PMID- 34470243
OWN - NLM
STAT- PubMed-not-MEDLINE
LR  - 20210902
IS  - 1089-7682 (Electronic)
IS  - 1054-1500 (Linking)
VI  - 31
IP  - 8
DP  - 2021 Aug
TI  - A two-frequency-two-coupling model of coupled oscillators.
PG  - 083124
LID - 10.1063/5.0056844 [doi]
AB  - We considered the phase coherence dynamics in a Two-Frequency and Two-Coupling 
      (TFTC) model of coupled oscillators, where coupling strength and natural 
      oscillator frequencies for individual oscillators may assume one of two values 
      (positive/negative). The bimodal distributions for the coupling strengths and 
      frequencies are either correlated or uncorrelated. To study how correlation 
      affects phase coherence, we analyzed the TFTC model by means of numerical 
      simulations and exact dimensional reduction methods allowing to study the 
      collective dynamics in terms of local order parameters [S. Watanabe and S. H. 
      Strogatz, Physica D 74(3-4), 197-253 (1994); E. Ott and T. M. Antonsen, Chaos 
      18(3), 037113 (2008)]. The competition resulting from distributed coupling 
      strengths and natural frequencies produces nontrivial dynamic states. For 
      correlated disorder in frequencies and coupling strengths, we found that the 
      entire oscillator population splits into two subpopulations, both phase-locked 
      (Lock-Lock) or one phase-locked, and the other drifting (Lock-Drift), where the 
      mean-fields of the subpopulations maintain a constant non-zero phase difference. 
      For uncorrelated disorder, we found that the oscillator population may split into 
      four phase-locked subpopulations, forming phase-locked pairs which are either 
      mutually frequency-locked (Stable Lock-Lock-Lock-Lock) or drifting (Breathing 
      Lock-Lock-Lock-Lock), thus resulting in a periodic motion of the global 
      synchronization level. Finally, we found for both types of disorder that a state 
      of Incoherence exists; however, for correlated coupling strengths and 
      frequencies, incoherence is always unstable, whereas it is only neutrally stable 
      for the uncorrelated case. Numerical simulations performed on the model show good 
      agreement with the analytic predictions. The simplicity of the model promises 
      that real-world systems can be found which display the dynamics induced by 
      correlated/uncorrelated disorder.
FAU - Hong, Hyunsuk
AU  - Hong H
AUID- ORCID: 0000000181321292
AD  - Department of Physics and Research Institute of Physics and Chemistry, Jeonbuk 
      National University, Jeonju 54896, South Korea.
FAU - Martens, Erik A
AU  - Martens EA
AUID- ORCID: 0000000294557517
AD  - Centre for Mathematical Sciences, Lund University, 221 00 Lund, Sweden.
LA  - eng
PT  - Journal Article
PL  - United States
TA  - Chaos
JT  - Chaos (Woodbury, N.Y.)
JID - 100971574
SB  - IM
EDAT- 2021/09/03 06:00
MHDA- 2021/09/03 06:01
CRDT- 2021/09/02 05:34
PHST- 2021/09/02 05:34 [entrez]
PHST- 2021/09/03 06:00 [pubmed]
PHST- 2021/09/03 06:01 [medline]
AID - 10.1063/5.0056844 [doi]
PST - ppublish
SO  - Chaos. 2021 Aug;31(8):083124. doi: 10.1063/5.0056844.