Chimera States for Coupled Oscillators

Predict R(x) and Θ(x) theoreticallyThe assumed evenness implies formulas for R(x) and Θ(x) that possess symmetryso R satisfies19To solve for a and c we first rewriteR 2 = (Re iΘ )(Re −iΘ ) (17)= (c + a cos(x))(c ∗ + a ∗ cos(x)) (18)= |c 2 | + 2Re(ca ∗ ) cos(x) + |a| 2 cos 2 (x) (19)he iΘ = (Re iΘ ) h R = ∆ − √ ∆ 2 − R 2 (x)c + a ∗ cos(x)(20)Making use of 15 we obtain/wc = e iβ 〈 ∆ − √ ∆ 2 − |c + a cos(x)| 2c + a ∗ cos(x)a = Ae iβ 〈 ∆ − √ ∆ 2 − |c + a cos(x)| 2c + a ∗ cos(x)〉 (21)cos(x) 〉 (22)