Fractional-order Complex-valued Neural Networks Research Articles

Adaptive Strategies and its Application in the Mittag-Leffler Synchronization of Delayed Fractional-Order Complex-Valued Reaction-Diffusion Neural Networks

Adaptive Strategies and its Application in the Mittag-Leffler Synchronization of Delayed Fractional-Order Complex-Valued Reaction-Diffusion Neural Networks

Quasi-synchronization of fractional-order complex-value neural networks with discontinuous activations

In this paper, under the framework of Filippov solutions, quasi-synchronization issue of fractional-order complex-valued neural networks (FCNNs) with discontinuous activations and uncertainties is investigated. Firstly, using Laplace transform and the property of Mittag-Leffler function, a novel fractional differential inequality is derived. Then combining the newly constructed inequality with delay feedback control scheme, several quasi-synchronization conditions are obtained for the considered FCNNs by means of non-decomposable method. Eventually, a numerical example is provided to substantiate validation of the proposed results.

Multiple Mittag-Leffler Stability of Fractional-Order Complex-Valued Memristive Neural Networks With Delays.

This article discusses the coexistence and dynamical behaviors of multiple equilibrium points (Eps) for fractional-order complex-valued memristive neural networks (FCVMNNs) with delays. First, based on the state space partition method, some sufficient conditions are proposed to guarantee that there are multiple Eps in one FCVMNN. Then, the Mittag-Leffler stability of those multiple Eps is proved by using the Lyapunov function. Simultaneously, the enlarged attraction basins are obtained to improve and extend the existing theoretical results in the previous literature. In addition, some existing stability results in the literature are special cases of a new result herein. Finally, two illustrative examples with computer simulations are presented to verify the effectiveness of theoretical analysis.

Results on finite time stability of various fractional order systems

This article deals with the existence of the solution of Hilfer–Katugampola fractional derivatives, and we prove the stability results of the equilibrium point of the presented problem. Numerous authors have made substantial use of the concepts of fractional derivatives and fixed-point theory in order to produce stability results in neural networks containing complex-valued or real-valued inputs. In this connection, we discuss the finite stability of Caputo fractional derivatives as well as Caputo fractional-order complex-valued neural networks. We provide a numerical result that supports the theoretical discussion.

Anti-synchronization of fractional-order complex-valued neural networks with a leakage delay and time-varying delays

In this paper, the anti-synchronization for fractional-order complex-valued neural networks (FCVNNs) with a leakage delay and time-varying delays is investigated. The solution of a fractional-order differential inequality is considered. By using the Laplace transform and the inverse Laplace transform, a new inequality is proved, which provides an important tool for studying the anti-synchronization of the FCVNNs with delays. Two different types of controllers are designed. Based on this new inequality and some inequality techniques, several sufficient conditions are obtained to ensure the anti-synchronization of the FCVNNs with a leakage term and time-varying delays. Finally, two numerical examples are presented to illustrate the validity and feasibility of the main results.

Numerical simulations and complex valued fractional order neural networks via ([formula omitted] – μ)-uniformly contractive mappings

In this article, we present some fixed point results for (ɛ−μ)-uniformly contractive mappings and Ćirić–Riech–Rus type (ɛ−μ)-uniformly locally contractive mappings. As an application, the fixed point approach in suprametric spaces is used to examine the uniform stability problem of fractional-order complex-valued neural networks with time delay and equilibrium point results for impulsive fractional-order complex-valued neural networks with time delay. In addition, we used topological concepts such as compactness, closed convex sets, etc. instead of the traditional method that would have been used in the literature for many years. A few numerical results are provided to show the feasibility and correctness of the results presented.

Quasi-projective synchronization analysis of discrete-time FOCVNNs via delay-feedback control

In this article, the quasi-projective synchronization (QPS) issues about discrete-time fractional-order complex-valued neural networks (DFOCVNNs) are discussed. To realize QPS, the delay-feedback controllers are designed. The main advantage of this controller is that it can search for control gain parameters over a wider range. Applying inequality techniques, Lyapunov method and some lemmas related to discrete fractional calculus, some criteria for QPS are inferred. Meanwhile, the error bound is effectively estimated. Eventually, we display two examples to verify the obtained criteria.

Synchronization of Discrete-Time Fractional-Order Complex-Valued Neural Networks with Distributed Delays

This research investigates the synchronization of distributed delayed discrete-time fractional-order complex-valued neural networks. The necessary conditions have been established for the stability of the proposed networks using the theory of discrete fractional calculus, the discrete Laplace transform, and the theory of fractional-order discrete Mittag–Leffler functions. In order to guarantee the global asymptotic stability, adequate criteria are determined using Lyapunov’s direct technique, the Lyapunov approach, and some novel analysis techniques of fractional calculation. Thus, some sufficient conditions are obtained to guarantee the global stability. The validity of the theoretical results are finally shown using numerical examples.

Fixed-deviation stabilization and synchronization for delayed fractional-order complex-valued neural networks.

In this paper, we study fixed-deviation stabilization and synchronization for fractional-order complex-valued neural networks with delays. By applying fractional calculus and fixed-deviation stability theory, sufficient conditions are given to ensure the fixed-deviation stabilization and synchronization for fractional-order complex-valued neural networks under the linear discontinuous controller. Finally, two simulation examples are presented to show the validity of theoretical results.

Stability and Synchronization of Fractional-Order Complex-Valued Inertial Neural Networks: A Direct Approach

This paper is dedicated to the asymptotic stability and synchronization for a type of fractional complex-valued inertial neural network by developing a direct analysis method. First, a new fractional differential inequality is presented for nonnegative functions, which provides an effective tool for the convergence analysis of fractional-order systems. Moreover, instead of the previous separation analysis for complex-valued neural networks, a class of Lyapunov functions composed of the complex-valued states and their fractional derivatives is constructed, and some compact stability criteria are derived. In synchronization analysis, unlike the existing control schemes for reduced-order subsystems, some feedback and adaptive control schemes, formed by the linear part and the fractional derivative part, are directly designed for the response fractional inertial neural networks, and some synchronization conditions are derived using the established fractional inequality. Finally, the theoretical analysis is supported via two numerical examples.

Fixed-time synchronization of fractional-order complex-valued neural networks with time-varying delay via sliding mode control

Taking into account fractional-order complex-valued neural networks with time-varying delay, the issue of achieving fixed-time synchronization is discussed in this paper. By utilizing the properties of fractional calculus and fractional-order comparison principle, an improved lemma is proposed to derive the fixed-time synchronization conditions. On the basis of sliding model control and Lyapunov stability theorem, an effective sliding mode surface is constructed, which only uses the synchronization error information of FOCVNNs and is composed of fractional and integer integral terms. Further, a suitable sliding model control is constructed, which makes synchronization error converges to zero in a fixed-time. Beyond that, several sufficient conditions are posed to guarantee fixed-time synchronization of the fractional-order complex-valued neural networks and the upper bound of synchronization settling time is estimated. Finally, two numerical simulations are given to demonstrate the effectiveness of the presented theoretical results.

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.

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.

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

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

Global Exponential Stability of Fractional Order Complex-Valued Neural Networks with Leakage Delay and Mixed Time Varying Delays

This paper investigates the global exponential stability of fractional order complex-valued neural networks with leakage delay and mixed time varying delays. By constructing a proper Lyapunov-functional we established sufficient conditions to ensure global exponential stability of the fractional order complex-valued neural networks. The stability conditions are established in terms of linear matrix inequalities. Finally, two numerical examples are given to illustrate the effectiveness of the obtained results.

Impulsive Synchronization Control Mechanism for Fractional-Order Complex-Valued Reaction-Diffusion Systems With Sampled-Data Control: Its Application to Image Encryption

This article is devoted to gain a better understanding of the synchronization control mechanism in networked, complex-valued reaction-diffusion systems via an impulsive and sampled-data controller. Different from the traditional control methods with hybrid mechanism, an impulsive and sampled-data control scheme is proposed for fractional-order complex-valued reaction-diffusion neural networks (FRDCVNNs). By utilizing Lyapunov functional and inequality techniques, finite-time Mittag-Leffler synchronization criteria via an impulsive and sampled-data controller are established and presented as linear matrix inequalities (LMIs), which can ensure the finite-time synchronization of error system containing the drive and response dynamics. In addition, synchronization control mechanism on the considered system via impulsive actuator saturation and sampled-data control are applied. Simulation examples are provided to verify the efficacy of the proposed synchronization criterion and the results of practical application to image encryption scheme based on the chaotic complex system is presented. Furthermore, the proposed cryptosystem have obvious advantages of large key space and high security.

Adaptive Synchronization of Fractional-Order Complex-Valued Neural Networks With Time-Varying Delays

In this paper, the adaptive synchronization of fractional-order complex-valued neural networks with time-varying delays(FOCVNNTDs) is investigated. First, two novel fractional-order differential inequalities with time delays are established, which can be seen as an extension of Halanay inequality. Besides, complete synchronization and quasi-projective synchronization of FOCVNNTDs are investigated based on the two novel inequalities using a novel adaptive controller. In addition, instead of separating the complex-valued neural networks into two real-valued networks, a non-decomposition method is adopted to study the adaptive synchronization of FOCVNNTDs, which avoids the difficulty and complexity of theoretical analysis. Finally, some numerical simulation examples are provided to demonstrate the validity of our theory.