Ott-Antonsen Chimera Ansatz
Exact mean-field reduction of nonlocally coupled Kuramoto oscillators
The Ott-Antonsen (OA) ansatz provides an exact dimensional reduction of the thermodynamic Kuramoto model: by assuming the phase distribution is Poisson (characterized by a single complex order parameter Z(x,t) = R e^{iΨ}), the infinite-dimensional dynamics collapse to ∂Z/∂t = −iZ · κ∫G(x−x′)[Z* Z(x′)e^{iα} − Z e^{−iα}]/2 dx′. Chimera states appear as stable inhomogeneous solutions with R(x)≈1 in coherent regions and 0<R<1 in incoherent ones. Adjust α near π/2 to find the chimera window.