Here is a tentative program of the communications.

Thursday September 12, 2002 | |

18h05 – 18h25 | R. Ouifki. Hopf bifurcation via the Poincaré procedure for a two delays differential equation. |

18h25 – 18h45 | R. Quesmi (U. Marrakech). A Maple program for the computation of the coefficients of a center manifold. |

Friday September 13, 2002 | |

15h45 – 16h05 | J. Batzel (U. Graz). Modeling the respiratory control system: delay dependent stability analysis and applications. |

16h05 – 16h25 | F. Crauste (U. Pau). Biological models of cellular replication: Dependence on the initial condition. |

17h45 – 18h05 | S. Djebali. Traveling wave solutions to a reaction-diffusion system from combustion theory. |

18h05 – 18h25 | S. Panigrahi (Indian Institute of Science, Bangalore, India). On Liapunov-type inequality for third-order differential equations. |

18h25 – 18h50 | M. Bachar (U. Graz). Integrated semigroup associated to a linear delay differential equation with impulses. |

Thursday September 19, 2002 | |

17h00 – 17h20 | M. Moussi. Non-autonomous retarded differential equations: variation of constants formulas and asymptotic behaviour. |

17h20 – 17h40 | D. Fofana. Chaotic dynamical systems. Statistical approach. |

17h40 – 18h00 | B. Hoff (Oxford University). TBA. |

18h00 – 18h20 | A. Razani (Imam Khomeini International University, Iran). Heteroclinic orbits for Majda's combustion model. |

18h20 – 18h40 | H. Bouzahir (ENSA Agadir). General results about FDEs with infinite delay |

- M. Bachar (U. Graz). Integrated semigroup associated to a linear
delay differential equation with impulses.

**Abstract**: We discuss the fundamental linear theory for a large class of delay differential equations with impulses. We show, using the general theory of integrated semigroups, that we can associate an integrated semigroup with any delay differential equation with impulses and we have determined the infinitesimal generator of this integrated semigroup.

Two papers relative to the talk are available in the restricted zone.

- J. Batzel (U. Graz). Modeling the respiratory control system: delay dependent stability analysis and applications.

- Hassane Bouzahir (ENSA Agadir). General results about FDEs with
infinite delay.

**Abstract**: We discuss the literature devoted to FDEs with infinite delay. We mainly give some comparisons with the case of finite delay. Special attention will be given to the recent progress in infinite dimension.

- F. Crauste (U. Pau). Biological models of cellular replication:
Dependence on the initial condition.

**Abstract**: We recall some models of cellular proliferation, especially the one obtained by Mackey and Rudnicki in 1994, and we give a result of existence and uniqueness of solutions depending oon stem cells, in a nonlinear case with time distributed delay and a nonlocal dependence in the maturity variable.

- S. Djebali. Traveling wave solutions to a reaction-diffusion system from combustion theory.

- D. Fofana. Chaotic dynamical systems. Statistical approach.

- M. A. Hammami. Stability of perturbed dynamical systems.

- B. Hoff (Oxford University, UK). TBA.

- R. Quesmi (U. Marrakech). A Maple program for the computation
of the coefficients of a center manifold.

**Abstract**: The center manifolds are instrumental in the analysis of dynamical systems described by differential equations with delays, particularly when singularities close to a bifurcation are to be characterized. However, the computation of homogeneous terms of a center manifold up to an arbitrary order is numerically hard. This work focuses on the computer programming of some recursive formulas developed earlier to compute higher order homogenuous terms of a center manifolds for a class of differential equations. A computer program to compute this terms is developed using the Maple symbolic language.

- M. Moussi. Non-autonomous retarded differential equations: variation of constants formulas and asymptotic behaviour.

- R. Ouifki. Hopf bifurcation via the Poincaré procedure for a two delays differential equation.

- S. Panigrahi (Indian Institute of Science, Bangalore, India). On Liapunov-type inequality for third-order differential equations.

- A. Razani (Imam Khomeini International University, Iran). Heteroclinic
orbits for Majda's combustion model.

**Abstract**: The existence of detonation waves is one of the most important problems in combustion. The rigorous mathematical treatment of this problem was initiated by Majda. He proposed a simplified model for the qualitative study of one dimensional combustion waves. The model was derived from the one-dimensional combustion equations for a simple exothermic chemical reaction. The existence of detonation waves is proved by the existence of some heteroclinic orbits between two rest points of a 2 dimensional ordinary differential equation.

J.A. Last modified: Wed Sep 18 05:10:40 Pacific Daylight Time 2002