Physica D 189 (2004) 70–80 Global manifold control in a driven laser: sustaining chaos and regular dynamics R. Meucci a , D. Cinotti a , E. Allaria a,∗ , L. Billings b , I. Triandaf c , D. Morgan c , I.B. Schwartz c a Istituto Nazionale di Ottica Applicata, Largo E. Fermi 6, 50125 Firenze, Italy b Department of Mathematical Sciences, Montclair State University, Upper Montclair, NJ 07043, USA c Naval Research Laboratory, Plasma Physics Division, Code 6792, Washington, DC 20375-5000, USA Received 27 June 2003; received in revised form 8 September 2003; accepted 26 September 2003 Communicated by R. Roy Abstract We present experimental and numerical evidence of a multi-frequency phase control able to preserve periodic behavior within a chaotic window as well as to re-excite chaotic behavior when it is destroyed by the presence of a mitigating unstable periodic orbit created in the presence of the multi-frequency drive. The mitigating saddle controlling the global behavior is identified and the controlling manifolds approximated. © 2003 Elsevier B.V. All rights reserved. Keywords: Driven laser; Chaos dynamics; Regular dynamics 1. Introduction Control of chaos represents one of the most inter- esting and stimulating ideas in the field of nonlinear dynamics [1]. The original basic idea is to stabilize the dynamics over one of the different unstable periodic orbits visited during the chaotic motion by applying small perturbations to the system [2]. Alternatively, one may wish to sustain chaos in certain situations where chaos is destroyed [3,4]. Both stabilizing un- stable orbits and sustaining chaos by exciting unsta- ble chaotic orbits may be considered as intervention techniques to control the dynamical flow. ∗ Corresponding author. Tel.: +39-055-23081; fax: +39-055-2337755. E-mail addresses: ric@ino.it (R. Meucci), allaria@ino.it (E. Allaria). Different methods for controlling chaos have been proposed based on determination of the stable and un- stable manifolds on the Poincaré section [2,5–7], on a self-controlling feedback procedure [8] and on the introduction of open loop small perturbations [9–16]. On the other hand, chaos can be a desirable behav- ior in biological [4], mechanical [17], electrical [18] and optical systems [19]. In mechanics, small ampli- tude chaos, where the energy is spread over several modes, may be preferable to high amplitude resonant behavior [20,21]. In such situations, the chaotic at- tracting window may be quite small, and sustained chaos techniques are therefore required. Once a chaotic regime appears, it typically and dramatically disappears as a result of a crisis, which is an abrupt change from chaos to periodic behavior at a critical parameter value of the system [22]. The 0167-2789/$ – see front matter © 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.physd.2003.09.033