\section{INTRODUCTION}

The development of huge networks of communications allows today to share a great amount of data. With the use of these new technologies, the need of informations becomes important. The easy sharing of data all over the world makes that interactions processes, at many different scales, are needed to analyse the present world in all its complexity. We need new models based on the basis of this complexity: interactions-based and multi-scales-based~\cite{bossomaier}.\\
  
The new technologies and especially the satellites give a great amount of data concerning geographical informations. The important improvement of computer sciences as the science of modelization and conceptualisation and the increasing performance of computers and networks, lead to buid efficient Geographic Information Systems (GIS). These GIS allow to represent heterogeneous informations which are strongly linked and stored in Geographical Data Bases (GDB). These GDB based on vector representation are generally composed of layered classes of objects. Each layer is associated to a semantic thematic like road traffic, fluvial tracing, buildings, vegetation, etc. \cite{maguire}\\

Moreover, the new challenges in geography concerns also the analysis and the understanding of the interactions all over the world about social, geopolitic and ecological aspects. These challenges need to develop and manage suitable conceptual and generic models. Complex modelling to describe complex processus over the structured networks of GDB, is an efficient way to answer to these challenges. On the practical aspect, GIS development is concerned today with one of these complex processus over GDB which is the updating processing for GIS \cite{cooper}.\\    

The constant evolution of the real world which must be represented in the geographical data bases induces the need to regularly update the Data Base. The knowledge of updating is generally associated to the concerned semantic layer. Each semantic layer has its own updating frequency which can differ from one layer to another \cite{johnes}. This heterogeneity can be the cause of some problems on the consistency maintenance of the whole GDB. On the figure \ref{coherence}, we describe the updating generated by a new road arrangement. The first part of this figure shows the initial map configuration. The second part shows a first uncorrect updating without checking the whole consistence, generating superposition of a new road portion over existing buildings (left bottom of the road crossing). The last part shows a correct updating after the propagation of some topological constraints between the layer of the road tracing and of the layer of the buildings position.\\

\begin{figure}[htb]
\begin{center}
%\rotatebox{-90} 
{\includegraphics[scale=0.60]{CoherenceHorizontale.eps}}
\caption{Updating within consistency maintenance}
\label{coherence}
\end{center}
\end{figure}

In this paper, we propose a solution for the Geographical Data Base updating problem with maintaining its consistency.  First, we will develop in the section 2, how Geographic Information Systems is expected to be transformed in Complex Geographic Information Systems by the application of complex processus over the geographical data network. Section 3 deals with the proposed formalism of evolutive GIS as one of these complex GIS. We explain where the complexity appears in the formalism to transform a complicated system in a complex system. Section 4 describes how we will build a dynamical interaction network from the application of influence tables over GDB. We will explain how the processus described can be compared with cellular automata. In section 5, we present the effective algorithm of updating based on a propagation processus and we focus on the major problem of updating which concerns the consistency maintenance. 
In Section 6, we present the emergent property of the global consistency maintenance from the local consistency maintenance.
Section 7 presents implementations and experiments and we conclude in section 8. 
