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Bautin bifurgation of a modified generalized Van der Pol-Mathieu equation

Zdeněk Kadeřábek (2016)

Archivum Mathematicum

The modified generalized Van der Pol-Mathieu equation is generalization of the equation that is investigated by authors Momeni et al. (2007), Veerman and Verhulst (2009) and Kadeřábek (2012). In this article the Bautin bifurcation of the autonomous system associated with the modified generalized Van der Pol-Mathieu equation has been proved. The existence of limit cycles is studied and the Lyapunov quantities of the autonomous system associated with the modified Van der Pol-Mathieu equation are computed....

Behavior of forced asymmetric oscillators at resonance.

Fabry, C. (2000)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Bifurcation and total stability

M. L. Bertotti, V. Moauro (1984)

Rendiconti del Seminario Matematico della Università di Padova

Bifurcation for second-order Hamiltonian systems with periodic boundary conditions.

Faraci, Francesca, Iannizzotto, Antonio (2008)

Abstract and Applied Analysis

Bifurcation from a saddle connection in functional differential equations: An approach with inclination lemmas [Book]

Hans-Otto Walther (1990)

Bifurcation from Periodic Solutions in Functional Differential Equations.

Hans-Otto Walther (1983)

Mathematische Zeitschrift

Bifurcation of closed orbits from a limit cycle in $R^{2}$

Vinicio Moauro (1981)

Rendiconti del Seminario Matematico della Università di Padova

Bifurcation of periodic and chaotic solutions in discontinuous systems

Michal Fečkan (1998)

Archivum Mathematicum

Chaos generated by the existence of Smale horseshoe is the well-known phenomenon in the theory of dynamical systems. The Poincaré-Andronov-Melnikov periodic and subharmonic bifurcations are also classical results in this theory. The purpose of this note is to extend those results to ordinary differential equations with multivalued perturbations. We present several examples based on our recent achievements in this direction. Singularly perturbed problems are studied as well. Applications are given...

Bifurcation of periodic solutions from inversion of stability of periodic O.D.E.'S.

M. Sabatini (1993)

Rendiconti del Seminario Matematico della Università di Padova

Bifurcation of periodic solutions in a rotationally symmetric oscillation system.

A. Vanderbauwhede (1985)

Journal für die reine und angewandte Mathematik

Bifurcation of periodic solutions in differential inclusions

Michal Fečkan (1997)

Applications of Mathematics

Ordinary differential inclusions depending on small parameters are considered such that the unperturbed inclusions are ordinary differential equations possessing manifolds of periodic solutions. Sufficient conditions are determined for the persistence of some of these periodic solutions after multivalued perturbations. Applications are given to dry friction problems.

Bifurcation of periodic solutions to differential inequalities in $ℝ^{3}$

Miroslav Bosák, Milan Kučera (1992)

Czechoslovak Mathematical Journal

Bifurcation of periodic solutions to variational inequalities in $ℝ^{κ}$ based on Alexander-Yorke theorem

Milan Kučera (1999)

Czechoslovak Mathematical Journal

Variational inequalities $U (t) \in K, (\dot{U} (t) - B_{λ} U (t) - G (λ, U (t)), Z - U (t)) \geq 0 for all Z \in K, a.a. t \in [0, T)$ are studied, where $K$ is a closed convex cone in $ℝ^{κ}$ , $κ \geq 3$ , $B_{λ}$ is a $κ \times κ$ matrix, $G$ is a small perturbation, $λ$ a real parameter. The assumptions guaranteeing a Hopf bifurcation at some $λ_{0}$ for the corresponding equation are considered and it is proved that then, in some situations, also a bifurcation of periodic solutions to our inequality occurs at some $λ_{I} \neq λ_{0}$ . Bifurcating solutions are obtained by the limiting process along branches of solutions to penalty problems starting at $λ_{0}$ constructed...

Bifurcations élémentaires et transition

G. Iooss (1979/1980)

Séminaire Équations aux dérivées partielles (Polytechnique)

Bifurcations of the periodic solutions in symmetric systems

Alois Klíč (1986)

Aplikace matematiky

Bifurcation phenomena in systems of ordinary differential equations which are invariant with respect to involutive diffeomorphisms, are studied. Teh "symmetry-breaking" bifurcation is investigated in detail.

Boundary layer phenomena for differential-delay equations with state dependent time lags: II.

Roger D. Nussbaum, John Mallet-Paret (1996)

Journal für die reine und angewandte Mathematik

Boundary value and periodic problem for the equation $x^{''} (t) + g (x (t)) = p (t)$

Svatopluk Fučík, Vladimír Lovicar (1974)

Commentationes Mathematicae Universitatis Carolinae

Boundary value problems for semilinear evolution inclusions: Carathéodory selections approach

Tiziana Cardinali, Lucia Santori (2011)

Commentationes Mathematicae Universitatis Carolinae

In this paper we prove two existence theorems for abstract boundary value problems controlled by semilinear evolution inclusions in which the nonlinear part is a lower Scorza-Dragoni multifunction. Then, by using these results, we obtain the existence of periodic mild solutions.

Bounded, almost-periodic and periodic solutions of certain singularly perturbed systems with delay

Marcos Lizana (1988)

Archivum Mathematicum

Bounded solutions on the Real line to non-autonomous Riccati Equations

Giuseppe Da Prato, Akira Ichikawa (1985)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si dà un risultato di esistenza e unicità di una soluzione limitata in $]-\infty,+\infty[$ per un'equazione di Riccati infinito-dimensionale.

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