Figure 1

(a) The dependencies of the four largest Lyapunov exponents on the coupling strength $\varepsilon$ for (8). (b) The quantitative measure $d$ (7) vs the coupling parameter strength $\varepsilon$. The critical values of the coupling parameter ${\varepsilon }_{\mathrm{LE}}=0.106$ and ${\varepsilon }_{\mathrm{LS}}=0.169$ are marked by arrows. (c–j) The phase portraits of Rössler oscillators for the different values of the coupling parameter: (c–d) $\varepsilon =0.01$ (the asynchronous state); (e–f) $\varepsilon =0.05$ (the PS regime); (g–h) $\varepsilon =0.12$ (the GS regime); (i–j) $\varepsilon =0.18$ (the LS regime). Figures 1c, (e), (g), and (i) show the chaotic attractor of the first system $\mathbf{x}\left(t\right)$ with three randomly chosen points ${\mathbf{x}}^k$ and its nearest neighbors ${\mathbf{x}}^{kn}$. Panels (d), (f), (h), and (j) illustrate the corresponding states ${\mathbf{u}}^{k,kn}$ in the phase subspace of the second system $\mathbf{u}\left(t\right)$. (k) The dependence of the mean distance $\Delta$ between shifted states of the interacted systems (8).Reuse & Permissions

Figure 2

(a) The dependencies of the four largest Lyapunov exponents on the coupling strength $\varepsilon$ for (9). (b) The quantitative measure $d$ (7) versus the coupling parameter strength $\varepsilon$. The critical value of the coupling parameter ${\varepsilon }_{\mathrm{LE}}=0.078$ corresponding to the zero-cross of the positive Lyapunov exponent is marked by arrow. (c)–(h) The reconstructed attractors of two mutually coupled Pierce diodes on $({\rho }_{1,2}(x=0.2,t),{\rho }_{1,2}(x=0.6,t))$ plane for the different values of the coupling parameter: (c, d) $\varepsilon =0.002$ (the asynchronous state), (e, f) $\varepsilon =0.05$ (the PS regime), (g, h) $\varepsilon =0.10$ (the GS regime). Figures (c, e, g) show the reconstructed attractor of the first Pierce diode with three randomly chosen points and its nearest neighbors. Figures (d, f, h) illustrate the corresponding states in the phase subspace of the second Pierce diode.Reuse & Permissions

Figure 3

The dependencies of the four largest Lyapunov exponents on the coupling strength $\varepsilon$.Reuse & Permissions

Figure 4

The phase portraits of two mutually coupled Lorenz oscillators (13) for $\varepsilon =5.7$ (a, b) and $\varepsilon =6.1$ (c, d). Figures (a, c) show the chaotic attractor of the first system $\mathbf{x}\left(t\right)$ with the reference point ${\mathbf{x}}^k$ and its nearest neighbors ${\mathbf{x}}^{kn}$. Panels b and d illustrate the corresponding to them states ${\mathbf{u}}^{k,kn}$ in the phase space of the second system $\mathbf{u}\left(t\right)$.Reuse & Permissions

Figure 5

(a) The fragment of the time series of two mutually coupled Lorenz oscillators (13) corresponding to the short-term period of the phase trajectory divergence. (b) The phase portraits of Lorenz systems and the phase trajectories corresponding to the time interval shown in panel a. The coupling strength $\varepsilon =5.7$, the GS regime is not observed.Reuse & Permissions

Figure 6

(a) The fragment of the time series of two mutually coupled Lorenz oscillators (13) corresponding to the short-term period of the phase trajectory divergence. (b) The phase portraits of Lorenz systems and the phase trajectories corresponding to the time interval shown in panel a. The coupling strength $\varepsilon =6.1$, the GS regime is detected.Reuse & Permissions

Figure 7

The dependencies of the seven largest Lyapunov exponents on the coupling strength $\varepsilon$ for the network consisting of five Rössler systems (15). The onset of the GS regime in the network ${\varepsilon }_{\mathrm{LE}}$ is shown by the arrow.Reuse & Permissions

Figure 8

The phase portraits of five Rössler oscillators for two different values of the coupling parameter: (a) $\varepsilon =0.03$ (the PS regime) and (b) $\varepsilon =0.04$ (the GS regime).Reuse & Permissions

Figure 9

$\langle E\rangle$ vs $\varepsilon$ for the network of Rössler oscillators (15). The onset of the GS regime in the network ${\varepsilon }_{\mathrm{LE}}$ is shown by the arrow.Reuse & Permissions

Figure 10

Boundaries of the GS regime on the “number of elements $N$-coupling parameter $\varepsilon$” plane for random (curve 1), regular (curve 2), and “small world” (curve 3) networks.Reuse & Permissions