Authors: Ilham Djellit; Wissame Selmani
Addresses: Department of Mathematics, Laboratory of Mathematics, Dynamics and Modelisation, Faculty of Sciences, University Badji Mokhtar, Annaba 23000, Algeria ' Department of Mathematics, Laboratory of Mathematics, Dynamics and Modelisation, Faculty of Sciences, University Badji Mokhtar, Annaba 23000, Algeria
Abstract: The dynamic behaviour of a dynamical system, described by a planar map, is analytically and numerically explored. We examine the analytical conditions for the stability and bifurcation of the fixed points of the system and by using the numerical methods, we compute bifurcation curves of fixed points and cycles with orders up to five under variation of three parameters, and compute all codimension-1 and codimension-2 bifurcations on the corresponding curves. These curves form stability boundaries of various types of cycles which emanate around codimension-2 bifurcation points. Mathematical underpinnings and numerical simulations confirm our results and contribute to reveal further complex dynamical behaviours.
Keywords: codimension-2 bifurcations; Blumberg's dynamics; fold and flip bifurcation curves; diffeomorphism; embedding.
International Journal of Computing Science and Mathematics, 2019 Vol.10 No.2, pp.140 - 149
Received: 24 Feb 2017
Accepted: 19 Jul 2017
Published online: 02 Apr 2019 *