Nonlinear analysis of dynamical complex networks

Copyright © 2013 Zidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Complex networks are composed of a large number of highly interconnected dynamical units and therefore exhibit very complicated dynamics. Examples of such complex networks include the Internet, that is, a network of routers or domains, the World Wide Web (WWW), that is, a network of websites, the brain, that is, a network of neurons, and an organization, that is, a network of people. Since the introduction of the small-world network principle, a great deal of research has been focused on the dependence of the asymptotic behavior of interconnected oscillatory agents on the structural properties of complex networks. It has been found out that the general structure of the interaction network may play a crucial role in the emergence of synchronization phenomena in various fields such as physics, technology, and the life sciences

Recent Advances and Applications of Fractional-Order Neural Networks

This paper focuses on the growth, development, and future of various forms of fractional-order neural networks. Multiple advances in structure, learning algorithms, and methods have been critically investigated and summarized. This also includes the recent trends in the dynamics of various fractional-order neural networks. The multiple forms of fractional-order neural networks considered in this study are Hopfield, cellular, memristive, complex, and quaternion-valued based networks. Further, the application of fractional-order neural networks in various computational fields such as system identification, control, optimization, and stability have been critically analyzed and discussed

Finite-time passivity for neutral-type neural networks with time-varying delays – via auxiliary function-based integral inequalities

In this paper, we investigated the problem of the finite-time boundedness and finitetime passivity for neural networks with time-varying delays. A triple, quadrable and five integral terms with the delay information are introduced in the new Lyapunov–Krasovskii functional (LKF). Based on the auxiliary integral inequality, Writinger integral inequality and Jensen’s inequality, several sufficient conditions are derived. Finally, numerical examples are provided to verify the effectiveness of the proposed criterion. There results are compared with the existing results.&nbsp

Fixed-time control of delayed neural networks with impulsive perturbations

This paper is concerned with the fixed-time stability of delayed neural networks with impulsive perturbations. By means of inequality analysis technique and Lyapunov function method, some novel fixed-time stability criteria for the addressed neural networks are derived in terms of linear matrix inequalities (LMIs). The settling time can be estimated without depending on any initial conditions but only on the designed controllers. In addition, two different controllers are designed for the impulsive delayed neural networks. Moreover, each controller involves three parts, in which each part has different role in the stabilization of the addressed neural networks. Finally, two numerical examples are provided to illustrate the effectiveness of the theoretical analysis

Event-Triggered State Estimation for a Class of Delayed Recurrent Neural Networks with Sampled-Data Information

The paper investigates the state estimation problem for a class of recurrent neural networks with sampled-data information and time-varying delays. The main purpose is to estimate the neuron states through output sampled measurement; a novel event-triggered scheme is proposed, which can lead to a significant reduction of the information communication burden in the network; the feature of this scheme is that whether or not the sampled data should be transmitted is determined by the current sampled data and the error between the current sampled data and the latest transmitted data. By using a delayed-input approach, the error dynamic system is equivalent to a dynamic system with two different time-varying delays. Based on the Lyapunov-krasovskii functional approach, a state estimator of the considered neural networks can be achieved by solving some linear matrix inequalities, which can be easily facilitated by using the standard numerical software. Finally, a numerical example is provided to show the effectiveness of the proposed event-triggered scheme

Global exponential synchronization of quaternion-valued memristive neural networks with time delays

This paper extends the memristive neural networks (MNNs) to quaternion field, a new class of neural networks named quaternion-valued memristive neural networks (QVMNNs) is then established, and the problem of drive-response global synchronization of this type of networks is investigated in this paper. Two cases are taken into consideration: one is with the conventional differential inclusion assumption, the other without. Criteria for the global synchronization of these two cases are achieved respectively by appropriately choosing the Lyapunov functional and applying some inequality techniques. Finally, corresponding simulation examples are presented to demonstrate the correctness of the proposed results derived in this paper