The finite-time Mittag-Leffler stability for fractional-order quaternion-valued memristive neural networks (FQMNNs) with impulsive effect is studied here. A new mathematical expression of the quaternion-value memductance (memristance) is proposed according to the feature of the quaternion-valued memristive and a new class of FQMNNs is designed. In quaternion field, by using the framework of Filippov solutions as well as differential inclusion theoretical analysis, suitable Lyapunov-functional and some fractional inequality techniques, the existence of unique equilibrium point and Mittag-Leffler stability in finite time analysis for considered impulsive FQMNNs have been established with the order $$0<\beta <1$$. Then, for the fractional order $$\beta $$ satisfying $$1<\beta <2$$ and by ignoring the impulsive effects, a new sufficient criterion are given to ensure the finite time stability of considered new FQMNNs system by the employment of Laplace transform, Mittag-Leffler function and generalized Gronwall inequality. Furthermore, the asymptotic stability of such system with order $$1<\beta <2$$ have been investigated. Ultimately, the accuracy and validity of obtained finite time stability criteria are supported by two numerical examples.

Finite-Time Mittag-Leffler Stability of Fractional-Order Quaternion-Valued Memristive Neural Networks with Impulses

Impulsive synchronization of coupled delayed neural networks with actuator saturation and its application to image encryption

Bifurcations in a fractional-order neural network with multiple leakage delays.

Enhanced Beetle Antennae Search with Zeroing Neural Network for online solution of constrained optimization

This paper discusses the quasi-uniform synchronization issue for fractional-orderneural networks (FONNs) with leakage and discrete delays. The impacts of leakage delay, discrete delay and fractional derivative on the quasi-uniform synchronization are simultaneously considered. By employing the Laplace transformation, the Gronwall inequality and analytical techniques, several sufficient criteria of the quasi-uniform synchronization for FONNs with leakage and discrete delays are established. The criterion conditions reveal the less conservatism because the order of fractional derivative is in the interval (0,2). The presented results are related to the classical exponential function, where it is not necessary to calculate fractional-order derivatives to reduce the complexities. Taking into account the different orders of fractional derivative, the validity and applicability of the proposed results are verified by the numerical simulations.

Quasi-uniform synchronization of Caputo type fractional neural networks with leakage and discrete delays★

This paper proposes a quaternion-valued one-layer recurrent neural network approach to resolve constrained convex function optimization problems with quaternion variables. Leveraging the novel generalized Hamilton-real (GHR) calculus, the quaternion gradient-based optimization techniques are proposed to derive the optimization algorithms in the quaternion field directly rather than the methods of decomposing the optimization problems into the complex domain or the real domain. Via chain rules and Lyapunov theorem, the rigorous analysis shows that the deliberately designed quaternion-valued one-layer recurrent neural network stabilizes the system dynamics while the states reach the feasible region in finite time and converges to the optimal solution of the considered constrained convex optimization problems finally. Numerical simulations verify the theoretical results.

Yanling Zheng

Papers

Constrained Quaternion-Variable Convex Optimization: A Quaternion-Valued Recurrent Neural Network Approach