Spatiotemporal intermittency

Table 8.6 traces the evolution of the approximating CA rules as e increases from 0 to 1 for 2 < s < 3. We see that as e increases, only 7 of the 32 possible rules are actually visited. Nonetheless, even at this crude first order approximation, a remnant of the CML s transition to spatiotemporal intermittency remains. In particular, there is a threshold value of e, = 2 — 4/s, that acts as a boundary point below which the approximating CA-rule is simple-periodic (class 1 or 2) and above which it is complex (class 3 or 4). The surprising fact is not that the CML s transition appears to bo approximated by the CA-rule path - after all, allowing for finite-length computer words, the CML itself is essentially just a very-high order CA... 

H. Chate. Spatiotemporal intermittency regimes of the one-dimensional complex ginzburg-landau equation. Nonlinearity, 7 185— 204, 1994. 

If this were the only context in which CML models were used, their utility would be severely limited. For values y beyond the stability limit, the Euler method fails and one obtains solutions that fail to represent the solutions of the reaction-diffusion equation. However, it is precisely the rich pattern formation observed in CML models beyond the stability limit that has attracted researchers to study these models in great detail. Coupled map models show spatiotemporal intermittency, chaos, clustering, and a wide range of pattern formation processes." Many of these complicated phenomena can be studied in detail using CML models because of their simplicity and, if there are generic aspects to the phenomena, for example, certain scaling properties, then these could be carried over to real systems in other parameter regimes. The CML models have been used to study chemical pattern formation in bistable, excitable, and oscillatory media." ... 

---