Global feedback

V.K. Vanag, L.F. Yang, M. Dolnik, A.M. Zhabotinsky, and l.R. Epstein. Oscillatory cluster patterns in a homogeneous chemical system with global feedback. Nature, 406(6794) 389-391, 2000. 

V. Zykov and H. Engel. Dynamics of spiral waves under global feedback in excitable domains of different shapes. Phys. Rev. E, 70 1-9, 2004. 

The above analysis shows that front propagation reversal occurs near any n 1 resonance. For ji = I, stationary kinks (i.e., 27r-froiits) and periodic sequences of standing kinks are possible (the existence of stationary solitary kinks under global feedback conditions has previously been shown [15]). For 71 = 1, stationary tt-fronts represent standing Bloch walls or their periodic secjuences. Such standing structures are oscillation amplitude does not vanish here. 

In this respect, feedback-mediated parametric modulation seems to be a more promising control strategy, since in this case the modulation period always coincides exactly with the actual rotation period of the spiral wave [20, 21]. Another important motivation to study feedback-mediated dynamics of spiral waves is related to the fact that a feedback is either naturally present or can be easily implemented in many excitable media [22-25]. For example, recent experimental investigations performed with the BZ medium [26, 27] and during the catalytic CO oxidation on platinum single crystal surfaces [28] reveal that global feedback can provide an efficient tool for the control of pattern formation. 

An increase in the radius of the integration domain S from zero to the radius of the gel layer describes the transition from one-point to global feedback control [48-50]. As this transition preserves the rotational symmetry existing for one-point control, one can expect that the drift direction for global feedback within a circular domain should be defined by an expression similar to Eq. (9.47). Indeed, it was shown [47, 50] that Eq. (9.47) has to be generalized and reads... 

In contrast to one-point feedback, under global feedback control phase c(> z, Rfi) and amplitude A( a ) of the first Fourier component in the feedback signal are nonlinear functions of z. An example of these functions obtained numerically for = 1.5A is plotted in Fig. 9.12(a). 

Fig. 9.13. (a) Drift velocity field obtained for global feedback in an elliptical domain... 

The theoretically predicted destruction of the resonance attractor in response to deviations from the circular shape of the integration domain has been confirmed experimentally within the light-sensitive BZ medium. A spiral wave was exposed to uniform illumination proportional to the total gray level obtained in an elliptical integration domain. Fig. 9.13(b) shows the resonant drift mediated during global feedback control. The spiral wave drifts towards a stable node of the drift velocity field. Close to this fixed point the drift velocity becomes very slow. Thus, the experimentally observed termination of the spiral drift at certain positions in a uniform medium is explained in the framework of the developed theory of feedback-mediated resonant drift. 

For some combinations of space-time assignment parameters, no localization can be found. It is best to detect this situation during the assignment phase instead of in a global feedback loop. 

Chemical systems with complex kinetics exhibit a fascinating range of dynamical phenomena. These include periodic and aperiodic (chaotic) temporal oscillation as well as spatial patterns and waves. Many of these phenomena mimic similar behavior in living systems. With the addition of global feedback in an unstirred medium, the prototype chemical oscillator, the Belousov-Zhabotinsky reaction, gives rise to clusters, i.e., spatial domains that oscillate in phase, but out of phase with other domains in the system. Clusters are also thought to arise in systems of coupled neurons. 

It should be noted that the example is shown for combination logic only. Sequential logic becomes more difficult as initiahzation, iUegal states, state machines, global feedback, and many other cases must be accounted for in the generation of BIST design and patterns. 

Because global feedback was just as effective as specific feedback when social comparison feedback was included, we presumed most of the 97 employees of the soft-drink bottling facility did not need an instructional intervention. They knew how to perform their jobs safely but needed some extrinsic motivation to follow the nine safety policies implied by the nine target behaviors. This was provided by a global percent safe score from a similar work group. 

Experimentally, there was a very narrow but finite range of parameters in which stationary fronts were observed [106]. In this case this is not due to a global feedback mechanism rather, most likely small inhomogeneities of the surface cause the fronts to stop [102]. 

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