Cyrille Bertelle

A multi-step differential transform method and application to non-chaotic or chaotic systems

The differential transform method (DTM) is an analytical and numerical method for solving a wide variety of differential equations and usually gets the solution in a series form. In this paper, we propose a reliable new algorithm of DTM, namely multi-step DTM, which will increase the interval of convergence for the series solution. The multi-step DTM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions for systems of differential equations. This new algorithm is applied to Lotka-Volterra, Chen and Lorenz systems. Then, a comparative study between the new algorithm, multi-step DTM, classical DTM and the classical Runge-Kutta method is presented. The results demonstrate reliability and efficiency of the algorithm developed.

SYNCHRONIZATION OF CHAOTIC FRACTIONAL-ORDER SYSTEMS VIA LINEAR CONTROL

The chaotic dynamics of fractional-order systems has attracted much attention recently. Chaotic synchronization of fractional-order systems is further studied in this paper. We investigate the chaos synchronization of two identical systems via a suitable linear controller applied to the response system. Based on the stability results of linear fractional-order systems, sufficient conditions for chaos synchronization of these systems are given. Control laws are derived analytically to achieve synchronization of the chaotic fractional-order Chen, Rossler and modified Chua systems. Numerical simulations are provided to verify the theoretical analysis.

Complex Systems and Self-organization Modelling

Sum m ary. In this paper we sum up our works on m ultiscale program s,m ainly sim ulations.W e rststartwith describing whatm ultiscaling isabout,how ithelps perceiving signalfrom a background noisein a ow ofdata forexam ple,fora direct perception by a user or for a further use by another program .W e then give three exam ples of m ultiscale techniques we used in the past,m aintaining a sum m ary, using an environm entalm arkerintroducing an history in the data and nally using a knowledgeon thebehaviorofthedi erentscalestoreally handlethem atthesam e tim e.The concern of this book is the use of emergent computing and self-organization modelling within various applications of complex systems. The authors focus their attention both on the innovative concepts and implementations in order to model self-organizations, but also on the relevant applicative domains in which they can be used efficiently. This book is the outcome of a workshop meeting within ESM 2006 (Eurosis), held in Toulouse, France in October 2006.

Emergent properties in natural and artificial dynamical systems

General Introduction.- From Trajectory Control to Task Space Control - Emergence of Self Organization in Complex Systems.- Natural Systems Modeling.- Competing Ants for Organization Detection Application to Dynamic Distribution.- Problem Solving and Complex Systems.- Changing Levels of Description in a Fluid Flow Simulation.- DNA Supramolecular Self Assemblies as a Biomimetic Complex System.- Dynamic Systems & Synchronization.- Slow Manifold of a Neuronal Bursting Model.- Complex Emergent Properties and Chaos (De)synchronization.- Robust ? Filtering Based Synchronization for a Class of Uncertain Neutral Systems.- Decision Support System.- Automata-Based Adaptive Behavior for Economic Modelling Using Game Theory.- A Novel Diagnosis System Specialized in Difficult Medical Diagnosis Problems Solving.- Constraint Programming and Multi-Agent System Mixing Approach for Agricultural Decision Support System.- Spline Functions.- Complex Systems Representation by C k Spline Functions.- Computer Algebra and C k Spline Functions: A Combined Tools toSolve Nonlinear Differential Problems.- Control.- Decoupling Partially Unknown Dynamical Systems by State Feedback Equations.- Eigenfrequencies Invariance Properties in Deformable Flexion-Torsion Loaded Bodies -1- General Properties.- Eigenfrequencies Invariance Properties in Deformable Flexion-Torsion Loaded Bodies -2- The Compliant Case.

Automata-based adaptive behavior for economic modeling using game theory

In this paper, we deal with some specific domains of applications to game theory. This is one of the major class of models in the new approaches of modelling in the economic domain. For that, we use genetic automata which allow to buid adaptive strategies for the players. We explain how the automata-based formalism proposed - matrix representation of automata with multiplicities - allows to define a semi-distance between the strategy behaviors. With that tools, we are able to generate an automatic processus to compute emergent systems of entities whose behaviors are represented by these genetic automata.

MODELING THE DYNAMICS OF COMPLEX INTERACTION SYSTEMS: FROM MORPHOGENESIS TO CONTROL

The aim of this paper is to contribute to the modeling and analysis of complex systems, taking into account the nature of complexity at different stages of the system life-cycle: from its genesis to its evolution. Therefore, some structural aspects of the complexity dynamics are highlighted, leading (i) to implement the morphogenesis of emergent complex network structures, and (ii) to control some synchronization phenomena within complex networks. Specific applications are proposed to illustrate these two aspects, in urban dynamics and in neural networks.

Emergence of cooperation in non-scale-free networks

Evolutionary game theory is one of the key paradigms behind many scientific disciplines from science to engineering. Previous studies proposed a strategy updating mechanism, which successfully demonstrated that the scale-free network can provide a framework for the emergence of cooperation. Instead, individuals in random graphs and small-world networks do not favor cooperation under this updating rule. However, a recent empirical result shows the heterogeneous networks do not promote cooperation when humans play a prisoners dilemma. In this paper, we propose a strategy updating rule with payoff memory. We observe that the random graphs and small-world networks can provide even better frameworks for cooperation than the scale-free networks in this scenario. Our observations suggest that the degree heterogeneity may be neither a sufficient condition nor a necessary condition for the widespread cooperation in complex networks. Also, the topological structures are not sufficed to determine the level of cooperation in complex networks.

Changing Levels of Description in a Fluid Flow Simulation

We describe here our perception of complex systems, of how we feel the different layers of description are important part of a correct complex system simulation. We describe a rough models categorization between rules based and law based, of how these categories handled the levels of descriptions or scales. We then describe our fluid flow simulation, which combines different fineness of grain in a mixed approach of these categories. This simulation is built keeping in mind an ulterior use inside a more general aquatic ecosystem.

A Resource Oriented Framework for Service Choreography over Wireless Sensor and Actor Networks

AbstractCurrent Internet of Things (IoT) development requires service distribution over Wireless Sensor and Actor Networks (WSAN) to deal with the drastic increasing of network management complexity. Because of the specific constraints of WSAN, some limitations can be observed in centralized approaches. Multi-hop communication used by WSAN introduces transmission latency, packet errors, router congestion and security issues. As it uses local services, a model of decentralized services avoids long path communications between nodes and applications. But the two main issues are then to design (1) the composition of such services and to map (2) them over the WSAN. This contribution proposes a model for decentralized services based on Resource Oriented Architecture in which their communications are designed thanks to an adaptation of Petri Network (1). In addition, the problem of decentralized service mapping and its deployment over a WSAN is successfully resumed by a Pseudo-Boolean Optimization in order to minimize network communication load (2). These contributions are presented using a proposed EMMA middleware as unifying thread.

Agent-Based Perception of an Environment in an Emergency Situation

We are interested in the problem of multiagent systems development for risk detecting and emergency response in an uncertain and partially perceived environment. The evaluation of the current situation passes by three stages inside the multiagent system. In a first time, the situation is represented in a dynamic way. The second step, consists to characterise the situation and finally, it is compared with other similar known situations. In this paper, we present an information modelling of an observed environment, that we have applied on the RoboCupRescue Simulation System. Information coming from the environment are formatted according to a taxonomy and using semantic features. The latter are defined thanks to a fine ontology of the domain and are managed by factual agents that aim to represent dynamically the current situation.