Results 1 to 10 of about 61,664 (222)

Complex length and persistence of limit cycles in a neighborhood of a hyperbolic polycycle [PDF]

Publicacions Matemàtiques, 2021
The author was partially supported by the grants NSF 0700973 and CNRS-RFBR 10-01-93115-NTSNILa. Complex limit cycle located in a neighborhood of a hyperbolic polycycle can not vanish under a small deformation that preserves the characteristic values of the vertexes of the polycycle.
Ilyashenko, Yu
core   +10 more sources

Polynomial differential systems with hyperbolic algebraic limit cycles

Electronic Journal of Qualitative Theory of Differential Equations, 2020
For a given algebraic curve of degree $n$, we exhibit differential systems of degree greater than or equal $n$, by introducing functions which are solutions of certain partial differential equations.
Salah Benyoucef
doaj   +3 more sources

A family of planar differential systems with hyperbolic algebraic limit cycles

Electronic Journal of Qualitative Theory of Differential Equations
In this paper, we characterize a family of planar polynomial differential systems of degree greater or equal than $n+1$, by presenting polynomial curves of degree $n,$ which generally contain closed components.
Maroua Ghelmi, Aziza Berbache
doaj   +2 more sources

Kolmogorov System with Explicit Hyperbolic Limit Cycle [PDF]

Journal of Siberian Federal University. Mathematics & Physics, 2017
Summary: A class of Kolmogorov differential system is introduced. We show that under suitable assumptions on parameters, an algebraic hyprbolic limit cycle can occur, the explicit expression of this limit cycle is given.
Benyoucef, Salah, Bendjeddou, Ahmed
openaire   +3 more sources

Studying the Stability of a Non-linear Autoregressive Model (Polynomial with Hyperbolic Cosine Function) [PDF]

Al-Rafidain Journal of Computer Sciences and Mathematics, 2014
In this paper we study the statistical properties of one of a non-linear autoregressive model with hyperbolic triangle function(polynomial with hyperbolic cosinefunction)by using the local linearization  approximation method to find the stability of the ...
Abdulghafoor Salim, Anas Youns Abdullah
doaj   +1 more source

Heterodimensional cycles, partial hyperbolicity and limit dynamics [PDF]

Fundamenta Mathematicae, 2002
A one-parametric family of diffeomorphisms is studied unfolding heteroclinic cycles. An open set of such arcs is constructed such that the resulting nonwandering set is the disjont union of two hyperbolic basis sets of different indices and a strong partially hyperbolic set which is robustly transitive.
Díaz, L. J., Rocha, J.
openaire   +1 more source

Stabilization of Stable Manifold of Upright Position of the Spherical Pendulum [PDF]

Modeling, Identification and Control, 2001
The stabilization problem of the upright position of the sherical pendulum is treated in detail. This problem is reduced to the stabilization of the stable manifold Omega_st of the upright position of the unforced spherical pendulum. It is shown that for
Hallgeir Ludvigsen, Anton Shiriaev, Olav Egeland   +2 more
doaj   +1 more source

Coexistence of Multiple Points, Limit Cycles, and Strange Attractors in a Simple Autonomous Hyperjerk Circuit with Hyperbolic Sine Function [PDF]

Complexity, 2020
In this contribution, a new elegant hyperjerk system with three equilibria and hyperbolic sine nonlinearity is investigated. In contrast to other models of hyperjerk systems where either hidden or self-excited attractors are obtained, the case reported in this work represents a unique one which displays the coexistence of self-excited chaotic ...
M. Fouodji Tsotsop, J. Kengne, G. Kenne, Z. Tabekoueng Njitacke   +3 more
openaire   +2 more sources

Limit sets as examples in noncommutative geometry [PDF]

, 2005
The fundamental group of a hyperbolic manifold acts on the limit set, giving rise to a cross-product C^* algebra. We construct nontrivial K-cycles for the cross-product algebra, thereby extending some results of Connes and Sullivan to higher dimensions ...
Lott, John
core   +4 more sources

New approach to study the van der Pol equation for large damping

Electronic Journal of Qualitative Theory of Differential Equations, 2018
We present a new approach to establish the existence of a unique limit cycle for the van der Pol equation in case of large damping. It is connected with the bifurcation of a stable hyperbolic limit cycle from a closed curve composed of two heteroclinic ...
Klaus Schneider
doaj   +1 more source