Feedback loops descriptions

A final observation is in order the quantitative application of the equilibrium thermodynamical formalism to living systems and especially to ecosystems is generally inadequate since they are complex in their organisation, involving many interactions and feedback loops, several hierarchical levels may have to be considered, and the sources and types of energy involved can be multiple. Furthermore, they are out-of-equilibrium open flow systems and need to be maintained in such condition since equilibrium is death. Leaving aside very simple cases, in the present state of the art we are, therefore, limited to general semiquantitative statements or descriptions (e.g. ecosystem narratives ). 

LOGICAL DESCRIPTION, ANALYSIS, AND SYNTHESIS OF BIOLOGICAL AND OTHER NETWORKS COMPRISING FEEDBACK LOOPS... 

Most systems involve several interconnected feedback loops. Such systems cannot be analyzed seriously without a proper formalism, but their detailed description using differential equations is often too heavy. For these reasons we (as many others before) turned to a logical (or Boolean) description, that is, a description in which variables and functions can take only a limited number of values, typically two (1 and 0). Section II is an updated description of a logical method ( kinetic logic ) whose essential aspects were first presented by Thomas and Thomas and Van Ham.2 A less detailed version of this part can be found in Thomas.3 The present paper puts special emphasis on the fact that for each system the Boolean trajectories and final states can be obtained analytically (i.e.,... 

But real systems are usually not simple feedback loops. In a virus such as bacteriophage the decision to kill the infected bacterial cell or to establish a symbiotic association with it depends on complex interactions involving a number of interconnected feedback loops. Such systems (and even simpler ones) would need a formal description in view of their complexity but as a matter of fact this complexity is such that the classical methods are much too heavy. This was a reason for trying a logical description, that is, a description using variables and functions which can take only a limited number of values—typically two (1 and 0). 

The by far most widespread mechanism by which an N-NDR is hidden is the adsorption of a species that inhibits the main electron-transfer process. The species might be dissolved in the electrolyte, e.g., it might be the anion of the supporting electrolyte, or it is formed in a side reaction path, as it is the case in nearly all oxidation reactions of small organic molecules. Before we introduce specific examples of this type of HN-NDR oscillators, it is useful to study the dynamics of a prototype model. This will then help us to identify the essential mechanistic steps in real systems whose quantitative description requires more variables such that the basic feedback loops are not as obvious. 

Eq. (42) gives rise to a negative feedback loop if the current potential curve is S-shaped, but not for Z-shaped characteristics. Thus, in S-NDR systems DL may stabilize the middle branch of the S, or it may induce oscillations. This is not possible in Z-shaped systems, where an incorporation of DL in the dynamic description only increases the width of the bistable region but never results in qualitatively different behavior. For this reason, DL is not an essential variable in the latter type of systems. Thus, they have to be classified as systems with chemical instabilities only and will not be further treated here. 

A theoretical analysis of Eq. (13.6) provides the domains of control, i.e. the ranges of delay time and amplification in the feedback loop for which the control is effective. These results are in a good correspondence with the numerical simulation of the ensemble dynamics with different neuron models used for the description of individual units (Bonhoefer - van der Pol or Hindmarsh-Rose equations [21], Rulkov map model [42]). 

Under non-equilibrium conditions, some nonlinear phenomena such as oscillation, chaos and stationary pattern occur are a result of the loss of stability by the steady states, caused by the feedback loops in the processes determining the dynamics of such systems. Such self-organization can be obvious itself as a function of either only time coordinate including simultaneous oscillations of the entire system s state or only spatial coordinate including Turing stmctures or both coordinates including both traveling and chemical waves. The universal fact discovered of such phenomenon in different systems is remarkable in the context of mathematical description. 

Taken together, the accumulated evidence is that the WCC complex plays the role of the primary photoreceptor of the Neurospora circadian clock but is inextricably linked to the function of the clock. In light, the WCC upregulates FRQ, WC-1, and WD transcription, while FRQ feeds back to block the transcriptional activity of the WCC, thereby downregulating its own transcription. However, FRQ also promotes WC-1 synthesis, indirectly contributing to increased WCC levels, because WC-1 is the limiting partner of the pair. WD also acts to limit WCC complex activity. The interacting feedback loops of these complex interactions form the core of the clock. What remains to be added are the full temporal and spatial descriptions that sum to a 24 h cycle. 

Temperature sensors for providing closed-loop feedback for APFC are being developed by Stanford University for the measurement of combustion species and temperature. Laser-diode sensors offer nonintrusive measurements of the combustion exit plane temperature pattern. A detailed description of the sensor measurement methodology can be found in the literature [1, 2]. There is... 

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