Figure 2
Ten coupled genetic oscillators. The parameter values in (1), (2), and (3) are set as follows: α a  = α b  = α c  = 216, α S  = 20, μ = 1.2, μ S  = 1, n = 2, γ S  = 1, η S  = 2, β S  = 0.1, β A  = β B  = β C  = 1, γ m  = 6.9315, γ p  = 1.1552 and Q e  = 0.09 [1]. Suppose the nonlinear stochastic coupled synthetic oscillators suffer from stochastic parameter fluctuations as shown in (8) with Δα a  = Δα b  = Δα c  = 2.16, Δα S  = 0.2, Δβ A  = Δβ B  = Δβ C  = 0.01, Δβ S  = 0.001, Δη S  = 0.02, Δγ m  = 0.06, Δγ p  = 0.01, and Δγ S  = 0.01. For the convenience of simulation, we assume that the extrinsic molecular noise v1~v10 is independent Gaussian white noise with a mean of zero and standard deviation of 0.02. It can be seen that coupled synthetic oscillators cannot achieve synchronization under these intrinsic kinetic parameter fluctuations and extrinsic molecular noise.