A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Filters
Bifurcation of limit cycles in a quintic Hamiltonian system under a sixth-order perturbation
2005
Chaos, Solitons & Fractals
Preserved Fulltext
To obtain the maximum number of limit cycles, a sixth-order polynomial perturbation is added to a quintic Hamiltonian system, and both local and global bifurcations are considered. ...
This paper intends to explore the bifurcation of limit cycles for planar polynomial systems with even number of degrees. ...
Acknowledgments This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC No. R2686A02). ...
doi:10.1016/j.chaos.2005.03.010
fatcat:sfrmh44suvf35a4zd5ygtjoxnu
Bifurcations of limit cycles in Kukles systems of arbitrary degree with invariant ellipse
2012
Applied Mathematics Letters
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Writing the system as a perturbation of a Hamiltonian system, we show that the first Poincaré-Melnikov integral of the system is a polynomial whose coefficients are the Lyapunov quantities. ...
In this paper, for a certain class of Kukles polynomial systems of arbitrary degree n with an invariant ellipse, we show that for certain values of the parameters, the system has an upper bound of limit ...
System (6.1) has an upper bound of two limit cycles, counting the infinitesimal and global limit cycles. ...
doi:10.1016/j.aml.2012.01.039
fatcat:wxmagyqwbfawzmuqqz4guammme
Page 2613 of Mathematical Reviews Vol. , Issue 2000d
[page]
2000
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
Summary: “In this paper, Mel/nikov functions which appear in the study of limit cycles of a perturbed planar Hamiltonian system are studied. There are two main contributions here. ...
The paper also includes other related results, for example, some estimations of the upper bound for the number of limit cycles in a perturbed Hamiltonian system.” ...
Bifurcation set and limit cycles forming compound eyes in a perturbed Hamiltonian system
1991
Publicacions matemàtiques
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
In this paper we consider a class of perturbation of a Hamiltonian cubic system with 9 finite critical points . ...
Using detection functions, we present explicit formulas for the global and local bifurcations of the flow . We exhibit various patterns of compound eyes of limit cycles . ...
Arnold in 1977 [1] , is to determine the number of limit cycles that can be generated from a polynomial Hamiltonian system of degree n -1 with perturbed terms of a polynomial of degree m + 1 . ...
doi:10.5565/publmat_35291_13
fatcat:22mslqfkvfd5jdn66pe4crkqb4
Perturbations of quadratic Hamiltonian two-saddle cycles
2015
Annales de l'Institut Henri Poincare. Analyse non linéar
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
We prove that the number of limit cycles which bifurcate from a two-saddle loop of a planar quadratic Hamiltonian system, under an arbitrary quadratic deformation, is less than or equal to three. ...
Part of this work has been done while the second author visited the University of Toulouse. He is very grateful for kind hospitality. ...
the first non-vanishing Poincaré-Pontryagin-Melnikov function M k associated to an arbitrary polynomial perturbation is an Abelian integral. ...
doi:10.1016/j.anihpc.2013.12.001
fatcat:hiz2yws5a5dgxpwgkvvzivaacm
Perturbations of quadratic Hamiltonian two-saddle cycles
[article]
2013
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
We prove that the number of limit cycles, which bifurcate from a two-saddle loop of a planar quadratic Hamiltonian system, under an arbitrary quadratic deformation, is less than or equal to three. ...
Part of this work has been done while the second author visited the University of Toulouse. He is very grateful for kind hospitality. ...
the first non-vanishing Poincaré-Pontryagin-Melnikov function M k associated to an arbitrary polynomial perturbation is an Abelian integral. ...
arXiv:1306.2340v1
fatcat:tge6h6fq3nezre64cu3rd436fm
Page 7211 of Mathematical Reviews Vol. , Issue 2002J
[page]
2002
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
The authors study bifurcations of limit cycles in perturbations of a vector field with an invariant normally hyperbolic 2-dimensional manifold, assuming that the restriction of the field on this manifold ...
In the standard Hamiltonian case this condition is expressed as vanishing of the Poincaré integral, the principal term of the dissipation of energy over a period of the non-perturbed system. ...
Page 5944 of Mathematical Reviews Vol. , Issue 2003h
[page]
2003
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
The paper under review studies the limit cycles of a nonlinear system on the plane. ...
In this expository paper the author reviews some methods for investigating the bifurcation of limit cycles in planar quadratic differential systems. ...
Perturbations of a Hamiltonian family of cubic vector fields
1991
Bulletin of the Australian Mathematical Society
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is application/pdf.
This paper is related with the configurations of limit cycles for cubic polynomial vector fields in two variables (xa)- It is an open question to decide whether every limit cycle configuration in X3 can ...
Finally, we analyse the rupture of saddle connection of the Hamiltonian field under perturbation, via Melnikov's integral, in order to complete the study of the global phase portrait and to consider the ...
In 1987, Li Ji-bin and Quiming [8] gave several new configurations obtained by perturbing of Hamiltonian systems, including one with 11 limit cycles. ...
doi:10.1017/s0004972700029531
fatcat:vrtxx7ane5bwlofjmknpmmxgli
Page 5361 of Mathematical Reviews Vol. , Issue 99h
[page]
1999
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
)
Limit cycles of polynomial Liénard systems. ...
Summary: “In this work we study the integrability of a two- dimensional autonomous system in the plane with linear part of center type and non-linear part given by cubic polynomials with degenerate infinity ...
HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
2003
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
It has not been proved, even for polynomial perturbations of a polynomial Hamiltonian system, that there are only finitely many generating limit cycles. ...
Bifurcations of limit cycles of Z 5 -equivariant perturbed Hamiltonian systems In this subsection we consider the perturbed Z 5equivariant vector field: dr dt = βr 4 sin 5θ − εr(pr 4 + qr 2 − λ) , dθ dt ...
There are two sequences of n = 2 k − 1 and n = 3 × 2 k−1 − 1, k = 2, 3, . . . , and a constant µ = (4 × ln 2) −1 such that the number H(n) of limit cycles of the systems (P H k ) grows at least as rapidly ...
doi:10.1142/s0218127403006352
fatcat:64mfgqneijgbvc4xlatt3yikfi
Dynamics of homogeneous magnetizations in strong transverse driving fields
1995
Zeitschrift für Physik B Condensed Matter
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Note that this fulltext copy is not of the "primary" version of this work. The version it corresponds to is:
1995 pre-print arXiv:chao-dyn/9501002v1 fatcat:gv37znzmejgfjaz7sm73rd755m
For the linearly polarized driven Hamiltonian system we apply canonical perturbation theory to uncover the main resonances as well as the global phase space structure. ...
In the case of circularly polarized driven dissipative motion we present the complete bifurcation diagram including bifurcations up to codimension three. ...
This work was performed within a program of the Sonderforschungsbereich 185 Darmstadt-Frankfurt, Germany. ...
doi:10.1007/bf02769944
fatcat:beigf5gpx5hvji625ex6i2vj74
Page 5112 of Mathematical Reviews Vol. , Issue 2003g
[page]
2003
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
Limit periodic sets play an important role in the study of appearance of limit cycles, and are, roughly speaking, defined as limits (in terms of the parameter 4) of limit cycles for the Hausdorff metric ...
Patrick Bonckaert (B-LMBG; Diepenbeek)
2003g:34056 34C05
Tang, Minying (PRC-YUN-AM; Kunming); Hong, Xiaochun Fourteen limit cycles in a cubic Hamiltonian system with nine-order perturbed term. ...
Simultaneity of centres in ℤ q -equivariant systems
2018
Proceedings of the Royal Society A
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
We study the simultaneous existence of centres for two families of planar Z q -equivariant systems. First, we give a short review about Z q -equivariant systems. ...
Next, we present the necessary and sufficient conditions for the simultaneous existence of centres for a Z 2 -equivariant cubic system and for a Z 2equivariant quintic system. ...
First, we give a survey on the existing results related to the local and global bifurcations of limit cycles for such systems perturbing their centres. ...
doi:10.1098/rspa.2017.0811
pmid:29888736
fatcat:enfq5o443bgaxe4nqh6nf2m6ki
Page 7772 of Mathematical Reviews Vol. , Issue 99k
[page]
1999
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
The structure of such sets can be to some extent (though not completely) described: roughly, they can be limit cycles or separatrix polygons, eventually containing arcs of non-isolated singularities. ...
the global prob- lem to a semilocal one (local with respect to parameters and an unspecified neighborhood of the limit periodic set), and is there- fore easier to verify. ...
« Previous
Showing results 1 — 15 out of 908 results