Lagrange stability of memristive quaternion-valued neural networks with neutral items

Stability and pinning synchronization of delayed memristive neural networks with fractional-order and reaction-diffusion terms

Global asymptotic stability and synchronization are explored in this paper for fractional delayed memristive neural networks with reaction-diffusion terms (FDRDMNNs) in sense of Riemann-Liouville. First, we introduce diffusion into the existing model of fractional delayed memristive neural networks. Next, in terms of Green's theorem and inequality technique, a less conservative criterion for the asymptotic stability of FDRDMNNs is given by endowing Lyapunov direct method. Then, the appropriate pinning feedback controllers and adaptive controllers are designed to achieve the synchronization of the FDRDMNNs, and two sufficient conditions for global asymptotic synchronization are acquired. In addition, the results based on algebraic inequalities enhance some existing ones. The numerical simulations finally verify the validity of the derived results.

Personalized Teaching Strategy of University Ideology Course Based on Lagrange Neural Network and Big Data Technology

Individualized instruction is a type of educational principle. On the one hand, it necessitates the creation of individualized teaching resources, courses, and methods. Students, on the other hand, require a high level of autonomy and the ability to make personalized plans based on their own cognitive characteristics and needs. The big data (BD) era opens up new possibilities for IE (ideological education) work in universities, but it also poses some challenges. IE development will be greatly aided by recognizing opportunities to meet challenges and optimizing and integrating PL (political lesson) resources. The LNN (Lagrange neural network) model has been established. The simulation results show that the LNN network can converge to the optimal solution quickly and effectively and then reconstruct sparse signals. Individualized college PL instruction using LNN and BD technology helps students communicate more effectively and improves the pertinence, immediacy, and positivity of IE.

Global Stabilization of a Single-Species Ecosystem with Markovian Jumping under Neumann Boundary Value via Laplacian Semigroup

By applying impulsive control, this work investigated the global stabilization of a single-species ecosystem with Markovian jumping, a time delay and a Neumann boundary condition. Variational methods, a fixed-point theorem, and Laplacian semigroup theory were employed to derive the unique existence of the global stable equilibrium point, which is a positive number. Numerical examples illuminate the feasibility of the proposed methods.