Eur. Phys. J. D 13, 385-391 (2001)
https://doi.org/10.1007/s100530170257

Theoretical and experimental study of discrete behavior of Shilnikov chaos in a CO₂ laser

¹ Centro de Investigaciones en Optica, Loma del Bosque 115, Col. Lomas del Campestre, 37150 Leon, Gto., Mexico
² Istituto Nazionale di Ottica Applicata, L.E. Fermi 6, 50125 Firenze, Italy
³ Department of Physics, University of Firenze, 50125 Firenze, Italy

Corresponding authors: ^a apisarch@foton.cio.mx - ^b ric@ino.it - ^c arecchi@ino.it

Received: 28 September 2000
Published online: 15 March 2001

Abstract

The discrete distribution of homoclinic orbits has been investigated numerically and experimentally in a CO₂ laser with feedback. The narrow chaotic ranges appear consequently when a laser parameter (bias voltage or feedback gain) changes exponentially. Up to six consecutive chaotic windows have been observed in the numerical simulation as well as in the experiments. Every subsequent increase in the number of loops in the upward spiral around the saddle focus is accompanied by the appearance of the corresponding chaotic window. The discrete character of homoclinic chaos is also demonstrated through bifurcation diagrams, eigenvalues of the fixed point, return maps, and return times of the return maps.