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Jean-Denis Mathias

Publications and source records attributed to Jean-Denis Mathias.

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Few self-involved agents among BC agents can lead to polarized local or global consensus

Social issues are generally discussed by highly-involved and less-involved people to build social norms defining what has to be thought and done about them. As self-involved agents share different attitude dynamics to other agents Wood, Pool et al, 1996, we study the emergence and evolution of norms through an individual-based model involving these two types of agents. The dynamics of self-involved agents is drawn from Huet and Deffuant, 2010, and the dynamics of others, from Deffuant et al, 2001. The attitude of an agent is represented as a segment on a continuous attitudinal space. Two agents are close if their attitude segments share sufficient overlap. Our agents discuss two different issues, one of which, called main issue, is more important for the self-involved agents than the other, called secondary issue. Self-involved agents are attracted on both issues if they are close on main issue, but shift away from their peer's opinion if they are only close on secondary issue. Differently, non-self-involved agents are attracted by other agents when they are close on both the main and secondary issues. We observe the emergence of various types of extreme minor clusters. In one or different groups of attitudes, they can lead to an already-built moderate norm or a norm polarized on secondary and/or main issues. They can also push disagreeing agents gathered in different groups to a global moderate consensus.

cs.MA

From lakes and glades to viability algorithms: Automatic classification of system states according to the Topology of Sustainable Management

The framework Topology of Sustainable Management by Heitzig et al. (2016) distinguishes qualitatively different regions in state space of dynamical models representing manageable systems with default dynamics. In this paper, we connect the framework to viability theory by defining its main components based on viability kernels and capture basins. This enables us to use the Saint-Pierre algorithm to visualize the shape and calculate the volume of the main partition of the Topology of Sustainable Management. We present an extension of the algorithm to compute implicitly defined capture basins. To demonstrate the applicability of our approach, we introduce a low-complexity model coupling environmental and socioeconomic dynamics. With this example, we also address two common estimation problems: an unbounded state space and highly varying time scales. We show that appropriate coordinate transformations can solve these problems. It is thus demonstrated how algorithmic approaches from viability theory can be used to get a better understanding of the state space of manageable dynamical systems.

math.OC