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We are interested in studying the spread of chaos in an interaction network modeled by a Coupled Map Network (CMN). This graph is formed by nodes characterized by a measurable state variable that may exhibit chaotic time series. The interaction between the nodes may propagate their states in the network leading through a coupling process to some synchronization phenomenon which is known as nonlinear oscillator synchronization. The interaction network that we aim to study contains initially only one chaotic node that is responsible of the spread of chaos. Our goal consists then to study how to identify the node which is the source of the spread of chaos in an interaction network and how to detect the set of nodes becoming disturbed by the propagation of the chaotic node state. In this paper, we seek some appropriate measures to quantify the dynamic complexity of the nodes in order to identify the group of chaotic nodes as well as the source of the spread of chaos in the graph. We show by some simulations on random graphs that the Shannon entropy calculated on the close returns plots is an appropriate measure to detect chaotic series from a node. The extension of close returns plots to joint recurrence plots enables to identify the source of the spread of the disturbance in the network.

International audience; Ant algorithms are usually derived from a stochastic modeling based on some specific probability laws. We consider in this paper a full deterministic model of “logistic ants” which uses chaotic maps to govern the behavior of the artificial ants. We illustrate and test this approach on a TSP instance, and compare the results with the original Ant System algorithm. This change of paradigm —deterministic versus stochastic— implies a novel view of the internal mechanisms involved during the searching and optimizing process of ants.

International audience; We are interested in addressing the problem of coordinating a large number of simple agents in order to achieve a given task. Stated in this way, the question leads naturally to the Swarm Intelligence field. In this paper we use a new type of model, directly inspired by Kaneko's coupled map gas model which we have adapted to the multi-agent system paradigm, so as to tackle this generic objective. This model is called a logistic multi-agent system (LMAS): it is composed of reactive situated agents whose individual behavior is governed by a logistic map or more generally a quadratic map. The collective behavior results from couplings between agents and local controls on agents adjusted by local environmental conditions. This way of modelling reveals to enable a wide range of pattern formations and various forms of adaptation to the environment. This paper focuses on the way to design the constitutive mechanisms of LMAS –particularly the perception and action processes– and on the way a self-adaptation process may result from these mechanisms. This study is illustrated with experiments on the predators-prey pursuit problem, in which a set of agents (predators) has to encircle a moving prey. We show that coupling the internal states of agents leads to amplifying the predator aggregation around the prey, whereas altering the internal control variable in each agent through environment perceptions modifies the predator sensitivity to the prey. We finally complete this study by relating the concept of adaptation with concepts of the dynamical system theory: a qualitative dynamical analysis of the capturing process leads to view the prey as a dynamical fixed point of the system.

International audience; Ant algorithms and flocking algorithms are the two main programming paradigms in swarm intelligence. They are built on stochastic models, widely used in optimization problems. However, though this modeling leads to high-performance algorithms, some mechanisms, like the symmetry break in ant decision, are still not well understood at the local ant level. Moreover, there is currently no modeling approach which joins the two paradigms. This paper proposes an entirely novel approach to the mathematical foundations of swarm algorithms: contrary to the current stochastic approaches, we show that an alternative deterministic model exists, which has its origin in deterministic chaos theory. We establish a reactive multi-agent system, based on logistic nonlinear decision maps, and designed according to the influence-reaction scheme. The rewriting of the decision functions leads to a new way of understanding the swarm phenomena in terms of state synchronization, and enables the analysis of their convergence behavior through bifurcation diagrams. We apply our approach on two concrete examples of each algorithm class, in order to demonstrate its general applicability.

International audience; Ant algorithms are one of the main programming paradigms in swarm intelligence. They are built on stochastic decision functions, which can also be found in other types of bio-inspired algorithms with the same mathematical form. However, though this modeling leads to high-performance algorithms, some phenomena, like symmetry break, are still not well understood or modeled at the ant level. This paper proposes an original analysis of the problem : we establish a reactive multi-agent system based on logistic nonlinear decision maps, and designed according to the influence-reaction scheme. Our proposition is an entirely novel approach to the mathematical foundations of ant algorithms : contrary to the current stochastic approaches, we show that an alternative deterministic model exists, which has its origin in deterministic chaos theory. The rewriting of the decision functions leads to a new way of understanding and visualizing the convergence behavior of ant algorithms. We apply our approach on a concrete example, namely the binary bridge problem.