ , either $γ$ is contained in $H$ or $γ$ cuts $H$ only finitely many times. In this paper we give a sufficient condition for $γ$ to be non oscillating. It is established in terms of the existence of “generalized iterated tangents”, i.e. the existence of a single limit point for any transform property for...

Nondegenerate linearizable centre of complex planar quadratic and symmetric cubic systems in C2.

Colin Christopher, Christiane Rousseau (2001)

Publicacions Matemàtiques

In this paper we consider complex differential systems in the plane, which are linearizable in the neighborhood of a nondegenerate centre. We find necessary and sufficient conditions for linearizability for the class of complex quadratic systems and for the class of complex cubic systems symmetric with respect to a centre. The sufficiency of these conditions is shown by exhibiting explicitly a linearizing change of coordinates, either of Darboux type or a generalization of it.

Nonwandering points and the set of central motions in discontinuous disperse dynamic systems

И.А. Чиркова (1986)

Matematiceskie issledovanija

Normal forms for certain singularities of vectorfields

Floris Takens (1973)

Annales de l'institut Fourier

$C^{\infty}$ normal forms are given for singularities of $C^{\infty}$ vectorfields on $R$ , which are not flat, and for $C^{\infty}$ vectorfields $X$ on $R^{2}$ with $X (0) = 0$ , the 1-jet of $X$ in the origin is a pure rotation, and some higher order jet of $X$ attracting or expanding.

On a codimension 3 bifurcation of plane vector fields with $Z_{2}$ symmetry

Milan Medveď (1990)

Czechoslovak Mathematical Journal

On a maximal number of period annuli.

Kozmina, Yelena, Sadyrbaev, Felix (2011)

Abstract and Applied Analysis

On algebraic approach in quadratic systems.

Mencinger, Matej (2011)

International Journal of Mathematics and Mathematical Sciences

On algebraic solutions of algebraic Pfaff equations

Henryk Żołądek (1995)

Studia Mathematica

We give a new proof of Jouanolou’s theorem about non-existence of algebraic solutions to the system $ẋ = z^{s}, ẏ = x^{s}, ż = y^{s}$ . We also present some generalizations of the results of Darboux and Jouanolou about algebraic Pfaff forms with algebraic solutions.

On centers of cubic systems

R. Conti (1990)

Annales Polonici Mathematici

On centers of type $B$ of polynomial systems

Roberto Conti (1990)

Archivum Mathematicum

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