TY - JOUR
T1 - Heteroclinic Dynamics of Localized Frequency Synchrony
T2 - Heteroclinic Cycles for Small Populations
AU - Bick, Christian
PY - 2019/12/1
Y1 - 2019/12/1
N2 - Many real-world systems can be modeled as networks of interacting oscillatory units. Collective dynamics that are of functional relevance for the oscillator network, such as switching between metastable states, arise through the interplay of network structure and interaction. Here, we give results for small networks on the existence of heteroclinic cycles between dynamically invariant sets on which the oscillators show localized frequency synchrony. Trajectories near these heteroclinic cycles will exhibit sequential switching of localized frequency synchrony: a population oscillators in the network will oscillate faster (or slower) than others and which population has this property sequentially changes over time. Since we give explicit conditions on the system parameters for such dynamics to arise, our results give insights into how network structure and interactions (which include higher-order interactions between oscillators) facilitate heteroclinic switching between localized frequency synchrony.
AB - Many real-world systems can be modeled as networks of interacting oscillatory units. Collective dynamics that are of functional relevance for the oscillator network, such as switching between metastable states, arise through the interplay of network structure and interaction. Here, we give results for small networks on the existence of heteroclinic cycles between dynamically invariant sets on which the oscillators show localized frequency synchrony. Trajectories near these heteroclinic cycles will exhibit sequential switching of localized frequency synchrony: a population oscillators in the network will oscillate faster (or slower) than others and which population has this property sequentially changes over time. Since we give explicit conditions on the system parameters for such dynamics to arise, our results give insights into how network structure and interactions (which include higher-order interactions between oscillators) facilitate heteroclinic switching between localized frequency synchrony.
KW - Heteroclinic cycle
KW - Higher-order interactions
KW - Oscillator networks
KW - Phase oscillators
KW - Symmetry
KW - Weak chimera
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U2 - 10.1007/s00332-019-09552-5
DO - 10.1007/s00332-019-09552-5
M3 - Article
AN - SCOPUS:85068838616
SN - 0938-8974
VL - 29
SP - 2547
EP - 2570
JO - Journal of nonlinear science
JF - Journal of nonlinear science
IS - 6
ER -