We present a data-driven numerical approach for modeling unknown dynamical systems with missing/hidden parameters. The method is based on training deep neural network (DNN) model the system using its trajectory data. A key feature that contains parameters are completely hidden, in sense no information about available through either measurement data or our prior knowledge of system. demonstrate ...

Numerical simulations indicate that cosmological halos display power-law radial profiles of pseudo phase-space density (PPSD), Q=rho/sigma^3, where rho is mass and sigma velocity dispersion. We test these predictions using the parameters derived from Markov Chain Monte Carlo (MCMC) analysis performed with MAMPOSSt code on observed kinematics a dispersion based stack (sigmav) 54 nearby regular c...

A new approach for evaluating lipid oxidation was developed by modelling data obtained by the oxygen consumption method. Based on the generalized scheme for lipid autoxidation, a compartment model involving the concentration of the four oxidation specimens of the unsaturated fatty acid, RH, R·, ROO·, and ROOH as well as the concentration of oxygen and the rate constants for initiation (a), form...

The nonlinear dynamical system modeling the immobilized enzyme kinetics with Michaelis-Menten mechanism for an irreversible reaction without external mass transfer resistance is considered. Laplace transform homotopy perturbation method is used to obtain the approximate solution of the governing nonlinear differential equation, which consists in determining the series solution convergent to the...

the study of the dynamic behavior of a rigid body with one fixed point (gyroscope) has a long history. a number of famous mathematicians and mechanical engineers have devoted enormous time and effort to clarify the role of dynamic effects on its movement (behavior) – stable, periodic, quasi-periodic or chaotic. the main objectives of this review are: 1) to outline the characteristic features of...

In this paper we study a three-component mathematical model for the spread of a viral disease in a population of spatially distributed hosts. The model is developed from the two-component model proposed by Tuckwell and Toubiana in 2007. The positions of the hosts are randomly generated in a rectangular map. Within-host viralimmune system parameters are generated randomly to provide variability ...

The success of modeling from an experimental time series is determined to a significant extent by the choice of dynamical variables. We propose a method for preliminary investigation of a time series whose purpose is to find out whether a global dynamical model with smooth functions can be constructed for the chosen variables. The method consists in the estimation of single valuedness and conti...

We consider the question of predicting nonlinear time series. Kernel Dynamical Modeling (KDM), a new method based on kernels, is proposed as an extension to linear dynamical models. The kernel trick is used twice: first, to learn the parameters of the model, and second, to compute preimages of the time series predicted in the feature space by means of Support Vector Regression. Our model shows ...

Chaotic dynamical systems are present in the nature in various forms such as the weather, activities in human brain, variation in stock market, flows and turbulence. In order to get a detailed understanding of a system, the modeling and analysis of the system is to be done in an effective way. A recurrent neural network (RNN) structure has been designed for modeling the dynamical system. The ne...