Search results for "BIF"

Bifurcations and Histeresis of Low Prandtl Number Free Convection in Square Enclosures with Internal Heat Generation

2003

Experimental study of Morris-Lecar neuron : design, coupling and interpretation

2015

We present in this manuscript an experimental electronic neuron based on complete Morris-Lecar model without simplifications, able to become an experimental unit tool to study collective association of robust coupled neurons. The circuit design is given in details according to the ionic currents of this model. The experimental results are compared with the theoretical prediction, leading to a good agreement between them, which therefore validates the circuit. We present the different areas according to the bifurcation control parameters, the membrane capacitance and the excitation current. We have highlighted the behavior of the neuron for each parameters zone. A coupling of such neurons is…

Heterocycles from α-aminonitriles.

2014

Owing to their various modes of reactivity, α-aminonitriles represent versatile building blocks for the construction of a wide range of nitrogen heterocycles. The present Concept article focuses on synthetic methodologies using their bifunctional nature which is the basis of their reactivity as α-amino carbanions and as iminium ions. Reactions exclusively taking place on either the amine or on the nitrile moiety will not be considered.

Global attractors from the explosion of singular cycles

1997

Abstract In this paper we announce recent results on the existence and bifurcations of hyperbolic systems leading to non-hyperbolic global attractors.

Spiking patterns emerging from wave instabilities in a one-dimensional neural lattice.

2003

The dynamics of a one-dimensional lattice (chain) of electrically coupled neurons modeled by the FitzHugh-Nagumo excitable system with modified nonlinearity is investigated. We have found that for certain conditions the lattice exhibits a countable set of pulselike wave solutions. The analysis of homoclinic and heteroclinic bifurcations is given. Corresponding bifurcation sets have the shapes of spirals twisting to the same center. The appearance of chaotic spiking patterns emerging from wave instabilities is discussed.

Efficient computation of stable bifurcating branches of nonlinear eigenvalue problems

1983

Ober Ein Rayleigh-Ritz-Verfahren zur Bestimmung Kritischer Werte

1980

This paper is concerned with the existence of critical points for a functional f defined on the level set of a second functional g. Existence of nontrivial solutions for the nonlinear eigenvalue-problem f′(u) = λg′(u) and convergence for a nonlinear analogue to the Rayleigh-Ritz-Method is proven. The results are applied to a nonlinear ordinary eigenvalue problem where it is shown that the lowest point in the continuous spectrum of the associated linearized operator is a bifurcation point of infinite multiplicity.

Kleine periodische L�sungen bei nichtlinearen stark-elliptischen Systemen von partiellen Differentialgleichungen I

1971

Strongly elliptic systems of nonlinear partial differential equations are considered in the case when the derivatives of the solutions occuring in the nonlinear terms have the same order as those in the linear principal part. The existence of periodic solutions for such systems is investigated. It is shown that this problem can be reduced to the study of algebraic bifurcation equations, whose small solutions correspond to the classical solutions of the given problem. A discussion of the bifurcation equations will be given in a forthcoming paper.

Instability and bistability during the growth of a corrosion scale on metals and alloys

1986

This paper summarizes the main results for the interpretation of the self organized corrosion scales observed in oxidation or sulfidation of some metals or alloys. It consists also of a reconsideration of the classical theoretical concepts used in Reactivity of Solids. It proposes new theoretical tools that have been fruitfully utilized in other topics : non linear and coupled processes, stability analysis and bifurcation theory. Some examples are developed, where the corrosion kinetics at high temperature are interpreted in term of chemical bistable system able to oscillate spontaneously and mechanochemical couplings are also taken into account. In according with experimental results, all …

A Singular Multi-Grid Iteration Method for Bifurcation Problems

1984

We propose an efficient technique for the numerical computation of bifurcating branches of solutions of large sparse systems of nonlinear, parameter-dependent equations. The algorithm consists of a nested iteration procedure employing a multi-grid method for singular problems. The basic iteration scheme is related to the Lyapounov-Schmidt method and is widely used for proving the existence of bifurcating solutions. We present numerical examples which confirm the efficiency of the algorithm.