Chimera States for Coupled Oscillators

Predict R(x) and Θ(x) theoreticallyh(R) from formula 11 can be made explicit, so we obtainWithR(x) exp[iΘ(x)] = e iβ ∫ πWhere ∆ = ω − Ω and β = π 2 − α−πG(|x ′ − x|) exp[iΘ(x ′ )]h(x ′ )dx ′ (12)h(x ′ ) = ∆ − √ ∆ 2 − R 2 (x ′ )R(x ′ )(13)17We take G(x) = 1 (1 + cos(x)) because2π1. The numerical curves suggests a cosine wave2. Equation 12 is solvable for any kernel of a finite Fourier form→ R(x) and Θ(x) can be obtained explicitly/w