scholarly journals Amplitude death in systems of coupled oscillators with distributed-delay coupling

2011 ◽  
Vol 84 (2) ◽  
pp. 307-315 ◽  
Author(s):  
Y. N. Kyrychko ◽  
K. B. Blyuss ◽  
E. Schöll
Keyword(s):  
Coupled Oscillators ◽  
Distributed Delay ◽  
Amplitude Death

Effects of frequency mismatch on amplitude death in delay-coupled oscillators

2021 ◽  
Vol 104 (5) ◽  
Author(s):  
Shinsuke Mizukami ◽  
Keiji Konishi ◽  
Yoshiki Sugitani ◽  
Takahiro Kouda ◽  
Naoyuki Hara
Keyword(s):  
Coupled Oscillators ◽  
Amplitude Death ◽  
Frequency Mismatch

scholarly journals Amplitude and phase dynamics in oscillators with distributed-delay coupling

2013 ◽  
Vol 371 (1999) ◽  
pp. 20120466 ◽  
Author(s):  
Y. N. Kyrychko ◽  
K. B. Blyuss ◽  
E. Schöll
Keyword(s):  
Distributed Delay ◽  
Average Frequency ◽  
Amplitude Death ◽  
Phase Dynamics ◽  
Delay Distribution ◽  
Oscillatory Dynamics ◽  
Phase Representation ◽  
Different Types ◽  
The Mean ◽  
Mean Time

This paper studies the effects of distributed-delay coupling on the dynamics in a system of non-identical coupled Stuart–Landau oscillators. For uniform and gamma delay distribution kernels, the conditions for amplitude death are obtained in terms of average frequency, frequency detuning and the parameters of the coupling, including coupling strength and phase, as well as the mean time delay and the width of the delay distribution. To gain further insights into the dynamics inside amplitude death regions, the eigenvalues of the corresponding characteristic equations are computed numerically. Oscillatory dynamics of the system is also investigated, using amplitude and phase representation. Various branches of phase-locked solutions are identified, and their stability is analysed for different types of delay distributions.

The Behavior of Synchronized Frequency in Weakly Coupled Nonidentical Periodic Oscillators

2017 ◽  
Vol 27 (01) ◽  
pp. 1750008
Author(s):  
Priyom Adhyapok ◽  
Mahashweta Patra ◽  
Soumitro Banerjee
Keyword(s):  
Coupled Oscillators ◽  
Chaotic Systems ◽  
Coupled Systems ◽  
Coupling Constant ◽  
Intensive Study ◽  
Amplitude Death ◽  
The Past ◽  
Weakly Coupled ◽  
Simplifying Assumptions ◽  
The Individual

Interaction between dynamical systems has been a subject of intensive study for the past couple of decades. These studies have mainly focused on synchronization of chaotic systems, conditions of different kinds of synchronized behavior, amplitude death, etc. Synchronization of periodic oscillators and the frequency of the resulting synchronized behavior have remained relatively unexplored. In this paper we consider synchronization of nonidentical periodic oscillators for different coupling schemes, and study the nature of the synchronized frequency. Based on numerical and experimental observations we show that for directly coupled oscillators, the synchronized frequency lies between the individual frequencies and its value does not depend on the coupling constant, while for indirectly coupled oscillators the synchronized frequency lies out of the range and depends on the strength of coupling. We explain the different frequency behaviors of directly and indirectly coupled systems by analytically deriving the expressions of synchronized frequency under certain simplifying assumptions.

Effects of initial conditions and coupling competition modes on behaviors of coupled non-identical fractional-order bistable oscillators

2016 ◽  
Vol 94 (11) ◽  
pp. 1158-1166
Author(s):  
Liming Wang
Keyword(s):  
Boundary Layer ◽  
Monte Carlo ◽  
Fractional Order ◽  
Coupled Oscillators ◽  
Chaos Synchronization ◽  
Phase Synchronization ◽  
Initial Conditions ◽  
Coupled System ◽  
Amplitude Death ◽  
Dynamic Behaviors

The effects of the initial conditions and the coupling competition modes on the dynamic behaviors of coupled non-identical fractional-order bistable oscillators are investigated intensively and the various phenomena are explored. The coupled system can be controlled to form chaos synchronization, chaos anti-phase synchronization, amplitude death, oscillation death, etc., by setting the initial conditions or selecting the coupling competition modes. Depending on whether the arbitrary initial conditions can let two coupled oscillators stop oscillating, the dynamic behaviors of the coupled system are further classified into three types, that is, both of oscillators stop oscillating, only one oscillator stops oscillating, and none of oscillators stop oscillating. Based on the principle of Monte Carlo method, the percentages of three types of dynamic behaviors are calculated for the different coupling competition modes and the dynamic behaviors of the coupled system are characterized from the perspective of statistics. Moreover, the mechanism behind the various phenomena is explained in detail by the concept of boundary layer and the optimum coupling competition modes are found.

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