Synchronization analysis of coupled fractional-order neural networks with time-varying delays

In this paper, the complete synchronization and Mittag-Leffler synchronization problems of a kind of coupled fractional-order neural networks with time-varying delays are introduced and studied. First, the sufficient conditions for a controlled system to reach complete synchronization are established by using the Kronecker product technique and Lyapunov direct method under pinning control. Here the pinning controller only needs to control part of the nodes, which can save more resources. To make the system achieve complete synchronization, only the error system is stable. Next, a new adaptive feedback controller is designed, which combines the Razumikhin-type method and Mittag-Leffler stability theory to make the controlled system realize Mittag-Leffler synchronization. The controller has time delays, and the calculation can be simplified by constructing an appropriate auxiliary function. Finally, two numerical examples are given. The simulation process shows that the conditions of the main theorems are not difficult to obtain, and the simulation results confirm the feasibility of the theorems

Fixed-time synchronization problem of coupled delayed discontinuous neural networks via indefinite derivative method

In this brief, we introduce a class of coupled delayed nonautonomous neural networks (CDNNs) with discontinuous activation function. Different from the conventional Lyapunov method, this brief uses the implementation of an indefinite derivative to deal with the nonautonomous system for the case that the topology between neurons is nonlinear coupling, and the system can achieve synchronization in fixed time by selecting the suitable control scheme. The settling time estimation of the system which can get rid of the dependence on the initial value is given. Finally, two examples are given to verify the correctness of the results in this paper

New results on finite-/fixed-time synchronization of delayed memristive neural networks with diffusion effects

In this paper, we further investigate the finite-/fixed-time synchronization (FFTS) problem for a class of delayed memristive reaction-diffusion neural networks (MRDNNs). By utilizing the state-feedback control techniques, and constructing a general Lyapunov functional, with the help of inequality techniques and the finite-time stability theory, novel criteria are established to realize the FFTS of the considered delayed MRDNNs, which generalize and complement previously known results. Finally, a numerical example is provided to support the obtained theoretical results

Robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses.

Fractional order system is playing an increasingly important role in terms of both theory and applications. In this paper we investigate the global existence of Filippov solutions and the robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses. By means of growth conditions, differential inclusions and generalized Gronwall inequality, a sufficient condition for the existence of Filippov solution is obtained. Then, sufficient criteria are given for the robust generalized Mittag-Leffler synchronization between discontinuous activation function of impulsive fractional order neural network systems with (or without) parameter uncertainties, via a delayed feedback controller and M-Matrix theory. Finally, four numerical simulations demonstrate the effectiveness of our main results.N/

Weighted Sum Synchronization of Memristive Coupled Neural Networks

Funding Information: This work is supported by the National Natural Science Foundation of China (No. 61971185) and the Open Fund Project of Key Laboratory in Hunan Universities (No. 18K010). Publisher Copyright: © 2020 Elsevier B.V.It is well known that weighted sum of node states plays an essential role in function implementation of neural networks. Therefore, this paper proposes a new weighted sum synchronization model for memristive neural networks. Unlike the existing synchronization models of memristive neural networks which control each network node to reach synchronization, the proposed model treats the networks as dynamic entireties by weighted sum of node states and makes the entireties instead of each node reach expected synchronization. In this paper, weighted sum complete synchronization and quasi-synchronization are both investigated by designing feedback controller and aperiodically intermittent controller, respectively. Meanwhile, a flexible control scheme is designed for the proposed model by utilizing some switching parameters and can improve anti-interference ability of control system. By applying Lyapunov method and some differential inequalities, some effective criteria are derived to ensure the synchronizations of memristive neural networks. Moreover, the error level of the quasi-synchronization is given. Finally, numerical simulation examples are used to certify the effectiveness of the derived results.Peer reviewe

SATURATED AND ASYMMETRIC SATURATED IMPULSIVE CONTROL SYNCHRONIZATION OF COUPLED DELAYED INERTIAL NEURAL NETWORKS WITH TIME-VARYING DELAYS

This paper considers control systems with impulses that are saturated and asymmetrically saturated which are used to examine the synchronization of inertial neural networks (INNs) with time-varying delay and coupling delays. Under the theoretical discussions, mixed delays, such as transmission delay and coupling delay are presented for inertial neural networks. The addressed INNs are transformed into first order differential equations utilizing variable transformation on INNs and then certain adequate conditions are derived for the exponential synchronization of the addressed model by substituting saturation nonlinearity with a dead-zone function. In addition, an asymmetric saturated impulsive control approach is given to realize the exponential synchronization of addressed INNs in the leader-following synchronization pattern. Finally, simulation results are used to validate the theoretical research findings

Sliding intermittent control for BAM neural networks with delays

Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2013/615947 Open AccessThis paper addresses the exponential stability problem for a class of delayed bidirectional associative memory (BAM) neural networks with delays. A sliding intermittent controller which takes the advantages of the periodically intermittent control idea and the impulsive control scheme is proposed and employed to the delayed BAM system. With the adjustable parameter taking different particular values, such a sliding intermittent control method can comprise several kinds of control schemes as special cases, such as the continuous feedback control, the impulsive control, the periodically intermittent control, and the semi-impulsive control. By using analysis techniques and the Lyapunov function methods, some sufficient criteria are derived for the closed-loop delayed BAM neural networks to be globally exponentially stable. Finally, two illustrative examples are given to show the effectiveness of the proposed control scheme and the obtained theoretical results

Passivity and synchronization of coupled reaction-diffusion complex-valued memristive neural networks

This paper considers two types of coupled reaction-diffusion complex-valued memristive neural networks (CRDCVMNNs). The nodes of the first type CRDCVMNN are coupled through their state and the second one is coupled by spatial diffusion coupling term. For the former, some novel criteria for the passivity and synchronization are derived by constructing an appropriate controller and utilizing some inequality techniques as well as Lyapunov functional method. For the latter, we establish some sufficient conditions which guarantee that this type of CRDCVMNNs can realize passivity and synchronization. Finally, the effectiveness and correctness of the acquired theoretical results are verified by two numerical examples

Synchronization of Complex-Valued Dynamical Networks

Dynamical networks (DNs) have been broadly applied to describe natural and human systems consisting of a large number of interactive individuals. Common examples include Internet, food webs, social networks, neural networks, etc. One of the crucial and significant collective behaviors of DNs is known as synchronization. In reality, synchronization phenomena may occur either inside a network or between two or more networks, which are called “inner synchronization” and “outer synchronization”, respectively. On the other hand, many real systems are more suitably characterized by complex-valued dynamical systems, such as quantum systems, complex Lorenz system, and complex-valued neural networks. The main focus of this thesis is on synchronization of complex-valued dynamical networks (CVDNs). In this thesis, we firstly design a delay-dependent pinning impulsive controller to study synchronization of time-delay CVDNs. By taking advantage of the Lyapunov function in the complex field, some delay-independent synchronization criteria of CVDNs are established, which generalizes some existing synchronization results. Then, by employing the Lyapunov functional in the complex field, several delay-dependent sufficient conditions on synchronization of CVDNs with various sizes of delays are constructed. Moreover, we study synchronization of CVDNs with time-varying delays under distributed impulsive controllers. By taking advantage of time-varying Lyapunov function/ functional in the complex domain, several synchronization criteria for CVDNs with time-varying delays are derived in terms of complex-valued linear matrix inequalities (LMIs). Then, we propose a memory-based event-triggered impulsive control (ETIC) scheme with three levels of events in the complex field to investigate the synchronization problem of CVDNs with both discrete and distributed time delays, and we further consider an event-triggered pinning impulsive control (ETPIC) scheme combining the proposed ETIC and a pinning algorithm to study synchronization of time-delay CVDNs. Results show that the proposed ETIC scheme and ETPIC scheme can effectively synchronize CVDNs with the desired trajectory. Secondly, we study generalized outer synchronization of drive-response time-delayed CVDNs via hybrid control. A hybrid controller is proposed in the complex domain to construct response complex-valued networks. Some generalized outer synchronization criteria for drive-response CVDNs are established, which extend the existing generalized outer synchronization results to the complex field. Thirdly, we study the average-consensus problem of potential complex-valued multi-agent systems. A complex-variable hybrid consensus protocol is proposed, and time delays are taken into account in both the continuous-time protocol and the discrete-time protocol. Delay-dependent sufficient conditions are established to guarantee the proposed complex-variable hybrid consensus protocol can solve the average-consensus problem. Lastly, as a practical application for complex-valued networked systems, the synchronization problem of master-slave complex-valued neural networks (CVNNs) is studied via hybrid control and delayed ETPIC, respectively. We also investigate the state estimation problem of CVNNs by designing the adaptive impulsive observer in the complex field

18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems: Proceedings

Proceedings of the 18th IEEE Workshop on Nonlinear Dynamics of Electronic Systems, which took place in Dresden, Germany, 26 – 28 May 2010.:Welcome Address ........................ Page I Table of Contents ........................ Page III Symposium Committees .............. Page IV Special Thanks ............................. Page V Conference program (incl. page numbers of papers) ................... Page VI Conference papers Invited talks ................................ Page 1 Regular Papers ........................... Page 14 Wednesday, May 26th, 2010 ......... Page 15 Thursday, May 27th, 2010 .......... Page 110 Friday, May 28th, 2010 ............... Page 210 Author index ............................... Page XII