Article

Identifying the Topology of a Coupled FitzHugh–Nagumo Neurobiological Network via a Pinning Mechanism

Sch. of Math. & Stat., Wuhan Univ., Wuhan, China
IEEE Transactions on Neural Networks (Impact Factor: 2.95). 11/2009; DOI: 10.1109/TNN.2009.2029102
Source: DBLP

ABSTRACT Topology identification of a network has received great interest for the reason that the study on many key properties of a network assumes a special known topology. Different from recent similar works in which the evolution of all the nodes in a complex network need to be received, this brief presents a novel criterion to identify the topology of a coupled FitzHugh-Nagumo (FHN) neurobiological network by receiving the membrane potentials of only a fraction of the neurons. Meanwhile, although incomplete information is received, the evolution of all the neurons including membrane potentials and recovery variables are traced. Based on Schur complement and Lyapunov stability theory, the exact weight configuration matrix can be estimated by a simple adaptive feedback control. The effectiveness of the proposed approach is successfully verified by neural networks with fixed and switching topologies.

0 Bookmarks
 · 
76 Views
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The topological structure of a dynamical network plays a pivotal part in its properties, dynamics and control. Thus, understanding and modeling the structure of a network will lead to a better knowledge of its evolutionary mechanisms and to a better cottoning on its dynamical and functional behaviors. However, in many practical situations, the topological structure of a dynamical network is usually unknown or uncertain. Thus, exploring the underlying topological structure of a dynamical network is of great value. In recent years, there has been a growing interest in structure identification of dynamical networks. As a result, various methods for identifying the network structure have been proposed. However, in most of the previous work, few of them were discussed in the perspective of optimization. In this paper, an optimization algorithm based on the projected conjugate gradient method is proposed to identify a network structure. It is straightforward and applicable to networks with or without observation noise. Furthermore, the proposed algorithm is applicable to dynamical networks with partially observed component variables for each multidimensional node, as well as small-scale networks with time-varying structures. Numerical experiments are conducted to illustrate the good performance and universality of the new algorithm.
    Physica A: Statistical Mechanics and its Applications 02/2013; 392(4):1038–1049. · 1.68 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Nowadays, the topology of complex networks is essential in various fields as engineering, biology, physics, and other scientific fields. We know in some general cases that there may be some unknown structure parameters in a complex network. In order to identify those unknown structure parameters, a topology identification method is proposed based on a chaotic ant swarm algorithm in this paper. The problem of topology identification is converted into that of parameter optimization which can be solved by a chaotic ant algorithm. The proposed method enables us to identify the topology of the synchronization network effectively. Numerical simulations are also provided to show the effectiveness and feasibility of the proposed method.
    Mathematical Problems in Engineering 10/2013; 2013. · 1.38 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: This paper presents a modified astrocyte model that allows a convenient digital implementation. This model is aimed at reproducing relevant biological astrocyte behaviors, which provide appropriate feedback control in regulating neuronal activities in the central nervous system. Accordingly, we investigate the feasibility of a digital implementation for a single astrocyte and a biological neuronal network model constructed by connecting two limit-cycle Hopf oscillators to an implementation of the proposed astrocyte model using oscillator-astrocyte interactions with weak coupling. Hardware synthesis, physical implementation on field-programmable gate array, and theoretical analysis confirm that the proposed astrocyte model, with considerably low hardware overhead, can mimic biological astrocyte model behaviors, resulting in desynchronization of the two coupled limit-cycle oscillators.
    IEEE transactions on neural networks and learning systems 03/2014; · 3.77 Impact Factor

Full-text (3 Sources)

View
85 Downloads
Available from
May 22, 2014