Feedback nonlinear negative

The nonlinearity of (11.8) comes from the terms 4>(z°(t)) and y (r) 2 (r) involved in the nonlinear negative feedback regulation. What we want to do is replace these nonlinear terms by a linear function in the vicinity of the equilibrium state (x, y, z ). This involves writing the Jacobian matrix of the linearized system (cf. Appendix A) ... 

Hunding, A. 1974. Limit cycles in enzyme systems with nonlinear negative feedback. Biophys. Struct. Meehan. 1 47-54. 

To simulate the disease episodes and subthreshold oscillations we again refer to our neuronal modeling approaches (Fig. 7.2b). The algorithms have been implemented with a simple but physiologically plausible approach, i.e. with two nonlinear feedback loops, one positive and one negative. Depending on the parameter setting, such a system can attain stable dynamics but also can develop oscillations. 

The feedback mechanisms are mediated via mineralocorticoid and glucocorticoid receptors (MR, GR), which means overlapping of nonlinear positive and negative feedback loops with nonlinear dependencies on cortisol (Michaelis-Menten kinetics, sigmoidal activation curves of corticoid receptors). 

In most electrochemical systems displaying nonlinear phenomena, the electrode potential is an essential variable, that is, it participates in one of the above-mentioned feedback loops.1 In the overwhelming number of cases it takes on the role of the activator variable, but occasionally it also acts as the negative feedback variable. Depending on the mechanistic role of the electrode potential, the instabilities that prevail the dynamic properties in these two classes of systems are fundamentally different. 

Concepts developed in nonlinear dynamics facilitated the classification of nonlinear phenomena in electrochemical systems and revealed the origins of the diversity of temporal and spatial patterns in electrochemical systems. The diversity results on the one hand from the fact that the electrode potential might act as a positive or as a negative feedback variable. On the other hand, it is a consequence of the different kinds of spatial coupling present in an electrochemical cell and of the unique property that the extent of the spatial couplings is influenced by parameters that can be easily manipulated in an experiment. 

Cortisol concentration is described by a nonlinear time-delay differential equation [47,519] with two terms, i.e., a secretion rate term that adheres to the negative feedback mechanism [520, 521] and drives the pulsatile secretion, and a first-order output term with rate constant ka ... 

Are these phenomena unique, or are they typical of biological systems From a mathematical perspective, enzyme systems fall into a class of nonlinear organization, and a chain of enzyme reactions with negative feedback easily can demonstrate oscillatory behavior [520]. Glass has noted that in general, any nonlinear system with multiple negative feedback may demonstrate oscillations that lead to chaotic behavior [595]. 

On the basis of the rate equations, differential equations can be set up. Due to the adsorption/chemisorption and feedback steps the solution of this set of differential equations is periodic or chaotic. Usually the occurrence of adsorption/chemisorption leads to nonlinearity and negative impedance. 

Another proving ground for mathematical modeling in cell signaling has been the dynamics of intracellular calcium. Spurred by the nonlinear nature of the calcium release mechanisms, which exhibit cooperativity and both positive and negative feedbacks, and by the availability of fluorescent dyes for... 

Model topology, that is, the interconnections between various components in the model as a whole, and the kinetic parameters associated with each connection determine the dynamies of the model. Interactions between components in the model can be either stimulatory or inhibitory. Series of interactions arranged in the form of loops can function as either positive or negative feedback. These feedback loops, depending on the parameter values, can display nonlinear dynamic behaviors such as oscillation and bistability (Bhalla etal., 2002 Hoffmann etal., 2002). These various features ean in turn modulate the response of the system to input signals, making complex dose responses such as switchlike or nonmonotonic ones possible. 

System behavior in system dynamics is modeled by using feedback (causal) loops, stock and flows (levels and rates), and the nonlinearities created by interactions between system components. In this view of the world, behavior over time (the dynamics of the system) can be explained by the interaction of positive and negative feedback loops [185]. The models are constructed from three basic building blocks ... 

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