Stability in biosensors derived from domain map analysis of bibliometric data.

In the presented work, advanced methods of analysis and visualization were used to compile trends and patterns in the scientific literature. The most relevant information for the stability of biosensors was selected on the basis of clusters constructed on the basis of keywords. The most significant publications in the clusters appearing over time were analyzed. The most explosive publications were identified, i.e., those that have had the greatest impact on science in the area of the subject under study. The scientific trend in the development of biosensor stability was determined on the basis of the most frequently cited words in recent publications. A map of cooperation and networking between countries in the field of interest of the above topic was presented. Leaders were identified by country of origin. Systematic Review Registration: https://ubb.edu.pl.

On Model of Recurrent Neural Network on a Time Scale: Exponential Convergence and Stability Research.

The majority of the results on modeling recurrent neural networks (RNNs) are obtained using delayed differential equations, which imply continuous time representation. On the other hand, these models must be discrete in time, given their practical implementation in computer systems, requiring their versatile utilization across arbitrary time scales. Hence, the goal of this research is to model and investigate the architecture design of a delayed RNN using delayed differential equations on a time scale. Internal memory can be utilized to describe the calculation of the future states using discrete and distributed delays, which is a representation of the deep learning architecture for artificial RNNs. We focus on qualitative behavior and stability study of the system. Special attention is paid to taking into account the effect of the time-scale parameters on neural network dynamics. Here, we delve into the exploration of exponential stability in RNN models on a time scale that incorporates multiple discrete and distributed delays. Two approaches for constructing exponential estimates, including the Hilger and the usual exponential functions, are considered and compared. The Lyapunov-Krasovskii (L-K) functional method is employed to study stability on a time scale in both cases. The established stability criteria, resulting in an exponential-like estimate, utilizes a tuple of positive definite matrices, decay rate, and graininess of the time scale. The models of RNNs for the two-neuron network with four discrete and distributed delays, as well as the ring lattice delayed network of seven identical neurons, are numerically investigated. The results indicate how the time scale (graininess) and model characteristics (weights) influence the qualitative behavior, leading to a transition from stable focus to quasiperiodic limit cycles.

Nonlinear Analytics for Electrochemical Biosensor Design Using Enzyme Aggregates and Delayed Mass Action.

The paper is devoted to the extension of Brown's model of enzyme kinetics to the case with distributed delays. Firstly, we construct a multi-substrate multi-inhibitor model using discrete and distributed delays. Furthermore, we consider simplified models including one substrate and one inhibitor, for which an experimental study has been performed. The algorithm of parameter identifications was developed which was tested on the experimental data of solution conductivity. Both the model and Kohlrausch's law parameters are obtained as a result of the optimization procedure. Comparison of plots constructed with the help of the estimated parameters has shown that in such case the model with distributed delays is more chemically adequate in comparison with the discrete one. The methods of generalization of the results to the multi-substrate multi-inhibitor cases are discussed.

A meta-analysis of the influence of the external conditions on the biosensor receptor layer component stability.

The manuscript presented here contains meta-analysis of the influence of the external conditions on the biosensor receptor layer component stability. The novelty of this paper is due to compilation and comparison of studies, based on proposed collective analyses. The presented meta-analysis allows to increase the precision and accuracy of the results by combining and co-analyzing data from five smaller experiments. To understand the significance of presented meta-analysis, the most important conclusions and observations resulting from the conducted five types of research [F1] to [F5] are given. The conducted meta-analysis showed the magnitude of stability differences caused by different external factors. An approach of numerical interpretation of the qualitative stability changes has been offered. The conducted meta-analysis showed that the tested factors influence the stability of the BSA in different ways.

On qualitative analysis of the nonstationary delayed model of coexistence of two-strain virus: Stability, bifurcation, and transition to chaos.

The model of interaction of two strains of the virus is considered in the paper. The model is based on a nonstationary system of differential equations with delays and takes into account populations of susceptible, first-time and re-infected individuals across two strains. For small values of the delays, the conditions of global asymptotic stability are obtained with the help of Lyapunov functionals technique. In some special cases the exponential estimates are constructed. On the basis of numerical modeling complex chaotic solutions of the model are obtained. Their investigation is performed with help of nonlinear characteristics, namely bifurcation maps based on Poincare sections and the maximal Lyapunov exponent were obtained.