Center manifolds and normal forms for a class of retarded functional differential equations with parameter associated with Fold-Hopf singularity

Applied Mathematics and Computation

Volumn 181, Issue 1, 2006, Pages 220-246

  Qesmi, R ^a   Ait Babram, M ^b   Hbid, M L ^a  

^a FACULTÉ DES SCIENCES SEMLALIA   (Morocco)

^b FACULTÉ DES SCIENCES ET TECHNIQUES GUÉLIZ   (Morocco)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; LINEAR ALGEBRA; PARAMETER ESTIMATION;

COMPUTER ALGEBRA SYSTEM; FOLD-HOPF SINGULARITY; FUNCTIONAL DIFFERENTIAL EQUATIONS;

DIFFERENTIAL EQUATIONS;

EID: 33749519969     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.01.030     Document Type: Article

References (13)

1. Ait Babram M., Arino O., and Hbid M.L. Approximation scheme of a system manifold for functional differential equations. J. Math. Anal. Appl. 213 (1997) 554-572
2. Babram M.A., Arino O., and Hbid M.L. Computational scheme of a center manifold for neutral functional differential equations. J. Math. Anal. Appl. 258 (2001) 396-414
3. Diekman O., Van Gils S.A., Verduyn Lunel S.M., and Whalter H.O. Delay equations. Functional-, complex-, and nonlinear analysis. Applied Mathematical Sciences Vol. 110 (1995), Springer-Verlag, New York
4. Faria T. On a planar system modeling a neuron network with memory. J. Differen. Equat. 168 (2000) 129-149
5. Faria T., and Magalhàes L.T. Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation. J. Differen. Equat. 122 (1995) 181-200
6. Faria T., and Magalhàes L.T. Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation. J. Differen. Equat. 122 (1995) 181-200
7. Gopalsamy K., and Leung I. Delay induced periodicity in a neural netlet of excitation and inhibition. Physica D 89 (1996) 395-426
8. Guckenheimer J., and Holmes P.J. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (1983), Springer-Verlag, New York, Heidelberg, Berlin
9. Hale J.K., and Verduyn Lunel S.M. Introduction to Functional Differential Equations (1993), Springer-Verlag, New York
10. Kuznetsov Yu.A. Elements of Applied Bifurcation Theory (1994), Springer-Verlag, New York
11. Olien L., and Bélair J. Bifurcations, stability, and monotonicity properties of a delayed neural network model. Physica D 102 (1997) 349-363
12. Qesmi R., Aitbabram M., and Hbid M.L. A Maple program for computing a terms of a center manifolds, and elements of bifurcations for a class of retarded functional differential equations with Hopf singularity. Appl. Math. Comput. 175 (2005) 42-78
13. Wiggins S. Introduction to applied nonlinear dynamical systems and chaos. Texts in Applied Mathematics 2 (1990), Springer-Verlag, New York