Coherence resonance control via nonlocal coupling in an ensemble of non-excitable oscillators

Abstract

Nonlocal interaction is shown to be an appropriate tool for controlling coherence resonance in ensembles of non-excitable oscillators. The constructive role of nonlocal coupling is demonstrated through numerical simulations on an example of coupled generalized Van der Pol oscillators close to the saddle-node bifurcation of limit cycles. In particular, increasing the coupling radius is found to enhance coherence resonance, which manifests itself in the evolution of power spectra and dependencies of the correlation time on the noise intensity. Nonlocal coupling is interpreted as an intermediate topology between local and global coupling, both of which are also examined as mechanisms for controlling coherence resonance.

Figures (4)

• Figure 1: Schematically illustrated bifurcation diagram of the coupling- and noise-free oscillators (see Eqs.(\ref{['eq:general']}) at $D=0$ and $f_i(x_1,x_2,...,x_N)\equiv 0$). The black dashed lines SN and AH indicate the saddle-node and subcritical Andronov-Hopf bifurcation, correspondingly. The red dashed line corresponds to the parameter set considered in the current paper ($\varepsilon=-0.04$, $\mu=0.5$). For more detailed description of the bifurcation analysis results, see Ref. semenov2015.
• Figure 2: Suppression of coherence resonance in ensemble (\ref{['eq:general']}) due to the action of local coupling defined by Eqs. (\ref{['eq:nonlocal_coupling']}) at $R=1$: (a)-(b) Space-time plots illustrating the stochastic dynamics as the coupling strength increases at fixed $D=0.002$; (c) Evolution of dependencies of the averaged correlation time on the noise intensity, as the coupling strength increases; (d) Transformation of the averaged power spectrum of oscillations $x_i(t)$ at fixed noise intensity, $D=0.002$ (corresponds to the vertical dashed line in panel (c)), and increasing coupling strength. The oscillators' parameters are $\varepsilon=-0.04$, $\mu=0.5$, $\omega_0=1$.
• Figure 3: Global-coupling-induced suppression of coherence resonance (see ensemble (\ref{['eq:general']}) with coupling terms (\ref{['eq:global_coupling']})): (a)-(b) Space-time plots illustrating the stochastic dynamics as the coupling strength increases at fixed $D=0.002$; (c) Evolution of dependencies of the averaged correlation time on the noise intensity, as the coupling strength increases; (d) Transformation of the averaged power spectrum of oscillations $x_i(t)$ at fixed noise intensity, $D=0.002$ (corresponds to the vertical dashed line in panel (c)), and increasing coupling strength. The oscillators' parameters are $\varepsilon=-0.04$, $\mu=0.5$, $\omega_0=1$.
• Figure 4: Enhancement of coherence resonance when increasing the coupling radius in model (\ref{['eq:general']}) with nonlocal coupling (\ref{['eq:nonlocal_coupling']}). The evolution of the dependencies of the averaged correlation time on the noise intensity (panels (a) and (b)) and the power spectrum transformation at $D=0.002$ (panels (c) and (d)) are used to visualise the coherence resonance control at $\sigma=0.1$ (panels (a) and (c)) and $\sigma=1$ (panels (b) and (d)). The oscillators' parameters are $\varepsilon=-0.04$, $\mu=0.5$, $\omega_0=1$.