Dynamics of an erbium-doped fiber dual-ring laser

AbstractWe report results of a numerical investigation on two-dimensional parameter-spaces of a set of four autonomous, seven-parameter, first-order ordinary differential equations, which models an erbium-doped fiber dual-ring laser. By using Lyapunov exponents to numerically characterize the dynamics of the model in the parameter-space, we show that it presents typical self-organized periodic structures embedded in a chaotic region.

[1]  Paulo C. Rech,et al.  Some two-dimensional parameter spaces of a Chua system with cubic nonlinearity. , 2010, Chaos.

[2]  Holokx A. Albuquerque,et al.  Complex periodic structures in bi-dimensional bifurcation diagrams of a RLC circuit model with a nonlinear NDC device , 2009 .

[3]  Paulo C. Rech,et al.  Spiral periodic structure inside chaotic region in parameter-space of a Chua circuit , 2012, Int. J. Circuit Theory Appl..

[4]  J. Gallas,et al.  Self-organized distribution of periodicity and chaos in an electrochemical oscillator. , 2011, Physical chemistry chemical physics : PCCP.

[5]  M. W. Phillips,et al.  Optical chaos and hysteresis in a laser-diode pumped Nd doped fibre laser , 1987 .

[6]  Vassilios Kovanis,et al.  Labyrinth bifurcations in optically injected diode lasers , 2010 .

[7]  Edward N. Lorenz,et al.  Compound windows of the Hénon-map , 2008 .

[8]  Paulo C. Rech,et al.  Self-similar structures in a 2D parameter-space of an inductorless Chua's circuit , 2008 .

[9]  Ke Shen,et al.  Generalized synchronization of chaos in erbium-doped dual-ring lasers , 2002 .

[10]  P. Glendinning,et al.  Global structure of periodicity hubs in Lyapunov phase diagrams of dissipative flows. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[11]  J. G. Freire,et al.  Non-Shilnikov cascades of spikes and hubs in a semiconductor laser with optoelectronic feedback. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Yang Senlin,et al.  Study on the method of controlling chaos in an Er-doped fiber dual-ring laser via external optical injection and shifting optical feedback light. , 2007, Chaos.

[13]  J. Gallas,et al.  Accumulation horizons and period adding in optically injected semiconductor lasers. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Andrey Shilnikov,et al.  Global organization of spiral structures in biparameter space of dissipative systems with Shilnikov saddle-foci. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  J. Gallas,et al.  Structure of the parameter space of the Hénon map. , 1993, Physical review letters.

[16]  Stephan,et al.  General analysis of instabilities in erbium-doped fiber lasers. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[17]  Liguo Luo,et al.  Chaotic behavior in erbium-doped fiber-ring lasers , 1998 .

[18]  J. Gallas,et al.  Periodicity hub and nested spirals in the phase diagram of a simple resistive circuit. , 2008, Physical review letters.

[19]  Jason A. C. Gallas,et al.  Mandelbrot-like sets in dynamical systems with no critical points , 2006 .

[20]  Yoshisuke Ueda,et al.  Chaotic phase similarities and recurrences in a damped-driven Duffing oscillator. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Jason A. C. Gallas,et al.  How similar is the performance of the cubic and the piecewise-linear circuits of Chua? , 2010 .

[22]  J. M. Gonzalez-Miranda.  Complex bifurcation Structures in the Hindmarsh-rose Neuron Model , 2007, Int. J. Bifurc. Chaos.

[23]  M S Baptista,et al.  Experimental observation of a complex periodic window. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Celso Grebogi,et al.  From High Dimensional Chaos to Stable Periodic Orbits: The Structure of Parameter Space , 1997 .

[25]  Enno de Lange,et al.  The Hindmarsh-Rose neuron model: bifurcation analysis and piecewise-linear approximations. , 2008, Chaos.

[26]  Iberê L. Caldas,et al.  Periodic window arising in the parameter space of an impact oscillator , 2010 .

[27]  C. DaCamara,et al.  Multistability, phase diagrams, and intransitivity in the Lorenz-84 low-order atmospheric circulation model. , 2008, Chaos.

[28]  Marco Thiel,et al.  Abundance of stable periodic behavior in a Red Grouse population model with delay: a consequence of homoclinicity. , 2010, Chaos.

[29]  Jason A. C. Gallas,et al.  The Structure of Infinite Periodic and Chaotic Hub Cascades in Phase Diagrams of Simple Autonomous Flows , 2010, Int. J. Bifurc. Chaos.

[30]  Paulo C. Rech,et al.  Dynamics of a neuron model in different two-dimensional parameter-spaces , 2011 .

[31]  Ruedi Stoop,et al.  Real-world existence and origins of the spiral organization of shrimp-shaped domains. , 2010, Physical review letters.

[32]  Paulo C. Rech,et al.  DYNAMICS OF A PARTICULAR LORENZ TYPE SYSTEM , 2010 .

[33]  Shen Ke,et al.  Controlling hyperchaos in erbium-doped fibre laser , 2003 .

[34]  Marco Storace,et al.  Experimental bifurcation diagram of a circuit-implemented neuron model , 2010 .

[35]  Cristian Bonatto,et al.  Self-similarities in the frequency-amplitude space of a loss-modulated CO2 laser. , 2005, Physical review letters.