Topological localized states in the time delayed Adler model: Bifurcation analysis and interaction law

Munsberg, L.; Javaloyes, J.; Gurevich, Svetlana V.

doi:10.1063/5.0002015

Cited by 15 publications

(8 citation statements)

References 41 publications

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“…occur at similar amplitudes and are mainly distinguished by different phase dynamics. In regard to this, we mention Adler's equation for phase injection locking [83][84][85] and Kuromoto's classic model [86], which has become a paradigmatic example of phase synchronization in coupled oscillators [87][88][89].…”

Section: Aim Of This Workmentioning

confidence: 99%

Steady-state statistics, emergent patterns and intermittent energy transfer in a ring of oscillators

Pedergnana

Noiray

2022

Nonlinear Dyn

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Networks of coupled nonlinear oscillators model a broad class of physical, chemical and biological systems. Understanding emergent patterns in such networks is an ongoing effort with profound implications for different fields. In this work, we analytically and numerically study a symmetric ring of N coupled self-oscillators of van der Pol type under external stochastic forcing. The system is proposed as a model of the thermo- and aeroacoustic interactions of sound fields in rigid enclosures with compact source regions in a can-annular combustor. The oscillators are connected via linear resistive coupling with nonlinear saturation. After transforming the system to amplitude-phase coordinates, deterministic and stochastic averaging is performed to eliminate the fast oscillating terms. By projecting the potential of the slow-flow dynamics onto the phase-locked quasi-limit cycle solutions, we obtain a compact, low-order description of the (de-)synchronization transition for an arbitrary number of oscillators. The stationary probability density function of the state variables is derived from the Fokker–Planck equation, studied for varying parameter values and compared to time series simulations. We leverage our analysis to offer explanations for the intermittent energy transfer between Bloch waves observed in acoustic pressure spectrograms observed of real-world gas turbines.

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Section: Aim Of This Workmentioning

confidence: 99%

Steady-state statistics, emergent patterns and intermittent energy transfer in a ring of oscillators

Pedergnana

Noiray

2022

Nonlinear Dyn

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“…Basing on asymptotic approach the equations governing slow evolution of the time separation and phase difference of the interacting TCSs are derived and analyzed. Asymptotic study of weak TCS interaction in DDE models of optical systems was already carried out earlier in [14,16,20]. However, only in Ref.…”

Section: Introductionmentioning

confidence: 99%

Short- and long-range temporal cavity soliton interaction in delay models of mode-locked lasers

Vladimirov

2022

Phys. Rev. E

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Weak interaction of temporal cavity solitons due to gain saturation and recovery in a delay differential model of a long cavity semiconductor laser is studied numerically and analytically using an asymptotic approach. It is shown that in addition to the usual soliton repulsion leading to a harmonic mode-locking regimes a soliton attraction is also possible in a laser with nonzero linewidth enhancement factor. It is shown numerically that this attraction can lead either to a pulse merging or to a pulse bound state formation.

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“…where φ j = ϕ j + ω 0 t and the amplitude-phase coordinates (A j , ϕ j ) are expressed in terms of U j and V j using Eqs. ( 91) and (92), respectively. The Jacobian of the mapping d reads…”

Section: Supplementary Materialsmentioning

confidence: 99%

“…occur at similar amplitudes and are mainly distinguished by different phase dynamics. In regard to this, we mention Adler's equation for phase injection locking [90,91,92] and Kuromoto's classic model [93], which has become a paradigmatic example of phase synchronization in coupled oscillators [94,95,96].…”

Section: Literature Reviewmentioning

confidence: 99%

Steady State Statistics of Emergent Patterns in a Ring of Oscillators

Pedergnana¹,

Noiray²

2021

Preprint

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Networks of coupled nonlinear oscillators model a broad class of physical, chemical and biological systems. Understanding emergent patterns in such networks is an ongoing effort with profound implications for different fields. In this work, we analytically and numerically study a symmetric ring of N coupled selfoscillators of Van der Pol type under external stochastic forcing. The system is proposed as a model of the thermo-and aeroacoustic interactions of sound fields in rigid enclosures with compact source regions in a canannular combustor.The oscillators are connected via linear resistive coupling with nonlinear saturation. After transforming the system to amplitude-phase coordinates, deterministic and stochastic averaging is performed to eliminate the fast oscillating terms. By projecting the potential of the slow-flow dynamics onto the phase-locked quasilimit cycle solutions, we obtain a compact, low-order description of the (de-)synchronization transition for an arbitrary number of oscillators. The stationary probability density function of the state variables is derived from the Fokker-Planck equation, studied for varying parameter values and compared to time series simulations. We leverage our analysis to offer explanations for features of acoustic pressure spectrograms observed in real-world gas turbines.

show abstract

Topological localized states in the time delayed Adler model: Bifurcation analysis and interaction law

Cited by 15 publications

References 41 publications

Steady-state statistics, emergent patterns and intermittent energy transfer in a ring of oscillators

Steady-state statistics, emergent patterns and intermittent energy transfer in a ring of oscillators

Short- and long-range temporal cavity soliton interaction in delay models of mode-locked lasers

Steady State Statistics of Emergent Patterns in a Ring of Oscillators

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