On the emerging asymptotic patterns of the Winfree model with frustrations

Nonlinearity ◽  
2021 ◽  
Vol 34 (4) ◽  
pp. 2454-2482
Author(s):  
Seung-Yeal Ha ◽  
Myeongju Kang ◽  
Bora Moon
Keyword(s):  
Winfree Model ◽  
Asymptotic Patterns

scholarly journals Emergence of phase-locked states for the Winfree model in a large coupling regime

2015 ◽  
Vol 35 (8) ◽  
pp. 3417-3436 ◽  
Author(s):  
Seung-Yeal Ha ◽  
◽  
Jinyeong Park ◽  
Sang Woo Ryoo ◽  
Keyword(s):  
Large Coupling ◽  
Winfree Model

scholarly journals Generalization of the Winfree model to the high-dimensional sphere and its emergent dynamics

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Hansol Park
Keyword(s):  
Influence Function ◽  
Equilibrium Solution ◽  
Phase Locking ◽  
Small Diameter ◽  
High Dimensional ◽  
Dimensional Sphere ◽  
Sphere Model ◽  
Dirac Delta ◽  
Delta Distribution ◽  
Winfree Model

<p style='text-indent:20px;'>We present a high-dimensional Winfree model in this paper. The Winfree model is a mathematical model for synchronization on the unit circle. We generalize this model compare to the high-dimensional sphere and we call it the Winfree sphere model. We restricted the support of the influence function in the neighborhood of the attraction point to a small diameter to mimic the influence function as the Dirac delta distribution. We can obtain several new conditions of the complete phase-locking states for the identical Winfree sphere model from restricting the support of the influence function. We also prove the complete oscillator death(COD) state from the exponential <inline-formula><tex-math id="M1">\begin{document}$ \ell^1 $\end{document}</tex-math></inline-formula>-stability and the existence of the equilibrium solution.</p>

Role of phase-dependent influence function in the Winfree model of coupled oscillators

2021 ◽  
Vol 104 (6) ◽  
Author(s):  
M. Manoranjani ◽  
R. Gopal ◽  
D. V. Senthilkumar ◽  
V. K. Chandrasekar
Keyword(s):  
Influence Function ◽  
Coupled Oscillators ◽  
Winfree Model

scholarly journals Synchronization scenarios in the Winfree model of coupled oscillators

2017 ◽  
Vol 96 (4) ◽  
Author(s):  
Rafael Gallego ◽  
Ernest Montbrió ◽  
Diego Pazó
Keyword(s):  
Coupled Oscillators ◽  
Winfree Model

scholarly journals Interplay of random inputs and adaptive couplings in the Winfree model

2021 ◽  
Vol 20 (11) ◽  
pp. 3959
Author(s):  
Seung-Yeal Ha ◽  
Doheon Kim ◽  
Bora Moon
Keyword(s):  
Initial Data ◽  
Random Effects ◽  
Natural Frequencies ◽  
Random Inputs ◽  
Structural Robustness ◽  
Death State ◽  
Winfree Model ◽  
Adaptive Coupling ◽  
Coupling Strengths

<p style='text-indent:20px;'>We study a structural robustness of the complete oscillator death state in the Winfree model with random inputs and adaptive couplings. For this, we present a sufficient framework formulated in terms of initial data, natural frequencies and adaptive coupling strengths. In our proposed framework, we derive propagation of infinitesimal variations in random space and asymptotic disappearance of random effects which exhibits the robustness of the complete oscillator death state for the random Winfree model.</p>

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