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Bull. Korean Math. Soc. 2014; 51(5): 1503-1510
Printed September 30, 2014
https://doi.org/10.4134/BKMS.2014.51.5.1503
Copyright © The Korean Mathematical Society.
Persistence of homoclinic orbits after discretization of a two dimensional degenerate differential system
Noureddine Mehidi and Nadia Mohdeb
Laboratoire de Math\'{e}matiques Appliqu\'{e}es, Laboratoire de Math\'{e}matiques Appliqu\'{e}es
The aim of this work is to construct a general family of two dimensional differential systems which admits homoclinic solutions near a non-hyperbolic fixed point, such that a Jacobian matrix at this point is zero. We then discretize it by using Euler's method and look after the persistence of the homoclinic solutions in the obtained discrete system.
Keywords: homoclinic orbits, degenerate system, non-hyperbolic fixed point, discrete system
MSC numbers: 34C37, 34A34, 39A05
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