Synchronization of a class of fractional-order neural networks with multiple time delays by comparison principles

This paper studies the synchronization of fractional-order neural networks with multiple time delays. Based on an inequality of fractional-order and comparison principles of linear fractional equation with multiple time delays, some sufficient conditions for synchronization of master-slave systems are obtained. Example and related simulations are given to demonstrate the feasibility of the theoretical results

New results of global Mittag-Leffler synchronization on Caputo fuzzy delayed inertial neural networks

This article is devoted to discussing the problem of global Mittag-Leffler synchronization (GMLS) for the Caputo-type fractional-order fuzzy delayed inertial neural networks (FOFINNs). First of all, both inertial and fuzzy terms are taken into account in the system. For the sake of reducing the influence caused by the inertia term, the order reduction is achieved by the measure of variable substitution. The introduction of fuzzy terms can evade fuzziness or uncertainty as much as possible. Subsequently, a nonlinear delayed controller is designed to achieve GMLS. Utilizing the inequality techniques, Lyapunov’s direct method for functions and Razumikhin theorem, the criteria for interpreting the GMLS of FOFINNs are established. Particularly, two inferences are presented in two special cases. Additionally, the availability of the acquired results are further confirmed by simulations

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

Global exponential synchronization of quaternion-valued memristive neural networks with time delays

This paper extends the memristive neural networks (MNNs) to quaternion field, a new class of neural networks named quaternion-valued memristive neural networks (QVMNNs) is then established, and the problem of drive-response global synchronization of this type of networks is investigated in this paper. Two cases are taken into consideration: one is with the conventional differential inclusion assumption, the other without. Criteria for the global synchronization of these two cases are achieved respectively by appropriately choosing the Lyapunov functional and applying some inequality techniques. Finally, corresponding simulation examples are presented to demonstrate the correctness of the proposed results derived in this paper

Lur’e Postnikov Lyapunov functional technique to global Mittag-Leffler stability of fractional-order neural networks with piecewise constant argument

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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

An improved data classification framework based on fractional particle swarm optimization

Particle Swarm Optimization (PSO) is a population based stochastic optimization technique which consist of particles that move collectively in iterations to search for the most optimum solutions. However, conventional PSO is prone to lack of convergence and even stagnation in complex high dimensional-search problems with multiple local optima. Therefore, this research proposed an improved Mutually-Optimized Fractional PSO (MOFPSO) algorithm based on fractional derivatives and small step lengths to ensure convergence to global optima by supplying a fine balance between exploration and exploitation. The proposed algorithm is tested and verified for optimization performance comparison on ten benchmark functions against six existing established algorithms in terms of Mean of Error and Standard Deviation values. The proposed MOFPSO algorithm demonstrated lowest Mean of Error values during the optimization on all benchmark functions through all 30 runs (Ackley = 0.2, Rosenbrock = 0.2, Bohachevsky = 9.36E-06, Easom = -0.95, Griewank = 0.01, Rastrigin = 2.5E-03, Schaffer = 1.31E-06, Schwefel 1.2 = 3.2E-05, Sphere = 8.36E-03, Step = 0). Furthermore, the proposed MOFPSO algorithm is hybridized with Back-Propagation (BP), Elman Recurrent Neural Networks (RNN) and Levenberg-Marquardt (LM) Artificial Neural Networks (ANNs) to propose an enhanced data classification framework, especially for data classification applications. The proposed classification framework is then evaluated for classification accuracy, computational time and Mean Squared Error on five benchmark datasets against seven existing techniques. It can be concluded from the simulation results that the proposed MOFPSO-ERNN classification algorithm demonstrated good classification performance in terms of classification accuracy (Breast Cancer = 99.01%, EEG = 99.99%, PIMA Indian Diabetes = 99.37%, Iris = 99.6%, Thyroid = 99.88%) as compared to the existing hybrid classification techniques. Hence, the proposed technique can be employed to improve the overall classification accuracy and reduce the computational time in data classification applications