zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Multi-stability and almost periodic solutions of a class of recurrent neural networks. (English) Zbl 1136.34311

The paper studies a class of reccurent neural networks described by the equations

x ˙ i (t)=-a i x i (t)+ j=1 n w ij f(x j (t))+c i ,f(x)(-1,1)i=1,,n·

Using Lyapunov functions, a sufficient condition for the complete stability is obtained. On this base applying the Mawhin coincidence degree theory, many sufficient conditions guaranteeing the existence of at least one almost periodic solution are obtained. These conditions are derived for an arbitrary activation function f. Few simulations done by Matlab illustrate that the simulation results fit well the theoretic analysis.

34C27Almost and pseudo-almost periodic solutions of ODE
34D20Stability of ODE
92B20General theory of neural networks (mathematical biology)