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Articles, 11 records found Research literature, 1 records found Course materials, 2 records found

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21 p, 392.8 KB

A new approach for the study of limit cycles / García-Saldaña, Johanna Denise (Universidad Católica de la Santísima Concepción. Departamento de Matemática y Física Aplicadas (Chile)) ; Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Giacomini, Hector (Centre national de la recherche scientifique (França). Institut Denis Poisson)
We prove that star-like limit cycles of any planar polynomial system can also be seen either as solutions defined on a given interval of a new associated planar non-autonomous polynomial system or as heteroclinic solutions of a 3-dimensional polynomial system. [...]
2020 - DOI (Digital Object Identifier)

10.1016/j.jde.2020.04.038
Journal of differential equations, Vol. 269, Issue 7 (September 2020) , p. 6269-6292

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14 p, 298.1 KB

Nilpotent global centers of linear systems with cubic homogeneous nonlinearities / García-Saldaña, Johanna Denise (Universidad Católica de la Santísima Concepción. Departamento de Matemática y Física Aplicadas (Chile)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
In this paper, we characterize the global nilpotent centers of polynomial differential systems of the linear form plus cubic homogeneous terms.
2020 - DOI (Digital Object Identifier)

10.1142/S0218127420500108
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 30, Issue 1 (January 2020) , art. 2050010

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28 p, 837.2 KB

Phase portraits of Abel quadratic differential systems of second kind with symmetries / Ferragut Amengual, Antoni Manel (Universitat Jaume I. Institut Universitari de Matemàtiques i Aplicacions de Castelló) ; García-Saldaña, Johanna Denise (Universidad Católica de la Santísima Concepción. Departamento de Matemática y Física Aplicadas (Chile)) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
We provide normal forms and the global phase portraits on the Poincaré disk of the Abel quadratic differential equations of the second kind having a symmetry with respect to an axis or to the origin. [...]
2019 - DOI (Digital Object Identifier)

10.1080/14689367.2018.1530732
Dynamical Systems, Vol. 34, Issue 2 (2019) , p. 301-333

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18 p, 299.1 KB

Linear type global centers of linear systems with cubic homogeneous nonlinearities / García-Saldaña, Johanna Denise (Universidad Católica de la Santísima Concepción. Departamento de Matemática y Física Aplicadas (Chile)) ; Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Valls, Clàudia 1973- (Universidade de Lisboa. Instituto Superior Técnico. Departamento de Matemática)
A center p of a differential system in R2 is global if R2\ { p} is filled of periodic orbits. It is known that a polynomial differential system of degree 2 has no global centers. Here we characterize the global centers of the differential systems x˙=ax+by+P3(x,y),y˙=cx+dy+Q3(x,y),with P3 and Q3 homogeneous polynomials of degree 3, and such that the center has purely imaginary eigenvalues, i. [...]
2019 - DOI (Digital Object Identifier)

10.1007/s12215-019-00433-0
Rendiconti del Circolo Matematico di Palermo, vol. 69 (July 2019) p. 771-785

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4 p, 262.6 KB

On the Homoclinic Orbits of the Lü System / Álvarez-Ramírez, Martha (Universidad Autónoma Metropolitana-Iztapalapa (Mèxic). Departamento de Matemáticas) ; García-Saldaña, Johanna Denise (Universidad Católica de la Santísima Concepción (Xile). Departamento de Matemática y Física Aplicadas)
In this paper, the existence of homoclinic orbits of the equilibrium point (0, 0, 0) is demonstrated in the case of the Lu ̈ system for parameter values not reported by G. A. Leonov. In addition, some simulations are shown that agree with our theoretical analysis.
2017 - DOI (Digital Object Identifier)

10.1142/S0218127417500705
International journal of bifurcation and chaos in applied sciences and engineering, Vol. 27 Núm. 5 (2017) , p. 1750070

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13 p, 358.8 KB

Detection of special curves via the double resultant / Ferragut Amengual, Antoni Manel (Universitat Jaume I. Departament de Matemàtiques) ; García-Saldaña, Johanna Denise (Universidad de Talca (Xile). Instituto de Matemática y Física) ; Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
We introduce several applications of the use of the double resultant through some examples of computation of different nature: special level sets of rational first integrals for rational discrete dynamical systems; remarkable values of rational first integrals of polynomial vector fields; bifurcation values in phase portraits of polynomial vector fields; and the different topologies of the offset of curves.
2017 - DOI (Digital Object Identifier)

10.1007/s12346-015-0180-x
Qualitative theory of dynamical systems, Vol. 16 (2017) , p. 101-117

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11 p, 1.1 MB

Weak periodic solutions of x x 1 = 0 and the Harmonic balance method / García-Saldaña, Johanna Denise (Universidad Católica de la Santísima Concepción. Departamento de Matemática y Física Aplicadas) ; Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Abstract. We prove that the differential equation x''x 1 = 0 has continuous weak periodic solutions and compute their periods. Then, we use the Harmonic Balance Method until order six to approximate these periods and to illustrate how the accuracy of the method increases with the order. [...]
2017
Journal of physics, Vol. 811 (2017) , p. 12003

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27 p, 1007.0 KB

Bifurcation diagram and stability for a one-parameter family of planar vector fields / García-Saldaña, Johanna Denise (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Giacomini, Hector (Université de Tours(France). Laboratoire de Mathématiques et Physique Théorique)
We consider the 1-parameter family of planar quintic systems, ˙x = y3−x3, y˙ = −x + my5, introduced by A. Bacciotti in 1985. It is known that it has at most one limit cycle and that it can exist only when the parameter m is in (0. [...]
2014 - DOI (Digital Object Identifier)

10.1016/j.jmaa.2013.11.047
Journal of mathematical analysis and applications, Vol. 413 (2014) , p. 321-342

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17 p, 381.0 KB

A theoretical basis for the Harmonic Balance method / García-Saldaña, Johanna Denise (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
The Harmonic Balance method provides a heuristic approach for finding truncated Fourier series as an approximation to the periodic solutions of ordinary differential equations. Another natural way for obtaining these type of approximations consists in applying numerical methods. [...]
2013 - DOI (Digital Object Identifier)

10.1016/j.jde.2012.09.011
Journal of differential equations, Vol. 254 Núm. 1 (2013) , p. 67-80

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10.

33 p, 1.1 MB

Bifurcation values for a familiy of planar vector fields of degree five / García-Saldaña, Johanna Denise (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Gasull, Armengol (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Giacomini, Hector (Université de Tours (France). Laboratoire de Mathématiques et Physique Théorique)
We study the number of limit cycles and the bifurcation diagram in the Poincar' sphere of a one-parameter family of planar diﬀerential equations of degree e ˙ ﬁve x = Xb (x) which has been already considered in previous papers. [...]
2015 - DOI (Digital Object Identifier)

10.3934/dcds.2015.35.669
Discrete and continuous dynamical systems. Series A, Vol. 35 Núm. 2 (2015) , p. 669-701

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Research literature	1 records found

170 p, 1.8 MB

A qualitative and quantitative study of some planar differential equations / García-Saldaña, Johanna Denise ; Gasull, Armengol, dir. (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Universitat Autònoma de Barcelona. Departament de Matemàtiques
La tesis consta de cinco capítulos y está dividida en dos partes muy diferenciadas. La primera dedicada tanto al uso del llamado Método del Balance Armónico (MBA) como a su fundamentación teórica. [...]
The thesis consists of five chapters and is divided into two parts. The first one is devoted to the use of the so-called Harmonic Balance Method (HBM) as well as its theoretical basis. The second one deals with the quantitative and qualitative study of two families of polynomial differential equations in the plane. [...]
[Barcelona] : Universitat Autònoma de Barcelona, 2014

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