Global spatiotemporal order and induced stochastic resonance due to a locally applied signal

We study the phenomenon of spatiotemporal stochastic resonance (STSR) in a chain of diffusively coupled bistable oscillators. In particular, we examine the situation in which the global STSR response is controlled by a locally applied signal and reveal a wave-front propagation. In order to deepen the understanding of the system dynamics, we introduce, on the time scale of STSR, the study of the effective statistical renormalization of a generic lattice system. Using this technique we provide a criterion for STSR, and predict and observe numerically a bifurcationlike behavior that reflects the difference between the most probable value of the local quasiequilibrium density and its mean value. Our results, tested with a chain of nonlinear oscillators, appear to possess some universal qualities and may stimulate a deeper search for more generic phenomena.

Figure 1

Locally induced global spatiotemporal pattern in the chain of bistable oscillators; parameters are specified in Fig. 2.

Figure 2

(a) Dynamics of the collective variables $Y$ (solid) and $Y^{\prime }$ (dash) with parameters $N=300$, $M=50$, $k=125$, $K=15$, $D=0.1$, and $m=0.25$; (b) fine structure of the transition region in (a) reveals a wave-front propagation.

Figure 3

Spatially homogeneous steady states $\overline{y}\ne 0$ as points of intersection of a characteristic surface $\overline{y}=\overline{y}(D,K)$ and two coordinate planes of the control parameters ($D=0.1$ and $K=15$ are marked). Instead of the two original steady states $\pm 0.5$ there are now four for specific values of $D$ and $K$, and zero otherwise.

Figure 4

Three output signals (collective variable $Y$, $N=M=500$) with (a) $D=0.5$; (b) $D=0.24$; and (c) $D=0.1$; correspondingly, above, near, and below the characteristic surface $\overline{y}=\overline{y}(D,K)$ at $K=15$ (see Fig. 3); effective stable steady states: (a) $0$ and (c) $\pm 0.43$. The difference appears to be not only quantitative but also, more importantly, qualitative.