Chimera States for Coupled Oscillators

Predict R(x) and Θ(x) theoretically12The spatial profiles on the previous slide were determined practically.Theoretical determining R(x) and Θ(x) can be done in two ways.First method in determining R(x) and Θ(x)Determine solutions depending on depend on R(x) and Θ(x) of 7R(x, t) exp[iΘ(x, t)] =Substitute these solutions in 8∂θ(x, t)∂t∫ π−πG(x ′ − x) exp[iθ(x ′ , t)]dx ′ (7)= ω − Ω − R(x, t) sin(θ(x, t) + α + Θ(x, t)) (8)Which will lead to an equation for determining R(x) and Θ(x)./w