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-/fixed-time synchronization of leakage and discrete delayed Hopfield neural networks with diffusion effects

In this paper, the problem on finite-/fixed-time synchronization (FFTS) is investigated for a class of diffusive Hopfield neural networks with leakage and discrete delays. Some new and useful criteria independent on time delays but dependent on the diffusion coefficients are established to guarantee the FFTS for the addressed network model under a unified framework. In sharp contrast to the existed results which can only finite-timely or fixed-timely synchronize the systems with both diffusion effects and leakage delays, the theoretical results of this paper are more general and practical. Finally, a numerical example is presented to show the effectiveness of the proposed control methods

Finite-time stabilization for fractional-order inertial neural networks with time varying delays

This paper deals with the finite-time stabilization of fractional-order inertial neural network with varying time-delays (FOINNs). Firstly, by correctly selected variable substitution, the system is transformed into a first-order fractional differential equation. Secondly, by building Lyapunov functionalities and using analytical techniques, as well as new control algorithms (which include the delay-dependent and delay-free controller), novel and effective criteria are established to attain the finite-time stabilization of the addressed system. Finally, two examples are used to illustrate the effectiveness and feasibility of the obtained results

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

Novel fixed-time stabilization of quaternion-valued BAMNNs with disturbances and time-varying coefficients

In this paper, with the quaternion number and time-varying coefficients introduced into traditional BAMNNs, the model of quaternion-valued BAMNNs are formulated. For the first time, fixed-time stabilization of time-varying quaternion-valued BAMNNs is investigated. A novel fixed-time control method is adopted, in which the choice of the Lyapunov function is more general than in most previous results. To cope with the noncommutativity of the quaternion multiplication, two different fixed-time control methods are provided, a decomposition method and a non-decomposition method. Furthermore, to reduce the control strength and improve control efficiency, an adaptive fixed-time control strategy is proposed. Lastly, numerical examples are presented to demonstrate the effectiveness of the theoretical results. © 2020 the Author(s), licensee AIMS Press

Nonlinear Systems

Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields, as highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods. The aim of this Special Issue is to highlight papers that show the dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. Potential topics include, but are not limited to: Stability analysis of discrete and continuous dynamical systems; Nonlinear dynamics in biological complex systems; Stability and stabilization of stochastic systems; Mathematical models in statistics and probability; Synchronization of oscillators and chaotic systems; Optimization methods of complex systems; Reliability modeling and system optimization; Computation and control over networked systems

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/

Mittag–Leffler synchronization for impulsive fractional-order bidirectional associative memory neural networks via optimal linear feedback control

In this paper, we are concerned with the synchronization scheme for fractional-order bidirectional associative memory (BAM) neural networks, where both synaptic transmission delay and impulsive effect are considered. By constructing Lyapunov functional, sufficient conditions are established to ensure the Mittag–Leffler synchronization. Based on Pontryagin’s maximum principle with delay, time-dependent control gains are obtained, which minimize the accumulative errors within the limitation of actuator saturation during the Mittag–Leffler synchronization. Numerical simulations are carried out to illustrate the feasibility and effectiveness of theoretical results with the help of the modified predictor-corrector algorithm and the forward-backward sweep method