zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
On a planar system modelling a neuron network with memory. (English) Zbl 0961.92002
In this paper delay differential equations modelling a network with two neurons are studied. Bifurcation analysis is made for situations without self-connections and two delays, and with self-connections and two delays. Some examples are given as well.

MSC:
92B20General theory of neural networks (mathematical biology)
34K18Bifurcation theory of functional differential equations
WorldCat.org
Full Text: DOI
References:
[1] Chow, S. -N.; Hale, J. K.: Methods of bifurcation theory. (1982) · Zbl 0487.47039
[2] Baptistini, M. Z.; Táboas, P. Z.: On the existence and global bifurcation of periodic solutions to planar differential delay equations. J. differential equations 127, 391-425 (1996) · Zbl 0849.34053
[3] Faria, T.; Magalhães, L. T.: Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation. J. differential equations 122, 181-200 (1995) · Zbl 0836.34068
[4] Godoy, S. M. S.; Dos Reis, J. G.: Stability and existence of periodic solutions of a functional differential equation. J. math. Anal. appl. 198, 381-398 (1996) · Zbl 0851.34074
[5] Gopalsamy, K.; Leung, I.: Delay induced periodicity in a neural netlet of excitation and inhibition. Physica D 89, 395-426 (1996) · Zbl 0883.68108
[6] Guckenheimer, J.: Multiple bifurcation problems of codimension two. SIAM J. Math. anal. 15, 1-49 (1984) · Zbl 0543.34034
[7] Hale, J. K.; Verduyn-Lunel, S. M.: Introduction to functional differential equations. (1993) · Zbl 0787.34002
[8] Kuang, Y.: Delay differential equations with applications in population dynamics. (1993) · Zbl 0777.34002
[9] Olien, L.; Bélair, J.: Bifurcations, stability, and monotonicity properties of a delayed neural network model. Physica D 102, 349-363 (1997) · Zbl 0887.34069
[10] Ruan, S.; Wei, J.: Periodic solutions of planar systems with two delays. Proc. royal soc. Edinburgh sect. A 129, 1017-1032 (1999) · Zbl 0946.34062
[11] Wei, J.; Ruan, S.: Stability and bifurcation in a neural network with two delays. Physica D 130, 255-272 (1999) · Zbl 1066.34511
[12] Táboas, P.: Periodic solutions of a planar delay equation. Proc. royal soc. Edinburgh sect. A 116, 85-101 (1990) · Zbl 0719.34125