De Witte, V., Govaerts, W., Kuznetsov, Y.A. and Friedman, M. (2012) Interactive Initialization and Continuation of Homoclinic and Heteroclinic Orbits in MATLAB. ACM Transactions on Mathematical Software (TOMS), 38, Article No. 18.
https://doi.org/10.1145/2168773.2168776

has been cited by the following article:

• TITLE: Computation of a Point-to-Point Homoclinic Orbit for a Semiconductor Laser Model

  AUTHORS: Panagiotis S. Douris, Michail P. Markakis

  KEYWORDS: Homoclinic Connections, Orthogonal Collocation on Finite Elements, Numerical Continuation, Limit Cycles

  JOURNAL NAME: Applied Mathematics, Vol.9 No.11, November 20, 2018

  ABSTRACT: In this paper, a methodology for the numerical location of a global point-to-point (P2P for short) homoclinic asymptotically connecting orbit is applied to a modified version of Shimizu-Morioka system, which models a semiconductor laser. This type of global bifurcation can be considered as a stylized mathematical description of self-pulsation in this laser type, associ-ated with saturation. The location is achieved by use of a custom algorithm based on the method of orthogonal collocation on finite elements with fourth order boundary conditions, constructed through scale order approximations. The effectiveness of the algorithm and the superiority of high-order boundary conditions over the widely used first order ones are justified throughout the obtained graphical results.