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A similar system of two asymmetrically interacting populations with a particular form of coupling matrix K was considered in PLEEE8 1063-651X 10.1103/PhysRevE.70.056125
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A similar system of two asymmetrically interacting populations with a particular form of coupling matrix K was considered in E. Montbrio, J. Kurths, and B. Blasius, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.056125 70, 056125 (2004). The formulation in the current paper is more general in two important aspects: K is arbitrary, and we allow for any number of interacting populations.
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Our system is similar to that studied in CHAOEH 1054-1500 10.1063/1.2148388
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Our system is similar to that studied in J. G. Restrepo, E. Ott, and B. R. Hunt, Chaos CHAOEH 1054-1500 10.1063/1.2148388 16, 015107 (2006). However, our formulation permits different natural frequency distributions for each population.
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The bracketed expression is valid for Re (s) >0 and may be analytically continued into the region where Re (s) ≤0. See PDNPDT 0167-2789 10.1016/S0167-2789(02)00663-2
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The bracketed expression is valid for Re (s) >0 and may be analytically continued into the region where Re (s) ≤0. See E. Ott, P. So, E. Barreto, and T. Antonsen, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(02) 00663-2 173, 29 (2002)
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Many interesting states require ασ σ′ 0, such as the chimera state observed in IJBEE4 0218-1274
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Many interesting states require ασ σ′ 0, such as the chimera state observed in D. M. Abrams and S.H. Strogatz, Int. J. Bifurcation Chaos Appl. Sci. Eng. IJBEE4 0218-1274 16, 21 (2006).
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Simulations used fourth-order Runge-Kutta with a time step of 0.01 s, N=10000 or 50000, and parameters as noted. The system was initialized in the incoherent state and an initial transient was discarded. The order parameters were then averaged over the subsequent 10 s. Because the standard deviations over this interval were small, no error bars were plotted.
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Simulations used fourth-order Runge-Kutta with a time step of 0.01 s, N=10000 or 50000, and parameters as noted. The system was initialized in the incoherent state and an initial transient was discarded. The order parameters were then averaged over the subsequent 10 s. Because the standard deviations over this interval were small, no error bars were plotted.
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MATLAB®, The MathWorks, Inc., Natick, MA
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MATLAB®, The MathWorks, Inc., Natick, MA, http://www.mathworks.com
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