Polynomial Inverse Integrating Factors, First Integral and Non-Existence of Limit Cycles in the Plane for Quadratic Systems
DOI:
https://doi.org/10.25271/2017.5.2.374Keywords:
Polynomial inverse integrating factors, first integral, limit cyclesAbstract
The main purpose of this paper is to study the existence of polynomial inverse integrating factor and first integral, and non-existence of limit cycles for all systems. Furthermore, we consider some applications.
References
ArrowSmith, D.K. and Place, C.M. (1982). Ordinary differential equations. Mathematics series.
Calanchi, M. and Ruf, B. (2002). On the number of closed solutions polynomial ODE and a special case of Hilberts. Adv.Diff.Eq, 1978-2016.
Chavarriga, J. (2004.). On the algebraic limit cycles of quadratic systems,. University Autonoma de Barcelona, .
Chavarriga, J., Giacomini, H. and Gine, J. (1997). The null divergence factor. Publicacions Matematiques, 41-56.
Chavarriga, J., Giacomini, H. and Gine, J. (1999). On a new of bifurcation of limit cycles for a planar cubic system. Nonlinear Analysis, 139-149.
Chavarriga, J., Giacomini, H. and Gine, J. (2000). Polynomial inverse integrating factors. Ann.of Diff.Eqs, 320-329.
Chavarriga, J., Llibre , J. and Sorolla , J. (2001). Algebraic limit cycles for quadratic systems. preprint Universitat de Lleida.
Ferragut, A. (2006). Polynomial inverse integrating factors of quadratic differential systems and other results. Ph.D. thesis, University Autonoma de Barcelona.
Mustafa, Y. T., and Easif F. H. (2005). On limit cycles of a Certain Quintic System, Journal of Duhok University, Vol. 9, No. 1.
Calanchi, M. and Ruf, B. (2002). On the number of closed solutions polynomial ODE and a special case of Hilberts. Adv.Diff.Eq, 1978-2016.
Chavarriga, J. (2004.). On the algebraic limit cycles of quadratic systems,. University Autonoma de Barcelona, .
Chavarriga, J., Giacomini, H. and Gine, J. (1997). The null divergence factor. Publicacions Matematiques, 41-56.
Chavarriga, J., Giacomini, H. and Gine, J. (1999). On a new of bifurcation of limit cycles for a planar cubic system. Nonlinear Analysis, 139-149.
Chavarriga, J., Giacomini, H. and Gine, J. (2000). Polynomial inverse integrating factors. Ann.of Diff.Eqs, 320-329.
Chavarriga, J., Llibre , J. and Sorolla , J. (2001). Algebraic limit cycles for quadratic systems. preprint Universitat de Lleida.
Ferragut, A. (2006). Polynomial inverse integrating factors of quadratic differential systems and other results. Ph.D. thesis, University Autonoma de Barcelona.
Mustafa, Y. T., and Easif F. H. (2005). On limit cycles of a Certain Quintic System, Journal of Duhok University, Vol. 9, No. 1.
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Published
2017-06-30
How to Cite
Hussien, A. M. (2017). Polynomial Inverse Integrating Factors, First Integral and Non-Existence of Limit Cycles in the Plane for Quadratic Systems. Science Journal of University of Zakho, 5(2), 232–238. https://doi.org/10.25271/2017.5.2.374
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Science Journal of University of Zakho
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