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Germes de difféomorphismes et de champs de vecteurs en classe de différentiabilité finie

F. Dumortier, Robert Roussarie (1983)

Annales de l'institut Fourier

Pour tout triplet d’entiers s , k , ℓ tels que 0 ≤ s ≤ k ≤ ℓ , se pose la question d’étudier les germes de difféomorphismes ou de champs de vecteurs sur R n , de classe ℓ , k -déterminés en classe s , c’est-à-dire respectivement conjugués ou équivalents en classe s , à tout germe ayant la même classe ℓ et le même k -jet. Cette question est abordée ici, avec quelque généralité en dimension 2 et pour les germes de champs de vecteurs de codimension 2, en dimension 3 et 4. Une conséquence de cette dernière étude est l’existence...

Global bifurcations in a dynamical model of recurrent neural networks

Anita Windisch, Péter L. Simon (2023)

Applications of Mathematics

The dynamical behaviour of a continuous time recurrent neural network model with a special weight matrix is studied. The network contains several identical excitatory neurons and a single inhibitory one. This special construction enables us to reduce the dimension of the system and then fully characterize the local and global codimension-one bifurcations. It is shown that besides saddle-node and Andronov-Hopf bifurcations, homoclinic and cycle fold bifurcations may occur. These bifurcation curves...

Global exponential stability of positive periodic solutions for an epidemic model with saturated treatment

Bingwen Liu (2016)

Annales Polonici Mathematici

This paper is concerned with an SIR model with periodic incidence rate and saturated treatment function. Under proper conditions, we employ a novel argument to establish a criterion on the global exponential stability of positive periodic solutions for this model. The result obtained improves and supplements existing ones. We also use numerical simulations to illustrate our theoretical results.

Global exponential stability of pseudo almost automorphic solutions for delayed Cohen-Grosberg neural networks with measure

Chaouki Aouiti, Hediene Jallouli, Mohsen Miraoui (2022)

Applications of Mathematics

We investigate the Cohen-Grosberg differential equations with mixed delays and time-varying coefficient: Several useful results on the functional space of such functions like completeness and composition theorems are established. By using the fixed-point theorem and some properties of the doubly measure pseudo almost automorphic functions, a set of sufficient criteria are established to ensure the existence, uniqueness and global exponential stability of a ( μ , ν ) -pseudo almost automorphic solution. The...

Global monotonicity and oscillation for second order differential equation

Miroslav Bartušek, Mariella Cecchi, Zuzana Došlá, Mauro Marini (2005)

Czechoslovak Mathematical Journal

Oscillatory properties of the second order nonlinear equation ( r ( t ) x ' ) ' + q ( t ) f ( x ) = 0 are investigated. In particular, criteria for the existence of at least one oscillatory solution and for the global monotonicity properties of nonoscillatory solutions are established. The possible coexistence of oscillatory and nonoscillatory solutions is studied too.

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