Nathalie Corson

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.

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.

Chaos in Fractional Order Cubic Chua System and Synchronization

This paper deals with fractional order Chua system with cubic nonlinearity (cubic Chua system), which is a modification of Chua system. The aim is, first, to study the chaotic behavior in fractional order cubic Chua system. We found that chaos indeed exists in the fractional version of this system. The necessary condition for exhibiting chaotic attractors similar to its integer order counterpart is presented. This condition is used to distinguish for which parameters and orders the system generates double scroll chaotic attractors. The synchronization problem between two coupled chaotic fractional order cubic Chua systems is then addressed. An adaptive feedback control scheme for the synchronization with suitable feedback nonlinear controller applied to the response system is presented. Numerical simulations are performed to verify the theoretical analysis.

Complex emergent properties in synchronized neuronal oscillations

This work adresses the dynamics and complexity of the Hindmarsh-Rose neuronal mathematical model. The general aim is the study of the asymptotic behaviour of neuron networks. In this paper, the analysis of these networks uses the synchronization theory via connections between neurons which give rise to emergent properties and self-organization. Our results lead to a classical law which describes many natural or artificial self-organized complex systems. This has been performed using numerical tools.

Multiscale Modeling: Application to Traffic Flow

Abstract: Traffic modeling is a particularly active field, the origins of which can be traced back to the pioneering work of Greenshield in the 1930s. Greenshield was the first to formulate a structural relation between the speed of vehicles on a road and the distance between them. This relation between the flow rate/density, at the heart of the so-called fundamental diagram, has been used by all families of traffic flow models developed ever since. These families of models can be grouped into three distinct but strongly interconnected subcategories: macroscopic models, which consider flows of vehicles, microscopic models, which consider individual vehicles and their interactions, and mesoscopic models, which lie in between the other two categories.

Symbolic-Numeric Methods for Nonlinear Integro-Differential Modeling

This paper presents a proof of concept for symbolic and numeric methods dedicated to the parameter estimation problem for models formulated by means of nonlinear integro-differential equations (IDE). In particular, we address: the computation of the model input-output equation and the numerical integration of IDE systems.

3 – Macro Models, Micro Models and Network-based Coupling

Abstract: In this chapter, we will discuss coupling models with different scales to describe the propagation of a virus within a population. This population is distributed throughout a set of cities connected by airline routes. Population movements between cities enable the virus to travel, carried by infected individuals. In each city, the description of virus propagation is based on an SIR-type model (presented in more detail). The first model, called EpiSim, is presented, first in its aggregate variant, and then in its individual-based variant. Comparing these two approaches will allow us to discuss the advantages and limitations of each of them. In the second section, we will present two approaches for coupling models based on networks. The first approach considers a network of coupled systems of equations. The second combines an agent-based model of microscale components with a model of macroscale components based on systems of equations. This coupled model, called MicMac, is presented in more detail. The added value of micro/macro coupling is examined in the article.

Sinusoidal disturbance induced topology identification of Hindmarsh-Rose neural networks

Topology identification of complex networks is an important problem. Existing research shows that the synchronization of network nodes is an obstacle in the identification of network topology. Identification of the structure of the network presents an interesting challenge during the synchronization of complex networks. We developed a new method using the sinusoidal disturbance to identify the topology when the complex network achieves synchronization. Compared with the disturbance of all the nodes, the disturbance of the key nodes alone can achieve a very good effect. Finally, numerical simulation data are provided to validate our hypothesis.概要中文概要拓扑识别是近年来复杂网络研究的重要问题, 研究表明, 网络上节点同步是拓扑识别过程中的重要障碍. 当节点到达同步时如何进行识别是一个非常有趣的问题. 本文主要研究了节点为Hindmarsh-Rose (HR) 系统的网络结构识别问题, 当网络上HR系统达到同步时, 它们不满足一致激励条件, 拓扑结构不能识别. 此时, 正弦信号扰动能够诱导拓扑识别. 相比于扰动网络上全部节点, 扰动关键节点也能达到拓扑识别的目的.创新点拓扑识别问题是复杂网络研究的重要问题, 研究结果表明, 当网络上的节点达到同步时候, 拓扑很难识别. 利用正弦扰动信号, 本文研究了当节点达到同步状态时的拓扑识别问题, 研究表明给节点添加适当的正弦扰动能够诱导出拓扑识别.