Experimental observation of ragged synchronizability

Synchronization thresholds of an array of nondiagonally coupled oscillators are investigated. We present experimental results which show the existence of ragged synchronizability, i.e., the existence of multiple disconnected synchronization regions in the coupling parameter space. This phenomenon has been observed in an electronic implementation of an array of nondiagonally coupled van der Pol’s oscillators. Numerical simulations show good agreement with the experimental observations.

Figure 1

The model of an open array of van der Pol’s oscillators (VdPO).

Figure 2

An electronic implementation of an open array of VdP oscillators shown in Fig. 1.

Figure 3

The largest transversal Lyapunov exponent ${\lambda }_T$, calculated for generic variational equation (7), versus product $\sigma \gamma$; $\eta =1.207$, $d=0.401$.

Figure 4

Comparison of numerical and experimental results, $d=0.401$, $\eta =1.207$; (a)–(c) desynchronizing mechanism: A projection from the MSF diagram (a), via eigenvalues ${\gamma }_k$ of connectivity matrix $\mathbf{G}$ (b), to the bifurcation diagram of synchronization error $e$ versus coupling coefficient $\sigma$ (c) (desynchronous intervals are shown in gray, complete synchronization takes place in $\sigma$ ranges where $e$ approaches zero value), (d) synchronization error $e$ versus $\sigma$; experimental results, gray line with scatters (marking measurement points), numerical results for the case of parameter mismatch; black line, the values of $d$ taken in Eqs. (2b, 2d, 2f) are, respectively, 0.400, 0.401, and 0.402.