Dynamics of a ring of three unidirectionally coupled Duffing oscillators with time-dependent damping

Barba-Franco, J. J.; Gallegos, A.; Jaimes-Reátegui, R.; Gerasimova, S. A.; Pisarchik, Alexander N.

doi:10.1209/0295-5075/134/30005

Cited by 18 publications

(9 citation statements)

References 38 publications

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“…To this aim, we analyze the system behavior using time series, bifurcation diagrams, Poincaré sections, Fourier spectra, and Lyapunov exponents. We will show that although the dynamics of this ring is similar to other coupled oscillators [55], it exhibits particular features inherent to laser systems. This paper is organized as follows.…”

Section: Of 16mentioning

confidence: 77%

“…In addition, unidirectional coupling is commonly used in electrical systems based on the Chua [50], Lorenz [51,52], and Duffing [53] models where rotating waves where discovered. Transitions from a stable equilibrium through quasiperiodicity to chaos and hyperchaos with respect to the coupling strength were observed in the rings of unidirectionally coupled Lorenz [51,54], Duffing [55], and Rulkov [56] oscillators. The mechanism leading to such transitions was studied in detail in autonomous Duffing oscillators [53,[57][58][59].…”

Section: Of 16mentioning

confidence: 99%

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Route to Chaos in a Unidirectional Ring of Three Diffusively Coupled Erbium-Doped Fiber Lasers

Torre¹,

García-López²,

Jaimes-Reátegui³

et al. 2023

Preprint

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We study the synchronous dynamics of three diffusively coupled erbium-doped fiber lasers (EDLFs) in the unidirectional ring configuration without external pump modulation. The dynamical behavior of the system is analyzed using time series, Fourier spectra, Poincaré sections, bifurcation diagrams, and Lyapunov exponents for different values of the coupling strength. For weak coupling, we observe a well-known route to chaos from a stable equilibrium through a Hopf bifurcation and a series of torus bifurcations as the coupling strength is increased. An interesting result is found for large values of the coupling strength, where the phase locking is close to zero. This allows a significant increase in the peak energy of the EDFLs pulses, i.e., above the coupling strength the lasers switch to a Q-switching mode with large-amplitude short pulses. This result allows us to propose a new method for increasing the laser pulse energy based on the control of the bistability by the rotating wave in the array of three unidirectionally ring-coupled EDFLs as a function of the coupling strength. In our system, we were able to increase the peak laser power by almost 20 times more than a continuous single EDFL.

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Section: Of 16mentioning

confidence: 77%

Section: Of 16mentioning

confidence: 99%

Route to Chaos in a Unidirectional Ring of Three Diffusively Coupled Erbium-Doped Fiber Lasers

Torre¹,

García-López²,

Jaimes-Reátegui³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…Since fiber and semiconductor lasers belong to the same class-B lasers [58], we anticipate observing a similar route to chaos in the ring of coupled EDFLs. Through the application of time series analysis, bifurcation diagrams, Poincaré sections, power spectra, and Lyapunov exponents, we demonstrate that while the dynamics of this ring share similarities with other coupled oscillators [50], it also possesses distinctive characteristics inherent to EDFLs.…”

Section: Introductionmentioning

confidence: 92%

“…Moreover, unidirectional rings were explored in coupled electrical circuits based on Chua [44], Lorenz [45,46], and Duffing [47,48] models where rotating waves were also discovered. Transitions from a stable equilibrium through quasiperiodicity to chaos and hyperchaos with respect to the coupling strength were observed in the rings of unidirectionally coupled Lorenz [45,49], Duffing [50], and Rulkov [51] oscillators.…”

Section: Introductionmentioning

confidence: 99%

Route to Chaos in a Unidirectional Ring of Three Diffusively Coupled Erbium-Doped Fiber Lasers

et al. 2023

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We numerically investigate the dynamics of a ring consisting of three unidirectionally coupled Erbium-Doped Fiber Lasers (EDLFs) without external pump modulation. The study focuses on the system behavior as the coupling strength is varied, employing a six-dimensional mathematical model that includes three variables for laser intensities and three variables for population inversions of all lasers. Our primary objective is to understand the system evolution towards chaos from a stable equilibrium in the ring, considering the impact of increasing coupling strength. To analyze the system’s behavior, we employ various techniques such as time series analysis, power spectra, Poincaré sections, bifurcation diagrams, and Lyapunov exponents. During the transition to chaos, the system undergoes a Hopf bifurcation and a series of torus bifurcations. An essential aspect of this study is the exploration of a rotating wave propagating along the ring, where the wave nature (periodic, quasiperiodic, or chaotic) depends on the coupling strength. Additionally, we observe the coexistence of periodic and chaotic orbits within a specific range of the coupling strength. However, for very strong coupling, this bistability disappears, resulting in a monostable system with a single limit cycle. This regime exhibits potential for applications that demand short laser pulses with a substantial increase in peak power, reaching nearly 20 times higher levels compared to the continuous mode when the lasers are uncoupled. This discovery holds particular importance for optical communication systems, especially considering the attenuation optical signals experience when transmitted over long distances.

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“…Recent progress in solid-state microelectronics, molecular biology, and neuroscience has led to the development of neuromorphic devices, integrating artificial and living biological systems for the real-time monitoring and control of neural activity. Breakthroughs in control theory and nonlinear dynamics have driven the evolution of mathematical theories and physical models of neurons as dynamical systems, from individual elements [1][2][3] to complex neural networks [4,5]. Synchronization processes have played a crucial role in encoding and decoding neural dynamics, revealing the importance of self-organization processes in neuronal dynamics [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Living-Neuron-Based Autogenerator

Gerasimova

Beltyukova

Fedulina

et al. 2023

Sensors

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We present a novel closed-loop system designed to integrate biological and artificial neurons of the oscillatory type into a unified circuit. The system comprises an electronic circuit based on the FitzHugh-Nagumo model, which provides stimulation to living neurons in acute hippocampal mouse brain slices. The local field potentials generated by the living neurons trigger a transition in the FitzHugh–Nagumo circuit from an excitable state to an oscillatory mode, and in turn, the spikes produced by the electronic circuit synchronize with the living-neuron spikes. The key advantage of this hybrid electrobiological autogenerator lies in its capability to control biological neuron signals, which holds significant promise for diverse neuromorphic applications.

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Dynamics of a ring of three unidirectionally coupled Duffing oscillators with time-dependent damping

Cited by 18 publications

References 38 publications

Route to Chaos in a Unidirectional Ring of Three Diffusively Coupled Erbium-Doped Fiber Lasers

Route to Chaos in a Unidirectional Ring of Three Diffusively Coupled Erbium-Doped Fiber Lasers

Route to Chaos in a Unidirectional Ring of Three Diffusively Coupled Erbium-Doped Fiber Lasers

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