TY - JOUR
T1 - Transition from homogeneous to inhomogeneous steady states in oscillators under cyclic coupling
AU - Bera, Bidesh K.
AU - Hens, Chittaranjan
AU - Bhowmick, Sourav K.
AU - Pal, Pinaki
AU - Ghosh, Dibakar
N1 - Publisher Copyright:
© 2015 Elsevier B.V. All rights reserved.
PY - 2016/1/8
Y1 - 2016/1/8
N2 - We report a transition from homogeneous steady state to inhomogeneous steady state in coupled oscillators, both limit cycle and chaotic, under cyclic coupling and diffusive coupling as well when an asymmetry is introduced in terms of a negative parameter mismatch. Such a transition appears in limit cycle systems via pitchfork bifurcation as usual. Especially, when we focus on chaotic systems, the transition follows a transcritical bifurcation for cyclic coupling while it is a pitchfork bifurcation for the conventional diffusive coupling. We use the paradigmatic Van der Pol oscillator as the limit cycle system and a Sprott system as a chaotic system. We verified our results analytically for cyclic coupling and numerically check all results including diffusive coupling for both the limit cycle and chaotic systems.
AB - We report a transition from homogeneous steady state to inhomogeneous steady state in coupled oscillators, both limit cycle and chaotic, under cyclic coupling and diffusive coupling as well when an asymmetry is introduced in terms of a negative parameter mismatch. Such a transition appears in limit cycle systems via pitchfork bifurcation as usual. Especially, when we focus on chaotic systems, the transition follows a transcritical bifurcation for cyclic coupling while it is a pitchfork bifurcation for the conventional diffusive coupling. We use the paradigmatic Van der Pol oscillator as the limit cycle system and a Sprott system as a chaotic system. We verified our results analytically for cyclic coupling and numerically check all results including diffusive coupling for both the limit cycle and chaotic systems.
KW - Cyclic coupling
KW - Homogeneous steady state
KW - Inhomogeneous steady state
KW - Pitchfork bifurcation
KW - Transcritical bifurcation
UR - http://www.scopus.com/inward/record.url?scp=84946593847&partnerID=8YFLogxK
U2 - 10.1016/j.physleta.2015.09.044
DO - 10.1016/j.physleta.2015.09.044
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AN - SCOPUS:84946593847
SN - 0375-9601
VL - 380
SP - 130
EP - 134
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 1-2
ER -