In this article, the stability of quaternion-valued neural networks (QVNNs) with hybrid impulses is investigated, which contain stabilizing impulses and destabilizing impulses simultaneously. Through constructing the relationship between impulses and quaternions, this article has obtained a unified criterion for the global exponential stability of the system. First, a new form of impulsive representation is constructed, and the established systems can be decomposed into four different real parts. According to the characteristics of the impulses, the system divides the average interval of impulses (AII) into two cases, that is, T < ∞ and T = ∞, which can process hybrid impulses simultaneously. Second, for QVNNs, by using the method of matrix p-norm and the inequality technology, the criterion of each interval is derived. Considering the impulsive effects on the overall stability of QVNNs, the uniform criterion for the global exponential stability can be obtained. In addition, the convergence rate of QVNNs with hybrid impulses is also discussed. Finally, in order to verify the theoretical conclusions, some numerical simulations are given.

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<abstract><p>The studies of impulsive dynamical systems have been thoroughly explored, and extensive publications have been made available. This study is mainly in the framework of continuous-time systems and aims to give an exhaustive review of several main kinds of impulsive strategies with different structures. Particularly, (i) two kinds of impulse-delay structures are discussed respectively according to the different parts where the time delay exists, and some potential effects of time delay in stability analysis are emphasized. (ii) The event-based impulsive control strategies are systematically introduced in the light of several novel event-triggered mechanisms determining the impulsive time sequences. (iii) The hybrid effects of impulses are emphatically stressed for nonlinear dynamical systems, and the constraint relationships between different impulses are revealed. (iv) The recent applications of impulses in the synchronization problem of dynamical networks are investigated. Based on the above several points, we make a detailed introduction for impulsive dynamical systems, and some significant stability results have been presented. Finally, several challenges are suggested for future works.</p></abstract>

Because of the limited sound insulation provided by a single material, it is common to use multiple layers of materials to improve the effects of sound insulation, but multiple materials increase the size of the model. In some cases, there are limits to the size of the model, or, if subwavelength sizes are required, it is necessary to investigate wideband sound insulation of subwavelength size. We designed a coded topological spherical model on the subwavelength scale, with two materials arranged periodically according to the coding idea. The results showed that at the subwavelength scale, the sound insulation effect of the coded topological spherical model was very significant; the sound pressure after using sound insulation was near 0.3 Pa, but the incident sound pressure was 100 Pa. These results overcome the excessive thickness problem of traditional materials used in sound insulation, which has long puzzled researchers, and expands the application of new sound insulation materials in the energy collection field.

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Summary Over the past decades, various successful results have shown the discoveries and progress of impulsive synchronization. Yet, little attention has been devoted to the effects of the impulsive elasticity coefficient on network synchronization for both impulsive control problems and impulsive disturbance problems. In this work, we study impulsive pinning synchronization for coupled neural networks from a large delay perspective. Some flexible synchronization criteria are derived based on the average impulsive interval method. It has shown that synchronization of coupled neural networks with arbitrarily finite delay can be achieved via controlling a small fraction of nodes. Specifically, by applying a strict comparison principle for impulsive delayed neural networks, the effects of the impulsive elasticity coefficient on synchronization are revealed to be dissimilar from the case of delay‐free neural networks. One can verify that increasing the elasticity coefficient may bring a desynchronizing impact on the original synchronized networks. More ulteriorly, the generated criteria will still hold if the delay is sufficiently large, which implies that the delay is independent of the size of the impulsive interval. Our work is an essential step toward investigating the role of the elasticity coefficient on synchronization. Furthermore, the synchronization region of different impulsive weights, impulsive intervals, and impulsive control proportions are described thoroughly.