Diversity-induced coherence resonance in spatially extended chaotic systems

The effect of parameter diversity on coupled Chua systems is investigated. In the absence of diversity, the systems jump back and forth between two variable domains of a chaotic attractor, and the residence times within a single domain are uncertain. By introducing parameter diversity, a combined numerical and analytical approach indicates that the systems can jump regularly from one domain to another at an intermediate range of diversity, a signature of coherence resonance. Furthermore, the influences of coupling strength and the number of units are also considered. Our results provide a possibility for the control of chaos in spatially extended chaotic systems by the manipulation of parameter diversity.

Figure 1

Spatiotemporal evolution of $x_i$ in $N=100$ coupled Chua systems with coupling strength $g=1.0$. The horizontal and vertical axes denote space and time, respectively. $\delta =\left(\text{a}\right)0$, (b) $0.08$, and (c) $0.15$.

Figure 2

Temporal evolution of variable $x$ and its representation by the step function $\Theta \left(t\right)$ in an uncoupled Chua system. The dashed line indicates the crossing levels.

Figure 3

Dependence of $R$ on the diversity $\delta$ in $N=100$ coupled Chua systems with coupling strength $g=1.0$. The inset depicts the dependence of the quota of units in the periodic windows on the diversity $\delta$.

Figure 4

(Color online) Dependence of $R$ on the diversity $\delta$ for different coupling strengths $g$ with $N=100$.

Figure 5

(Color online) Dependence of $R$ on the diversity $\delta$ for different numbers of units $N$ with $g=1.0$.

Figure 6

Bifurcation diagram of an uncoupled Chua system. Some periodic windows can be observed.

Figure 7

Bifurcation diagram of the reduced system Eq. (4). Poincaré section of the mean field $X_x$ and of the shape parameter $W_x$ with coupling strength $g=1.0$ (top) and $1.2$ (bottom).

Figure 8

Dependence of $R$ on the diversity $\delta$ for Chua systems when the parameter $\beta$ is selected for diversity with $g=1.0$ (solid squares), and for Lorenz systems with $g=6.0$ (hollow circles). The number of unit of the two systems is $N=100$.