This article explores the asymptotic stability of fractional delayed memristive neural networks with reaction-diffusion terms. A novel hybrid impulsive controller triggered by a specific event is proposed to stabilize the network, thereby replacing the conventional approach of modifying network parameters. The proposed controller is proven to prevent Zeno behavior. Sufficient conditions for the asymptotic stability of fractional delayed memristive neural networks with reaction-diffusion terms are established through Lyapunov direct method, inequality techniques, Green’s theorem and impulse analysis. Furthermore, the proposed controller is theoretically shown to be more resource-efficient than the conventional one, and our work extends existing research to make it more suitable for practical application such as pattern recognition, image processing and so on. Finally, an example is provided to illustrate the validity of the findings.

This study investigates the asymptotic synchronization in fractional memristive neural networks of the Riemann–Liouville type, considering mixed time delays and jump mismatches. Addressing the challenges associated with discrepancies in the circuit switching speed and the accuracy of the memristor, this paper introduces an enhanced model that effectively navigates these complexities. We propose two novel event-based hybrid impulsive controllers, each characterized by unique triggering conditions. Utilizing advanced techniques in inequality and hybrid impulsive control, we establish the conditions necessary for achieving synchronization through innovative Lyapunov functions. Importantly, the developed controllers are theoretically optimized to minimize control costs, an essential consideration for their practical deployment. Finally, the effectiveness of our proposed approach is demonstrated through two illustrative simulation examples.

We designed a kind of new vortex beam generator based on a planar all-dielectric metamaterial in the mid-infrared band. The height of this generator remains constant in the plane, and the effective refractive index increases gradually in the azimuthal direction which depends on subwavelength aperture columns with gradual diameters in the dielectric flat plate. Two types of vortex beam generators including transmissive- and reflective-type generators are designed where the thickness of the latter is half of the former. Simulation results show that both vortex beam generators successfully produce mid-infrared vortex beams with a topological charge number of one. This planar vortex beam generator based on a dielectric metamaterial has the advantages of simple structure, easy processing and low optical absorption.