Nonlinear Dynamics is the well-known area of the modern science which studies numerous aspects of nonlinear evolutions and processes in natural and artificial (technical) systems. We will then present a number of research results into mathematical modeling, theoretical analysis, synthesis and numerical simulation of nonlinear phenomena in dynamical systems and corresponding applications.

â  abstract: in this paper, artificial neural network (ann) was used for modeling the nonlinear structure of a debutanizer column in a refinery gas process plant. the actual input-output data of the system were measured in order to be used for system identification based on root mean square error (rmse) minimization approach. it was shown that the designed recurrent neural network is able to pr...

In recent years two nonlinear dispersive partial differential equations have attracted much attention due to their integrable structure. We prove that both equations arise in the modeling of the propagation of shallow water waves over a flat bed. The equations capture stronger nonlinear effects than the classical nonlinear dispersive Benjamin–Bona–Mahoney and Korteweg–de Vries equations. In par...

nonlinear, black box model, behavioral model, input-output model, time-series, embedology This technical report describes the groundwork for our nonlinear modeling technologies. Future technical reports will go into detail about the specific solutions we are developing to build accurate models for nonlinear electronic devices from input-output measurements for possible use in CAD simulators suc...

The existence of inertial manifolds for a Smoluchowski equation – a nonlinear Fokker-Planck equation on the unit sphere which arises in modeling of colloidal suspensions – is investigated. A nonlinear and nonlocal transformation is used to eliminate the gradient from the nonlinear term.

Many physical phenomena are suuciently complex that the corresponding equations aaord little insight, or no analytical method provides an exact solution. Decompositional modeling (DM) captures a modeler's tacit skill at solving non-linear algebraic systems. DM divides statespace into a patchwork of simpler subregimes, called caricatures, each of which preserves only the dominant characteristics...

The principal innovative idea in this note is to transform the original complex nonlinear modeling problem into a combination of linear problem and very simple nonlinear problems. The key step is the generalized linearization of nonlinear terms. This paper only presents the introductory strategy of this methodology. The practical numerical experiments will be provided subsequently.

We review the current state of Cepheid modeling and discuss its dominant deficiency, namely the use of time dependent mixing length. Notwithstanding, Cepheid modeling has achieved some excellent successes, and we mention some of the most recent ones. Discrepancies between observations and modeling appear not so much in the gross properties of single mode Cepheids, but rather when more subtle no...

In this paper, a new approach of modeling for Artificial Neural Networks (ANNs) models based on the concepts of fuzzy regression is proposed. For this purpose, we reformulated ANN model as a fuzzy nonlinear regression model while it has advantages of both fuzzy regression and ANN models. Hence, it can be applied to uncertain, ambiguous, or complex environments due to its flexibility for forecas...

evolving models have found applications in many real world systems. in this paper, potentials of the evolving linear models (elms) in tracking control design for nonlinear variable structure systems are introduced. at first, an elm is introduced as a dynamic single input, single output (siso) linear model whose parameters as well as dynamic orders of input and output signals can change through ...