When does noise destroy or enhance synchronous behavior in two mutually coupled light-controlled oscillators?

We study the influence of white Gaussian noise in a system of two mutually coupled light-controlled oscillators (LCOs). We show that under certain noise intensity conditions, noise can destroy or enhance synchronization. We build some Arnold tonguelike structures in order to explain the effects due to noise. It is remarkable that noise-enhanced synchronization is possible only when the variances of the noise acting on each of the LCOs are different.

Figure 1

Determining synchronization regions for two nonidentical noisy LCOs and different coupling strengths using as criterion [(a) and (i)] the LPD mean value and [(b) and (j)] the CPD variance as a function of the noise intensity. The LCOs’ noise variances are (a)–(h) ${\sigma }_1^2=0.0005$ and ${\sigma }_2^2=0.001$, and (i)–(p) ${\sigma }_1^2=0.003$ and ${\sigma }_2^2=0.0003$. For a determined coupling strength $\left(\beta =450\right)$, the corresponding LPD evolution and the CPD distribution are represented for different noise intensities: (c) and (f) $\sqrt{D}=0.20$, (d) and (g) $\sqrt{D}=0.65$, (e) and (h) $\sqrt{D}=1.00$, (k) and (n) $\sqrt{D}=1.15$, (l) and (o) $\sqrt{D}=1.80$, and (m) and (p) $\sqrt{D}=2.00$.

Figure 2

(Color online) Patches representing synchronization regions for different noise variances. (a) ${\sigma }_2^2\ge {\sigma }_1^2$, (b) ${\sigma }_2^2<{\sigma }_1^2$, with ${\sigma }_2^2=0.001$; (c) ${\sigma }_1^2\le {\sigma }_2^2$, (d) ${\sigma }_1^2>{\sigma }_2^2$, with ${\sigma }_1^2=0.003$.

Figure 3

(a) Synchronization regions for specific values of $\beta$ with ${\sigma }_1^2=0.003$ and ${\sigma }_2^2=0.0003$ and (b) its generalization in a surface. (c) Synchronization regions for different ${\text{LCO}}_2$ noise variances ${\sigma }_2^2$ with ${\sigma }_1^2=0.003$ and $\beta =166$ and (d) its generalization in a surface.

Figure 4

$⟨\text{LPD}⟩$ as a function of noise intensity $\sqrt{D}$ and the mean coupling frequency ratio $⟨{\Omega }_1/{\Omega }_2⟩$. The values for noise variances are ${\sigma }_1^2=0.003$ and ${\sigma }_2^2=0.0003$, and for the coupling strength $\beta =166$.

Figure 5

(Color online) Patches representing synchronization regions for different noise variances. (a) ${\sigma }_1^2=0.001$ and (b) ${\sigma }_1^2=0.003$.