Recently, the study of random nonlinear systems driven by second-order moment processes rather than Brownian motion has attracted increasing attention. This paper investigates random reaction–diffusion neural networks with time-varying delay. An integral-type boundary controller is designed, and sufficient conditions are derived to ensure asymptotic stability while revealing the influence of system parameters and time delay on stability. Under weaker assumptions, the noise-to-state stability of the controlled system is further established. This work constitutes an initial attempt to study random systems in a partial differential equation setting, particularly for time-delay reaction–diffusion equations. Finally, numerical simulations are presented to verify the theoretical results.
Nonreciprocal circulators have enabled robust topological edge transport in acoustic systems, yet creating their passive nonreciprocal counterparts in mechanics is a challenge: existing mechanical topological systems based on the Maxwell framework are largely limited to quasi-static responses and are generally incapable of supporting mechanical signal transport along complex pathways. Here, we propose and experimentally validate a passive, highly nonlinear, and nonreciprocal mechanical circulator based on angular bias, achieving giant nonreciprocal transmission of mechanical displacement signals with strong isolation. Building on this design, we further develop a mechanical reflection mechanism and realize a mechanical topological-like insulator assembled from multiple circulators, in which mechanical signals propagate as transition waves rather than conventional harmonic waves. Although the intrinsic nonlinearity of the system prevents a rigorous definition of topological invariants, experiments demonstrate stable topological-like transport featuring edge localization, robustness against sharp corners and defects, and pronounced nonreciprocity. Our work extends nonreciprocal circulators to nonlinear mechanics and advances topological-like mechanical behavior from static response to dynamic transport.
Piezo-On-Insulator (POI) wafers are gaining more and more popularity for the design of Long Term Evolution and 5G telecommunication filters on a spectral range spreading from 600 MHz to 3.5 GHz and even above. For all these applications, a critical need for spectral purity control is imposed by the coexistence of the multiple bands composing the communication modules. The POI wave guide structure naturally induces the possible existence of spurious elastic wave contributions which can be minimized according to the various stack parameters. We demonstrate in this paper the possibility to define POI composition to limit these contributions and to comply with spectral standard specifications. We focus on S band applications (2-3 GHz).
Humans just don't fall asleep like a log - or step-function. Rather, the sleep-onset period (SOP) exhibits dynamic and non-monotonous changes of electroencephalogram (EEG) with high, and so far poorly understood, intra- and inter-individual variability. Computational models of the sleep regulation network have suggested that the transition to sleep can be viewed as a noisy bifurcation at a saddle node which is determined by an underlying control signal or "sleep drive". However, such models do not describe how internal control signals in the SOP can produce rapid switches between stable wake and sleep states, nor how these state-space changes are translated in the macroscopic EEG. Here, we propose a minimally-parameterized stochastic dynamical model, in which one slowly-varying control parameter drives the wake-to-sleep transition while exhibiting noise-driven bistability. We provide a procedure for estimating the parameters of the model given single observations of experimental sleep EEG data, and show that it can reproduce a wide variety of SOP phenomenology. Using the model to analyze a pre-existing sleep EEG dataset, we find that the estimated model parameters correlate with subjective sleepiness reports. These results suggest that the bistable characteristics of the SOP can serve as biomarkers for tracking intra- and inter-individual variability of sleep-onset disorders.
