Fractional-order Neural Networks Research Articles

Finite-time Mittag–Leffler synchronization of fractional-order complex-valued memristive neural networks with time delay

Without dividing the complex-valued systems into two real-valued ones, a class of fractional-order complex-valued memristive neural networks (FCVMNNs) with time delay is investigated. Firstly, based on the complex-valued sign function, a novel complex-valued feedback controller is devised to research such systems. Under the framework of Filippov solution, differential inclusion theory and Lyapunov stability theorem, the finite-time Mittag–Leffler synchronization (FTMLS) of FCVMNNs with time delay can be realized. Meanwhile, the upper bound of the synchronization settling time (SST) is less conservative than previous results. In addition, by adjusting controller parameters, the global asymptotic synchronization of FCVMNNs with time delay can also be realized, which improves and enrich some existing results. Lastly, some simulation examples are designed to verify the validity of conclusions.

Uniform Stability of a Class of Fractional-Order Fuzzy Complex-Valued Neural Networks in Infinite Dimensions

In this paper, the problem of the uniform stability for a class of fractional-order fuzzy impulsive complex-valued neural networks with mixed delays in infinite dimensions is discussed for the first time. By utilizing fixed-point theory, theory of differential inclusion and set-valued mappings, the uniqueness of the solution of the above complex-valued neural networks is derived. Subsequently, the criteria for uniform stability of the above complex-valued neural networks are established. In comparison with related results, we do not need to construct a complex Lyapunov function, reducing the computational complexity. Finally, an example is given to show the validity of the main results.

Lag quasi-synchronization of incommensurate fractional-order memristor-based neural networks with nonidentical characteristics via quantized control: A vector fractional Halanay inequality approach

This work realizes lag quasi-synchronization of incommensurate fractional-order memristor-based neural networks (FMNNs) with nonidentical characteristics via quantized control. The motivations behind this research work are threefold: (1) quantized controllers, which generate discrete control signals, can be more easily realized in computers than non-quantized controllers, and can consume smaller communication capacity; (2) incommensurate orders in a single FMNN and nonidentical characteristics in drive-response FMNNs are inescapable due to the differences among the circuit elements used to implement FMNNs; (3) convergence analysis of delayed incommensurate fractional-order nonlinear systems, which is the basis for the derivation of synchronization criterion, has not been handled perfectly. As an effective tool for convergence analysis of delayed incommensurate fractional-order nonlinear systems, especially for estimation of ultimate state bound, a vector fractional Halanay inequality is established at first. Then, a quantized synchronization controller, in which the dead-zone is introduced into some logarithmic quantizers to avoid chattering phenomenon, is designed. By means of vector Lyapunov function together with the newly derived vector fractional Halanay inequality, the synchronization criterion is proved theoretically. Lastly, numerical simulations supplementarily illustrate the correctness of the synchronization criterion. In contrast with the hypotheses in the relevant literature, the hypotheses in this paper are weaker.

Quasi-Synchronization and Quasi-Uniform Synchronization of Caputo Fractional Variable-Parameter Neural Networks with Probabilistic Time-Varying Delays

Owing to the symmetry between drive–response systems, the discussions of synchronization performance are greatly significant while exploring the dynamics of neural network systems. This paper investigates the quasi-synchronization (QS) and quasi-uniform synchronization (QUS) issues between the drive–response systems on fractional-order variable-parameter neural networks (VPNNs) including probabilistic time-varying delays. The effects of system parameters, probability distributions and the order on QS and QUS are considered. By applying the Lyapunov–Krasovskii functional approach, Hölder’s inequality and Jensen’s inequality, the synchronization criteria of fractional-order VPNNs under controller designs with constant gain coefficients and time-varying gain coefficients are derived. The obtained criteria are related to the probability distributions and the order of the Caputo derivative, which can greatly avoid the situation in which the upper bound of an interval with time delay is too large yet the probability of occurrence is very small, and information such as the size of time delay and probability of occurrence is fully considered. Finally, two examples are presented to further confirm the effectiveness of the algebraic criteria under different probability distributions.

Probing into bifurcation for fractional-order BAM neural networks concerning multiple time delays

This paper mainly examines the stability and the existence of Hopf bifurcation of fractional-order BAM neural networks with multiple delays. Based on Laplace transform, stability criterion and Hopf bifurcation theory of fractional-order differential equations, a new sufficient criterion to guarantee the stability and the existence of Hopf bifurcation for the involved fractional-order BAM neural networks with multiple delays is established. The investigation manifests that time delay plays an important role in maintaining network stability and controlling the appearance of Hopf bifurcation of fractional-order BAM neural networks. Numerical simulations are performed to check the rationality of the analytical conclusions. The obtained theoretical predictions of this paper have extremely vital guiding significance in designing and controlling networks.

Finite-Time Synchronization of Fractional-Order Complex-Valued Cohen-Grossberg Neural Networks with Mixed Time Delays and State-Dependent Switching

This paper discussed the finite-time synchronization of fractional-order complex-valued Cohen-Grossberg neural networks (FCVCGNNs), which contain mixed time delays and state-dependent switching that make the model more comprehensive. Different from other methods, we use a method of nonseparating real and imaginary parts to get our conclusions. By applying fractional-order inequalities and the Lyapunov function, effective controllers with suitable conditions are derived. Additionally, the maximum time for the drive-response system to reach synchronization is also given. Finally, numerical examples are designed to illustrate the effectiveness of our obtained theoretical results.

Finite-time synchronisation of delayed fractional-order coupled neural networks

This paper considers the global synchronisation and finite-time synchronisation for a class of delayed fractional-order complex neural networks (DFOCNNs). Based on the properties of fractional-order calculus and the Razumikhin-type Lyapunov theorem of a fractional-order system, two new lemmas are proved. These lemmas are employed to formulate a couple of novel criteria for both finite-time synchronisation and global synchronisation of DFOCNNs. Moreover, the upper bound of the setting time for synchronisation is given. Three examples are provided to verify the effectiveness of the obtained results.

Exploration of bifurcation for a fractional-order BAM neural network with n+2 neurons and mixed time delays

This article aims to deal with the stability and Hopf bifurcation analysis for a type of fractional-order bidirectional associative memory (BAM) neural network involving two neurons in the X-layer and n neurons in the Y-layer, respectively. In view of the universal existence and multiplicity of time delay in many real systems, leakage delay and nonuniform communication delays are both taken into account. Coates’s flow-graph formula is efficiently adopted to solve the high-order characteristic equation of the associated linearized system. By making some assumptions on the mixed time delays, the obtained characteristic equation only contains the leakage delay, which is selected as the bifurcation parameter. Utilizing the discriminated criteria of stability for fractional-order dynamical systems and Hopf bifurcation theory, we obtain the critical value of the bifurcation point, greater than which the Hopf bifurcation would occur. Particularly, the stability and Hopf bifurcation is also analyzed for the case of no leakage delay to get an insight into the effect of the leakage delay. Finally, the validity of our theoretical results is substantiated through a simulation example.

New results of quasi-projective synchronization for fractional-order complex-valued neural networks with leakage and discrete delays

In this paper, the non-decomposition method is employed to investigate the quasi-projective synchronization of fractional-order complex-valued neural networks (FOCVNNs) with leakage and discrete delays. Firstly, two new inequalities are established in complex domain, which provides a powerful tool to explore the synchronization and stability of complex-valued systems. Secondly, by means of the Banach fixed point theorem, the existence and uniqueness of solution of the delayed FOCVNNs is discussed under certain conditions. Thirdly, a linear complex-valued controller is designed to induce quasi-projective synchronization of the delayed FOCVNNs, and some novel results are given by using the presented inequalities, the non-decomposition method and the Lyapunov stability theory. Further, the error bounds are estimated. It is found that a smaller error bound can be obtained by appropriately increasing the feedback gains. Finally, two numerical examples are given to verify the effectiveness of the theoretical results and the practicability of the synchronization strategy in secure communication.

Quasi-projective Synchronization for Caputo Type Fractional-order Complex-valued Neural Networks with Mixed Delays

Quasi-projective Synchronization for Caputo Type Fractional-order Complex-valued Neural Networks with Mixed Delays

Results on passivity analysis of delayed fractional-order neural networks subject to periodic impulses via refined integral inequalities

Results on passivity analysis of delayed fractional-order neural networks subject to periodic impulses via refined integral inequalities

New results for the stability of fractional-order discrete-time neural networks

Fractional-order discrete-time neural networks represent a class of discrete systems described by non-integer order difference operators. Even though the stability of these networks is a prerequisite for their successful applications, very few papers have been published on this topic. This paper aims to make a contribution to these stability issues by presenting a network model based on the nabla Caputo h-discrete operator and by proving its Mittag–Leffler stability. Additionally, a class of variable fractional-order discrete-time neural network is introduced and a novel theorem is proved to assure its asymptotic stability. Finally, simulation results are carried out to highlight the effectiveness of the stability approach illustrated herein.

New finite-time passivity criteria for delayed fractional-order neural networks based on Lyapunov function approach

This paper deals with the problem of finite-time passivity analysis for a class of fractional-order neural networks with constant time delay. Firstly, based on the existing passivity definition, some new concepts namely, finite-time passivity, finite-time input strict passivity, finite-time output strict passivity, and finite-time strict passivity are introduced in terms of Lyapunov function for fractional-order neural networks. In this paper, for the first time, by defining an appropriate controller and by exploiting the introduced definitions, some novel delay-dependent and order-dependent sufficient conditions ensuring the passivity performances are obtained for the addressed system. In addition, the finite-time stability conditions are also presented with an explicit formula for determining the value of setting time for stability. Finally, one numerical example is given to verify the effectiveness of the obtained theoretical results and the simulation results are provided for better understanding of the proposed problem.

Fractional Order Neural Transient Modeling of Primary Circuit of ACP1000 Based Nuclear Power Plant in LabVIEW

The primary circuit of the nuclear power plant is the most advanced and sophisticated loop of the Advanced Chinese Pressurized Water Reactor (ACP1000). The primary circuit is composed of most technologically advanced nuclear systems and controllers. In this research work, closed loop dynamics of primary circuit (CLPC) of ACP1000 based nuclear power plant is identified. The closed loop dynamics is comprised of highly nonlinear coupled sevencontrol systems. The turbine power, pressurizer temperature, cold leg temperature, hot leg temperature, coolant average temperature and feed water flow are the selected parameters of interest as inputs while neutron power, reactor coolant pressure, pressurizer level, steam generator pressure, steam generator level and steam generator flow as outputs. Therefore, a closed loop multi-input multi-out (MIMO) is configured. The control oriented closed loop dynamics of the primary circuit of ACP1000 is estimated by state-of-the-art novel fractional order neural network (FO-ANN) tool developed in LabVIEW. The parameters of FO-ANN of CLPC (FO-ANN-CLPC) are optimized using fractional order backpropagation (FO-BP) algorithm. The performance of FO-ANN-CLPC is tested and validated in transient conditions and the proposed model predicted the desired reactor power with minimizing error function. The robust performance of the proposed closed loop model is evaluated by dynamic simulation for a prescribed turbine load power increase transient from 20 % to 100 % and validated against reactor power and behaviour of various thermal hydraulics parameters are observed and analyzed.

Global asymptotic stability of delayed fractional-order complex-valued fuzzy cellular neural networks with impulsive disturbances

Global asymptotic stability of delayed fractional-order complex-valued fuzzy cellular neural networks with impulsive disturbances

A 6D Fractional-Order Memristive Hopfield Neural Network and its Application in Image Encryption

This paper proposes a new memristor model and uses pinched hysteresis loops (PHL) to prove the memristor characteristics of the model. Then, a new 6D fractional-order memristive Hopfield neural network (6D-FMHNN) is presented by using this memristor to simulate the induced current, and the bifurcation characteristics and coexistence attractor characteristics of fractional memristor Hopfield neural network is studied. Because this 6D-FMHNN has chaotic characteristics, we also use this 6D-FMHNN to generate a random number and apply it to the field of image encryption. We make a series of analysis on the randomness of random numbers and the security of image encryption, and prove that the encryption algorithm using this 6D-FMHNN is safe and sensitive to the key.

Dynamic Analysis and Bifurcation Study on Fractional-Order Tri-Neuron Neural Networks Incorporating Delays

In this manuscript, we principally probe into a class of fractional-order tri-neuron neural networks incorporating delays. Making use of fixed point theorem, we prove the existence and uniqueness of solution to the fractional-order tri-neuron neural networks incorporating delays. By virtue of a suitable function, we prove the uniformly boundedness of the solution to the fractional-order tri-neuron neural networks incorporating delays. With the aid of the stability theory and bifurcation knowledge of fractional-order differential equation, a new delay-independent condition to guarantee the stability and creation of Hopf bifurcation of the fractional-order tri-neuron neural networks incorporating delays is established. Taking advantage of the mixed controller that contains state feedback and parameter perturbation, the stability region and the time of onset of Hopf bifurcation of the fractional-order trineuron neural networks incorporating delays are successfully controlled. Software simulation plots are displayed to illustrate the established key results. The obtained conclusions in this article have important theoretical significance in designing and controlling neural networks.

Passivity Analysis of Fractional-Order Neutral-Type Fuzzy Cellular BAM Neural Networks with Time-Varying Delays

In this paper, passivity analysis of fractional-order neutral-type fuzzy cellular bidirectional associative memory (BAM) neural networks with time-varying delays is investigated. Based on the Lyapunov–Krasovskii functional, delay-dependent sufficient conditions for solvability of the passive problem are obtained in terms of linear matrix inequalities (LMIs), which can be easily checked by using the MATLAB LMI toolbox. Finally, numerical examples are provided to show the effectiveness of the main results.

Hybrid control design for Mittag-Leffler projective synchronization on FOQVNNs with multiple mixed delays and impulsive effects

This article discusses the global Mittag-Leffler projective synchronization (GM-LPS) on fractional-order quaternion-valued neural networks (FOQVNNs) including mixed delays and impulses. The effects of various types of delay factors and impulses on Mittag-Leffler projective synchronization performance are simultaneously explored. Based on Banach contractive mapping principle, the existence result of solution to the considered systems is derived Applying the Lyapunov direct method, inequality analysis technique and generalized fractional Razumikhin theorem, the algebraic criteria for ensuring global Mittag-Leffler projective synchronization by designing the hybrid controllers are proposed. The result of algebraic inequality greatly reduces the computational complexity to some extent. Combining the different orders of Caputo derivative and MATLAB toolbox, the simulations are given to further validate the obtained results.

Finite-time reliable sampled-data control for fractional-order memristive neural networks with quantisation

ABSTRACT This paper addresses the reliable finite-time stabilisation problem for a class of fractional-order memristor neural networks under sampled-data controller influenced by the quantisation signal and actuator failures. Precisely, the framework of observer has been initiated for estimating unmeasured state and remunerate the actuator faults with nonlinearities in the controller. Precisely, quantiser is incorporated in the network can reduce the process of transmitting data. Subsequently, activation function approach bringing together with traditional indirect Lyapunov theory endows some sufficient conditions in the frame of linear matrix inequalities to assure the finite-time stabilisation criterion for the addressed neural networks under the proposed reliable sampled-data control. Explicitly, the state feedback control and observer gain matrices are attained by solving the developed linear matrix inequalities. Convincingly, two numerical simulations are explored to substantiate the excellence and potentiality of the developed control law.