1995
DOI: 10.1142/s0218339095000381
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Feedback Loops, Stability and Multistationarity in Dynamical Systems

Abstract: By fairly simple considerations of stability and multistationarity in nonlinear systems of first order differential equations it is shown that under quite mild restrictions a negative feedback loop is a necessary condition for stability, and that a positive feedback loop is a necessary condition for multistationarity.

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Cited by 135 publications
(101 citation statements)
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“…It is important to note here that a positive mechanical feedback loop ensured by the mechanical induction of twist is essential for this role, as positive feedback loops are associated with transitions towards new differentiation states, in contrast with negative feedback loops that tend to stabilize a given cellular state, i.e. homeostasis (Plahte et al, 1995).…”
Section: Physiological Function For Mechanical Induction Of Twist Durmentioning
confidence: 99%
“…It is important to note here that a positive mechanical feedback loop ensured by the mechanical induction of twist is essential for this role, as positive feedback loops are associated with transitions towards new differentiation states, in contrast with negative feedback loops that tend to stabilize a given cellular state, i.e. homeostasis (Plahte et al, 1995).…”
Section: Physiological Function For Mechanical Induction Of Twist Durmentioning
confidence: 99%
“…Since then, these conjectures have been proven in different frameworks [20,21,22,23,24,25,26,27,28,29]. As for intersecting circuits, we will argue here that beyond the impact that circuits have on the dynamical behaviour of a network, the interactions of circuits via their intersections also account significantly for certain dynamical properties of networks.…”
Section: Circuits and Intersecting Circuitsmentioning
confidence: 90%
“…The association of the DHAK genes with a PTS gene, and PTSdependent regulation of the operon strongly suggest that the DHAK operon belongs to the PTS regulon. to inactivation of ptsI has been observed repeatedly (5,6). Expression of the mannose operon, of which manX is the first cistron, of ptsI and of ptsG is repressed by Mlc, a transcriptional repressor of the PTS.…”
Section: Heterodimeric Dihydroxyacetone Kinase From a Ptsi Mutant Of mentioning
confidence: 99%
“…A positive feedback loop combined with a non-linear relationship is necessary for multistationarity, as first conjectured by biologists (9) and later demonstrated by mathematicians (5,6). It is significant that adaptation to environmental changes is often controlled by a regulator that in some instances positively regulates its own synthesis, in addition to controlling the expression of the genes of the regulons involved in this response.…”
Section: Is This Hypothesis Likely ?mentioning
confidence: 99%
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