Zakaria, L. and Tuwankotta, J. M. (2016) DYNAMICS AND BIFURCATIONS IN A TWO- DIMENSIONAL MAP DERIVED FROM A GENERALIZED ∆∆SINE-GORDON EQUATION. Far East Journal of Dynamical Systems, 28 (3). pp. 165-194. ISSN 09721118

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Abstract

In this paper, we consider a generalization of a double discrete sine-Gordon equation. The generalization is done by introducing a number of parameters in the Lax-pair matrices. By restricting to the traveling wave solution, we derive a three-parameter family of discrete integrable dynamical systems using the so-called staircase methods. Special focus is on the cases where the resulting family of dynamical systems is of low dimension, i.e., two-dimensional. In those cases, the dynamics and bifurcation in the system is described by means of analyzing the level sets of the integral functions. Local bifurcation such as period-doubling bifurcation for map has been detected. Apart from that, we have observed nonlocal bifurcations which involve collision between heteroclinic and homoclinic connection between critical points.

Item Type:	Article
Subjects:	Q Science > QA Mathematics
Depositing User:	Mr Zakaria La
Date Deposited:	06 Aug 2020 09:01
Last Modified:	06 Aug 2020 09:01
URI:	http://repository.lppm.unila.ac.id/id/eprint/23557

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• DYNAMICS AND BIFURCATIONS IN A TWO- DIMENSIONAL MAP DERIVED FROM A GENERALIZED ∆∆SINE-GORDON EQUATION. (deposited 06 Aug 2020 09:01) [Currently Displayed]
  • DYNAMICS AND BIFURCATIONS IN A TWO- DIMENSIONAL MAP DERIVED FROM A GENERALIZED ∆∆SINE-GORDON EQUATION. (deposited 13 Aug 2020 02:16)

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