Noise Synchronization and Stochastic Bifurcations in Lasers

Wieczorek, Sebastian

doi:10.1002/9783527639823.ch11

Cited by 4 publications

(2 citation statements)

References 35 publications

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“…Therefore, other methods of detecting (2) had to be developed. As suggested by the auxiliary system approach [Abarbanel et al, 1996], relationships (2) and (3) are implied by an (invariant) attracting trajectory in the (x, y,t) phase space of the nonautonomous forced system (4) [Wieczorek, 2011]. In the remainder of the paper, such an attracting trajectory is denoted with AT and referred to as an attracting climatic trajectory or synchronized solution.…”

Section: Synchronizationmentioning

confidence: 99%

Is the astronomical forcing a reliable and unique pacemaker for climate? A conceptual model study

2012

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There is evidence that ice age cycles are paced by astronomical forcing, suggesting some kind of synchronisation phenomenon. Here, we identify the type of such synchronisation and explore systematically its uniqueness and robustness using a simple paleoclimate model akin to the van der Pol relaxation oscillator and dynamical system theory. As the insolation is quite a complex quasiperiodic signal involving different frequencies, the traditional concepts used to define synchronisation to periodic forcing are no longer applicable. Instead, we explore a different concept of generalised synchronisation in terms of (coexisting) synchronised solutions for the forced system, their basins of attraction and instabilities. We propose a clustering technique to compute the number of synchronised solutions, each of which corresponds to a different paleoclimate history. In this way, we uncover multistable synchronisation (reminiscent of phase-or frequency-locking to individual periodic components of astronomical forcing) at low forcing strength, and monostable or unique synchronisation at stronger forcing. In the multistable regime, different initial conditions may lead to different paleoclimate histories. To study their robustness, we analyse Lyapunov exponents that quantify the rate of convergence towards each synchronised solution (local stability), and basins of attraction that indicate critical levels of external perturbations (global stability). We find that even though synchronised solutions are stable on a long term, there exist short episodes of desynchronisation where nearby climate trajectories diverge temporarily (for about 50 kyr). As the attracting trajectory can sometimes lie close to the boundary of its basin of attraction, a small perturbation could quite easily make climate to jump between different histories, reducing the predictability. Our study brings new insight into paleoclimate dynamics and reveals a possibility for the climate system to wander throughout different climatic histories related to preferential synchronisation regimes on obliquity, precession or combinations of both, all over the history of the Pleistocene.

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Section: Synchronizationmentioning

confidence: 99%

Is the astronomical forcing a reliable and unique pacemaker for climate? A conceptual model study

2012

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“…12 Consistency has also been referred to as reliability and also investigated in the contexts of generalized synchronization or noise synchronization. [13][14][15][16] Given its relevance, some theoretical and experimental works on consistency in nonlinear delay systems have been presented recently. [9][10][11]17 We aim to extend the phenomenology and understanding of consistency by studying a paradigmatic nonlinear dynamical system: a delay optoelectronic intensity oscillator.…”

Section: Introductionmentioning

confidence: 99%

Consistency in experiments on multistable driven delay systems

Oliver

Larger

Fischer

2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We investigate the consistency properties in the responses of a nonlinear delay optoelectronic intensity oscillator subject to different drives, in particular, harmonic and self-generated waveforms. This system, an implementation of the Ikeda oscillator, is operating in a closed-loop configuration, exhibiting its autonomous dynamics while the drive signals are additionally introduced. Applying the same drive multiple times, we compare the dynamical responses of the optoelectronic oscillator and quantify the degree of consistency among them via their correlation. Our results show that consistency is not restricted to conditions close to the first Hopf bifurcation but can be found in a broad range of dynamical regimes, even in the presence of multistability. Finally, we discuss the dependence of consistency on the nature of the drive signal.

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