Fractional-order Neural Networks Research Articles

Global Synchronization of Fractional-Order Multi-Delay Coupled Neural Networks with Multi-Link Complicated Structures via Hybrid Impulsive Control

This study discusses the global asymptotical synchronization of fractional-order multi-delay coupled neural networks (FMCNNs) via hybrid control schemes. In addition to internal delays and different coupling delays, more importantly, multi-link complicated structures are introduced into our model. Unlike most existing works, the synchronization target is not the special solution of an isolated node, and a more universally accepted synchronization goal involving the average neuron states is introduced. A generalized multi-delay impulsive comparison principle with fractional order is given to solve the difficulties resulting from different delays and multi-link structures. To reduce control costs, a pinned node strategy based on the principle of statistical sorting is provided, and then a new hybrid impulsive pinning control method is established. Based on fractional-order impulsive inequalities, Laplace transforms, and fractional order stability theory, novel synchronization criteria are derived to guarantee the asymptotical synchronization of the considered FMCNN. The derived theoretical results can effectively extend the existing achievements for fractional-order neural networks with a multi-link nature.

Dynamic Behavior of a Class of Six-Neuron Fractional BAM Neural Networks

In this paper, the stability and Hopf bifurcation of a six-neuron fractional BAM neural network model with multiple delays are considered. By transforming the multiple-delays model into a fractional-order neural network model with a delay through the variable substitution, we prove the conditions for the existence of Hopf bifurcation at the equilibrium point. Finally, our results are verified by numerical simulations.

Dynamical detections of a fractional-order neural network with leakage, discrete and distributed delays

Dynamical detections of a fractional-order neural network with leakage, discrete and distributed delays

Finite-time [formula omitted]-almost periodic synchronization of fractional-order octonion-valued Hopfield neural networks

In this paper, we consider a fractional-order octonion-valued Hopfield neural network. Based on the fixed point theorem and analytical technique, we first establish the existence and uniqueness of Sp-almost periodic solutions of the network by direct method. Then, we take the fractional-order octonion-valued Hopfield neural network as the driving system and introduce the corresponding response system to study their finite-time synchronization. Finally, we use an example to illustrate the validity of our results. Even when the neural network under consideration degenerates into real-valued one, our results are completely new.

Hybrid Impulsive Feedback Control for Drive–Response Synchronization of Fractional-Order Multi-Link Memristive Neural Networks with Multi-Delays

This article addresses the issue of drive–response synchronization in fractional-order multi-link memristive neural networks (FMMNN) with multiple delays, under hybrid impulsive feedback control. To address the impact of multiple delays on system synchronization, an extended fractional-order delayed comparison principle incorporating impulses is established. By leveraging Laplace transform, Mittag–Leffler functions, the generalized comparison principle, and hybrid impulsive feedback control schemes, several new sufficient conditions are derived to ensure synchronization in the addressed FMMNN. Unlike existing studies on fractional-order single-link memristor-based systems, our response network is a multi-link model that considers impulsive effects. Notably, the impulsive gains αi are not limited to a small interval, thus expanding the application range of our approach (αi∈(−2,0)∪(−∞,−2)∪(0,+∞)). This feature allows one to choose impulsive gains and corresponding impulsive intervals that are appropriate for the system environment and control requirements. The theoretical results obtained in this study contribute to expanding the relevant theoretical achievements of fractional-order neural networks incorporating memristive characteristics.

Dynamical Analysis of the Incommensurate Fractional-Order Hopfield Neural Network System and Its Digital Circuit Realization

Dynamical analysis of the incommensurate fractional-order neural network is a novel topic in the field of chaos research. This article investigates a Hopfield neural network (HNN) system in view of incommensurate fractional orders. Using the Adomian decomposition method (ADM) algorithm, the solution of the incommensurate fractional-order Hopfield neural network (FOHNN) system is solved. The equilibrium point of the system is discussed, and the dissipative characteristics are verified and discussed. By varying the order values of the proposed system, different dynamical behaviors of the incommensurate FOHNN system are explored and discussed via bifurcation diagrams, the Lyapunov exponent spectrum, complexity, etc. Finally, using the DSP platform to implement the system, the results are in good agreement with those of the simulation. The actual results indicate that the system shows many complex and interesting phenomena, such as attractor coexistence and an inversion property, with dynamic changes of the order of q0, q1, and q2. These phenomena provide important insights for simulating complex neural system states in pathological conditions and provide the theoretical basis for the later study of incommensurate fractional-order neural network systems.

Asymptotic synchronization of conformable fractional-order neural networks by L’ Hopital’s rule

This paper focuses on the globally asymptotic synchronization (GAS) for delayed drive-response (DR) conformable fractional-order neural networks (CFONNS). Two differential inequalities (DIS) of conformable fractional-order (FO) are established, which play a central role in studying the GAS of DR CFONNS. By applying the new established two DIS of conformable FO and using L’ Hopital’s rule and limit algorithms of functions, two criteria on the GAS for the discussing networks are obtained. Since the studies on the synchronization for the CFONNS are very rare, the studies for the CFONNS are of important meaning in theory.

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.

Evaluation of the performance of a FONN-based MPPT control for a photovoltaic watering system

This study aims to increase the effectiveness of photovoltaic pumping systems. A practical installation and cost-effective design are suggested. This paper examines the nonlinear behaviour of photovoltaic generators from a distinct perspective; where it repeatedly transitions between a constant current and a constant voltage source and shows how this affects the behaviour of the induction motors. A Fractional-order Neural Network (FONN) is suggested to forecast the harvested solar-energy. The results showed that FONN improved forecasting accuracy by effectively capturing the nonlinear behaviour of PV panels. A Fractional Order MPPT (FO-MPPT) control augmented with Gray Wolf, Anti-lion, and Whale metaheuristic optimizers is proposed and shows capacity to maximize the harvest power for the PV-driven Induction Motor-Pump. The proposed FO-MPPT is compared to conventional techniques using several performance metrics. According to the comparison study, the optimized FO-MPPT enhances the standard MPPT and shows superiority in managing the nonlinear and unpredictable dynamical loads.

Hopf bifurcation in a fractional-order neural network with self-connection delay

Hopf bifurcation in a fractional-order neural network with self-connection delay

Multi-UUV Maneuvering Counter-Game for Dynamic Target Scenario Based on Fractional-Order Recurrent Neural Network.

In this article, a multi-underwater unmanned vehicle (UUV) maneuvering decision-making algorithm is proposed for a counter-game with a dynamic target scenario. The game is modeled with interval-valued intuitionistic fuzzy rules, and an optimal maneuvering strategy is realized using a fractional-order recurrent neural network (RNN). First, underwater environments with weak connectivity, underwater noise, and dynamic uncertainties are analyzed and incorporated into the interval-valued intuitionistic fuzzy set. Then, the maneuvering decision-making model and the expected return of the multi-UUV countermeasure are designed based on the interval-valued intuitionistic fuzzy rules. Subsequently, to optimize the counter-game maneuvering strategy, a fractional-order RNN is formulated based on the Karush-Kuhn-Tucker optimality conditions. In addition, the existence and uniqueness of the optimal maneuvering solutions as well as the stability of the equilibrium point are discussed. Finally, simulation and experimental results are compared to determine the effectiveness of the proposed algorithm. The influence of the fractional order on the convergence rate and optimization error of the proposed algorithm is also minutely examined.

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.

Function matrix projective synchronization for unknown and delayed fractional-order neural network

Function matrix projective synchronization for unknown and delayed fractional-order neural network

Stabilization of reaction–diffusion fractional-order memristive neural networks

This paper investigates the stabilization control of fractional-order memristive neural networks with reaction–diffusion terms. With regard to the reaction–diffusion model, a novel processing method based on Hardy–Poincarè inequality is introduced, as a result, the diffusion terms are estimated associated with the information of the reaction–diffusion coefficients and the regional feature, which may be beneficial to obtain conditions with less conservatism. Then, based on Kakutani’s fixed point theorem of set-valued maps, new testable algebraic conclusion for ensuring the existence of the system’s equilibrium point is obtained. Subsequently, by means of Lyapunov stability theory, it is concluded that the resulting stabilization error system is global asymptotic/Mittag-Leffler stable with a prescribed controller. Finally, an illustrative example about is provided to show the effectiveness of the established results.

Finite-time synchronization of fractional-order delayed memristive fuzzy neural networks

This paper deals with the finite-time synchronization (FTS) for a class of fractional-order memristive fuzzy neural networks (FOMFNNs) with leakage and transmission delays. Two types of discontinuous control schemes with leakage and transmission delays are designed: one is the state feedback control and the other is the fractional-order adaptive control. Based on differential inclusion theory and fractional-order differential inequalities, several new delay-independent algebraic conditions are derived to guarantee the FTS of drive-response FOMFNNs with leakage and transmission delays. Moreover, the estimation of the upper bound of the settling time for the FTS is given as well. Ultimately, two numerical examples with simulations are furnished to demonstrate the feasibility and availability of the theoretical results.

New Result on Finite-Time Stability for Caputo–Katugampola Fractional-Order Neural Networks with Time Delay

New Result on Finite-Time Stability for Caputo–Katugampola Fractional-Order Neural Networks with Time Delay

Quasi-synchronization of discrete-time fractional-order quaternion-valued memristive neural networks with time delays and uncertain parameters

In this paper, quasi-synchronization of discrete-time fractional-order quaternion-valued memristive neural networks (DTFQMNNs) with time delays and uncertain parameters is investigated. Firstly, some related preliminaries are introduced and two new inequalities are obtained based on nabla fractional difference, quaternion theory and nabla h-Laplace transform. Then, a quaternion-valued controller with time delay is designed to realize quasi-synchronization goal, and some sufficient criteria are derived to guarantee quasi-synchronization of DTFQMNNs by using our created inequalities and some analysis techniques. Finally, a numerical example is provided to verify the correctness of our theoretical results.

Output feedback passification of a class of fractional-order static neural networks

In this paper, a linear matrix inequality (LMI)-based design is proposed for the passivity-based output feedback control problem of fractional-order static neural networks (FOSNNs). Different from the current works, the studied model is the static fractional-order neural network. The novel convex Lyapunov function is constructed to obtain new conditions for the existence of output feedback controllers which guarantee the closed-loop systems are passive. In addition, we also extend the obtained results to generalized fractional-order neural networks. A numerical example is presented to verify the proposed results.

Quasi-Synchronization and Dissipativity Analysis for Fractional-Order Neural Networks with Time Delay

The objective of this research is to examine the global dissipativity and quasi-synchronization of fractional-order neural networks (FNNs). A global dissipativity criterion is established through the creation of an appropriate Lyapunov function, together with some fractional-order inequality techniques. Additionally, the issue of quasi-synchronization for drive-response FNNs is investigated using linear state feedback control. The study reveals the synchronization error converges to a bounded region by choosing an appropriate control parameter. Finally, the effectiveness of the obtained works are validated through three numerical examples.

Stabilization control of quaternion-valued fractional-order discrete-time memristive neural networks

In this paper, the stabilization control of the memristive neural networks with discrete-time terms and fractional derivative is proposed. By employing the Lyapunov functional method and fully considering the integrity of the quaternion system, some sufficient criteria are derived based on nonlinear scalarization approach and several inequality techniques. The stabilization criteria are established in the form of algebraic inequality, which can be directly resolved by a simple calculation. Finally, two numerical examples are proposed to demonstrate the validity of theoretical results.