TY - JOUR

T1 - Chimera States in Networks of Locally and Non-locally Coupled SQUIDs

AU - Hizanidis, Johanne

AU - Lazarides, Nikos

AU - Tsironis, Giorgos P.

N1 - Funding Information:
This research has been financially supported by the General Secretariat for Research and Technology (GSRT) and the Hellenic Foundation for Research and Innovation (HFRI) (Code: 203).

PY - 2019/7/12

Y1 - 2019/7/12

N2 - Planar and linear arrays of SQUIDs (superconducting quantum interference devices) operate as non-linear magnetic metamaterials in microwaves. Such SQUID metamaterials are paradigmatic systems that serve as a test-bed for simulating several non-linear dynamics phenomena. SQUIDs are highly non-linear oscillators which are coupled together through magnetic dipole-dipole forces due to their mutual inductance; that coupling falls-off approximately as the inverse cube of their distance, i.e., it is non-local. However, it can be approximated by a local (nearest-neighbor) coupling which in many cases suffices for capturing the essentials of the dynamics of SQUID metamaterials. For either type of coupling, it is numerically demonstrated that chimera states as well as other spatially non-uniform states can be generated in SQUID metamaterials under time-dependent applied magnetic flux for appropriately chosen initial conditions. The mechanism for the emergence of these states is discussed in terms of the multistability property of the individual SQUIDs around their resonance frequency and the attractor crowding effect in systems of coupled non-linear oscillators. Interestingly, controlled generation of chimera states in SQUID metamaterials can be achieved in the presence of a constant (dc) flux gradient with the SQUID metamaterial initially at rest.

AB - Planar and linear arrays of SQUIDs (superconducting quantum interference devices) operate as non-linear magnetic metamaterials in microwaves. Such SQUID metamaterials are paradigmatic systems that serve as a test-bed for simulating several non-linear dynamics phenomena. SQUIDs are highly non-linear oscillators which are coupled together through magnetic dipole-dipole forces due to their mutual inductance; that coupling falls-off approximately as the inverse cube of their distance, i.e., it is non-local. However, it can be approximated by a local (nearest-neighbor) coupling which in many cases suffices for capturing the essentials of the dynamics of SQUID metamaterials. For either type of coupling, it is numerically demonstrated that chimera states as well as other spatially non-uniform states can be generated in SQUID metamaterials under time-dependent applied magnetic flux for appropriately chosen initial conditions. The mechanism for the emergence of these states is discussed in terms of the multistability property of the individual SQUIDs around their resonance frequency and the attractor crowding effect in systems of coupled non-linear oscillators. Interestingly, controlled generation of chimera states in SQUID metamaterials can be achieved in the presence of a constant (dc) flux gradient with the SQUID metamaterial initially at rest.

KW - SQUID

KW - SQUID metamaterials

KW - attractor crowding

KW - chimera states

KW - coupled non-linear oscillators

KW - magnetic metamaterials

KW - snaking resonance curve

KW - synchronization-desynchronization transition

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U2 - 10.3389/fams.2019.00033

DO - 10.3389/fams.2019.00033

M3 - Article

AN - SCOPUS:85072026406

VL - 5

JO - Frontiers in Applied Mathematics and Statistics

JF - Frontiers in Applied Mathematics and Statistics

SN - 2297-4687

M1 - 33

ER -