Laser Dynamics and Delayed Feedback

Lüdge, Kathy; Lingnau, Benjamin

doi:10.1007/978-1-0716-0421-2_729

Cited by 2 publications

(2 citation statements)

References 81 publications

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“…2 is chosen to allow for a complete picture of the bifurcation scenario. Nevertheless, the bifurcation structure also changes with the feedback parameters and sensitively depends on the feedback delay time, feedback phase and feedback strength [56][57][58][59] which will become important later on. The reservoir computing specific parameters, such as virtual node distance and regularization parameter, do not change the bifurcation structure, but they have to be adjusted for different operation conditions in order to reach optimal performance (See Methods section IV).…”

Section: Resultsmentioning

confidence: 99%

Reservoir computing using spin-VCSELs - the influence of timescales and data injection schemes

Lüdge,

Jaurigue,

Jaurigue

et al. 2024

Preprint

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Reservoir computing implemented in photonic systems promises fast and energy efficient computations. Due to their particularly fast spin-flip dynamics, vertically emitting semiconductor lasers with two spin polarized charge carrier populations (spin-VCSEL), are good candidates for high-speed reservoir computing. However, spin-VCSELs are complex dynamical systems, and in order to properly utilise their dynamics for computation, a thorough understanding of the interplay of dynamical variables and external control parameters is needed. With our work, we numerically show the crucial impact of dynamic coupling and decay timescales on the prediction performance of a spin-VSCEL reservoir computer. We present numerical evidence of the critical impact of different data injection schemes and internal timescales. Injection schemes based on the phase of the injected light and on generating spin polarized charge-carriers are compared as a function of the spin carrier lifetimes. A central finding is that the internal relaxation dynamics of the charge carriers is only beneficial for the performance with encoding via the spin polarized current. If the data is encoded via an optical phase difference, these carrier dynamics, and with it the additional memory, cannot be utilised. We find strong correlations with the underlying delay induced bifurcation structure, which allows to transfer the results also to other physical reservoir computing systems.

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Section: Resultsmentioning

confidence: 99%

Reservoir computing using spin-VCSELs - the influence of timescales and data injection schemes

Lüdge,

Jaurigue,

Jaurigue

et al. 2024

Preprint

Self Cite

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“…Delayed processes are ubiquitous in physical, chemical and especially biological systems (Just et al 2010;Lüdge and Lingnau 2020;Totz et al 2017;Milton 2015;Glass 2001). Typically time delays reflect a combination of transmission and processing times or the time it takes to react to a stimulus.…”

Section: Distributed Delaymentioning

confidence: 99%

Phase response approaches to neural activity models with distributed delay

et al. 2021

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In weakly coupled neural oscillator networks describing brain dynamics, the coupling delay is often distributed. We present a theoretical framework to calculate the phase response curve of distributed-delay induced limit cycles with infinite-dimensional phase space. Extending previous works, in which non-delayed or discrete-delay systems were investigated, we develop analytical results for phase response curves of oscillatory systems with distributed delay using Gaussian and log-normal delay distributions. We determine the scalar product and normalization condition for the linearized adjoint of the system required for the calculation of the phase response curve. As a paradigmatic example, we apply our technique to the Wilson-Cowan oscillator model of excitatory and inhibitory neuronal populations under the two delay distributions. We calculate and compare the phase response curves for the Gaussian and log-normal delay distributions. The phase response curves obtained from our adjoint calculations match those compiled by the direct perturbation method, thereby proving that the theory of weakly coupled oscillators can be applied successfully for distributed-delay-induced limit cycles. We further use the obtained phase response curves to derive phase interaction functions and determine the possible phase locked states of multiple inter-coupled populations to illuminate different synchronization scenarios. In numerical simulations, we show that the coupling delay distribution can impact the stability of the synchronization between inter-coupled gamma-oscillatory networks. KeywordsCoupled oscillators • Distributed delay • Phase response curve • Wilson-Cowan model Communicated by James Maclaurin.

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Laser Dynamics and Delayed Feedback

Cited by 2 publications

References 81 publications

Reservoir computing using spin-VCSELs - the influence of timescales and data injection schemes

Reservoir computing using spin-VCSELs - the influence of timescales and data injection schemes

Phase response approaches to neural activity models with distributed delay

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