Dynamics of one continual sociological model

In this paper, we study a dynamical system modeling an iterative process of choice in a group of agents between two possible results. The studied model is based on the principle of bounded confidence introduced by Hegselmann and Krause. According to this principle, at each step of the process, any agent chaqnges his/her opinion being influenced by agents with close opinions. The resulting dynamical system is nonlinear and discontinuous. The principal novelty of the model studied in this paper is that we consider not a finite but an infinite (continual) group of agents. Such an approach requires application of essentially new methods of research. The structure of possible fixed points of the appearing dynamical system is described, their stability is studied. It is shown that any trajectory tends to a fixed point.

Nonlinear Time-Series Prediction Using a Single MEMS Reservoir

In this work, we show the computational potential of MEMS devices by predicting the dynamics of a 10th order nonlinear auto-regressive moving average (NARMA10) dynamical system. Modeling this system is considered complex due to its high nonlinearity and dependency on its previous values. To model the NARMA10 system, we used a reservoir computing scheme by utilizing one MEMS device as a reservoir, produced by the interaction of 100 virtual nodes. The virtual nodes are attained by sampling the input of the MEMS device and modulating this input using a random modulation mask. The interaction between virtual nodes within the system was produced through delayed feedback and temporal dependence. Using this approach, the MEMS device was capable of adequately capturing the NARMA10 response with a normalized root mean square error (NRMSE) = 6.18% and 6.43% for the training and testing sets, respectively. In practice, the MEMS device would be superior to simulated reservoirs due to its ability to perform this complex computing task in real time.

Mathematical study for the phase-based transmissibility of a novel COVID-19 Coronavirus

In this paper, a mathematical dynamical system modeling a SEIRW model of infectious disease transmission for a transmissibility of a novel COVID-19 Coronavirus is studied. A qualitative analysis such as the local and global stability of equilibrium points is carried out.It is proved that if $\R \leq 1$, then the disease-free equilibrium is globally asymptotically stable and if $\R > 1$, then the disease-persistence equilibrium is globally asymptotically stable.

Dynamics of drainage under stochastic rainfall in river networks

We consider a linearized dynamical system modeling the flow rate of water along the rivers and hillslopes of an arbitrary watershed. The system is perturbed by a random rainfall in the form of a compound Poisson process. The model describes the evolution, at daily time scales, of an interconnected network of linear reservoirs and takes into account the differences in flow celerity between hillslopes and streams as well as their spatial variation. The resulting stochastic process is a piece-wise deterministic Markov process of the Orstein–Uhlembeck type. We provide an explicit formula for the Laplace transform of the invariant density of streamflow in terms of the geophysical parameters of the river network and the statistical properties of the precipitation field. As an application, we include novel formulas for the invariant moments of the streamflow at the watershed’s outlet, as well as the asymptotic behavior of extreme discharge events, and conditions for the statistical scaling of streamflow with respect to Horton order.