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Sustainable Network Dynamics


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  • Arnaud Dragicevic
  • Bernard Sinclair-Desgagné



We propose a dynamic graph-theoretic model for ecosystem management as a control over networked system composed of target nodes and unmarked nodes. The network is represented by a complete graph, in which all vertices are connected by a unique edge. Target nodes are attracted by the objective function issued from the external ecosystem management. They pull the network towards the objective position, which is either non-null or stationary. The management policy is considered successful if the graph remains connected in time, that is, target nodes attain the objective and unmarked nodes stay in the convex hull. At the time of the ecosystem network transfer, the model yields an Impossibility Theorem as well as a Sustainability Criterion to maintain full connectivity of the network. The latter can be easily linked to the general definition of sustainability as ecosystem integrity preservation. At last, we identify three management rules to ensure the maintenance of connectivity in time, given the properties of the objective transposition function, the nature of connections and utility updating time-delays between the nodes Nous proposons un modèle dynamique de gestion des écosystèmes par la théorie des graphes en tant que contrôle d’un système en réseau composé de nœuds cibles et de nœuds non identifiés. Le réseau est représenté par un graphe complet dans lequel tous les nœuds sont connectés par une arête unique. Les nœuds cibles sont attirés par une fonction objectif issue d’un processus externe de gestion des écosystèmes. Ils tirent le réseau vers la position de l’objectif qui peut être non-nulle ou stationnaire. La politique de gestion est considérée réussie si le graphe reste connecté dans le temps, c'est-à-dire que les nœuds cibles atteignent l’objectif et les nœuds non identifiés restent dans l’enveloppe convexe. Lors de la transposition du réseau écosystémique dans le temps, le modèle génère un Théorème de l’Impossibilité ainsi qu’un Critère de Durabilité qui maintient la pleine connectivité du réseau. Ce dernier peut aisément être relié à la définition générale de la durabilité comme la préservation de l’intégrité écologique. Enfin, nous identifions trois règles de gestion pour assurer le maintien de la connectivité dans le temps, sachant les propriétés de la fonction objectif de transposition, la nature des connexions, et les retards de réactualisation de l’utilité entre les nœuds.

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 2011s-51.

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Date of creation: 01 Jun 2011
Date of revision:
Handle: RePEc:cir:cirwor:2011s-51

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Keywords: bioeconomics; ecosystem management; graph theory; connectedness.; bioéconomie; gestion des écosystèmes; théorie des graphes; connectivité;

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