We consider dynamical and quasi-static thermoelastic contact problems in R modeling the evolution of temperature and displacement in an elastic body that may come into contact with a rigid foundation. The existence of solutions to these dynamical and quasi-static nonlinear problems and the exponential stability are investigated using a penalty method. Interior smoothing effects in the quasi-sta...

State models of piecewise-linear (PWL) autonomous dynamical systems used as prototypes in practical realizations of electronic chaotic oscillators are expressed in more generalized form that includes all previous models as special cases with the same optimum eigenvalue sensitivities. Key-Words: Dynamical systems, piecewise-linear, modeling, sensitivity optimization

While agreeing that dynamical models play a major role in cognitive science, we reject Stepp, Chemero, and Turvey's contention that they constitute an alternative to mechanistic explanations. We review several problems dynamical models face as putative explanations when they are not grounded in mechanisms. Further, we argue that the opposition of dynamical models and mechanisms is a false one a...

Dynamical systems driven by Gaussian noises have been considered extensively in modeling, simulation, and theory. However, complex systems in engineering and science are often subject to non-Gaussian fluctuations or uncertainties. A coupled dynamical system under a class of Lévy noises is considered. After discussing cocycle property, stationary orbits, and random attractors, a synchronization ...

Metastable attractors and heteroclinic orbits are present in the dynamics of various complex systems. Although their occurrence is well-known, their identification and modeling is a challenging task. The present work reviews briefly the literature and proposes a novel combination of their identification in experimental data and their modeling by dynamical systems. This combination applies recur...

The dynamical core, which governs the evolution of resolved fluid-dynamical processes, is a critical element of any atmospheric model. Its governing equations must include all relevant dynamical terms, and the numerical formulae used to approximate them must be accurate, stable and efficient. This is particularly so in a unified modeling environment in which the same dynamical core is used for ...

We investigate the problem of learning to predict dynamical systems that exhibit switching behavior as a function of exogenous variables. The family of dynamical systems we present is significant to the modeling of gene expression and organismal response to environmental conditions and change. We first develop a framework for learning to predict events such as state or phase changes as a functi...

The basic features of complex dynamical and control systems, including systems having hierarchical structure, are considered. Special attention is paid to the problems of synthesis of dynamical models of complex systems, construction of efficient control models, and to the development of simulation techniques. An approach to the synthesis of dynamic models of complex systems that integrates exp...

In the article, we discuss the architecture of the polynomial neural network that corresponds to the matrix representation of Lie transform. The matrix form of Lie transform is an approximation of general solution of the nonlinear system of ordinary differential equations. Thus, it can be used for simulation and modeling task. On the other hand, one can identify dynamical system from time serie...