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Stability in contractive nonlinear neural networks
IEEE Transactions on Biomedical Engineering, 1990We consider models of the form mu chi = -x + p + WF(x) where x = x(t) is a vector whose entries represent the electrical activities in the units of a neural network. W is a matrix of synaptic weights, F is a nonlinear function, and p is a vector (constant or slowly varying over time) of inputs to the units.
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Nonlinear Contracts, Zero Profits and Moral Hazard
Economica, 1987Contracts that base payments on an ex post variable are examined. It is shown that a quadratic contract form may elicit truthful responses from auction participants and offer zero expected profits to the winning bidder, but not eliminate adverse incentives ex post. A general impossibility theorem is proven.
Fishe, Raymond P H, McAfee, R Preston
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Nonlinear AIMD Congestion Control and Contraction Mappings
SIAM Journal on Control and Optimization, 2006This papers analyzes a class of nonlinear additive-increase multiplicative-decrease (AIMD) protocols that are widely deployed in communication networks. It is demonstrated that the use of these protocols guarantees that the system has a unique stable outcome to which it converges geometrically under all starting points.
Uriel G. Rothblum, Robert Shorten
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On nonlinear quasi-contractions
2008Lj. Ciric [2] first introduced the notion of quasi - contractions and proved the fixed point theorem for this class of mappings. Ciri'c's result was extended to nonlinear quasi - contractions by A. A. Ivanov [4]. In this paper we present new generalizations of Ivanov's fixed point theorem.
Aranđelović, Ivan +2 more
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Contraction mappings for nonlinear boundary value problems
Computing, 1968This paper treats mildly nonlinear boundary value problems of the form $$\begin{gathered} y'' (t) + p (t) y'(t) + f(t,y (t)) = 0 \hfill \\ y(\alpha ) = A, y(b) = B \hfill \\ \end{gathered} $$ byPicard-like methods.A priori bounds on a solution are used to ...
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Contraction theory for nonlinear stability analysis and learning-based control: A tutorial overview
Annual Reviews in Control, 2021Hiroyasu Tsukamoto +2 more
exaly
On the nonlinear contractions in Fréchet \(L\)-spaces
1986Summary: In the paper a fixed point theorem in \(L\)-spaces of Fréchet type is contained. The theorem is a generalization of some new results of \textit{S. Kasahara} [Math. Semin. Notes, Kobe Univ. 5, No. 1, 29--35 (1977; Zbl 0359.54039)] and \textit{A. F. Monna} [Indag. Math. 23, 89--96 (1961; Zbl 0097.15901)].
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