Hybrid dynamical systems are systems that combine features of continuous-time dynamical systems and discrete-time dynamical systems, and can be modeled by a combination of differential equations or inclusions, difference equations or inclusions, and constraints. Pre-asymptotic stability is a concept that results from separating the conditions that asymptotic stability places on the behavior of ...

we use molecular dynamics simulation to describe a method that can be used to model liquid drop evaporation. For application, the liquid is taken to be water. Using the properties of the liquid and a Lennard-Jones potential, we derive dynamical equations, which are used to describe the gross dynamical behavior of the liquid-vapor molecular system. The resulting dynamical equations are solved nu...

The behavior of any physical system is governed by its underlying dynamical equations. Much of physics is concerned with discovering these dynamical equations and understanding their consequences. In this Letter, we show that, remarkably, identifying the underlying dynamical equation from any amount of experimental data, however precise, is a provably computationally hard problem (it is NP hard...

Since the advent of Taylor Series, polynomial methods have been used to solve di↵erential equations and learn the properties of di↵erential equations. There are many polynomial methods for solving di↵erential equations and understanding dynamical systems. For example, Taylor polynomials, Chebyshev Polynomials and Adomian Polynomials are used to generate approximate solutions. Automatic di↵erent...

This paper presents probability and possibility as two measures to model different types of uncertainty in continuous dynamical systems. We analyze and compare how probability and possibility distribution evolve in a dynamical system modeled by differential equations, where initial conditions and/or parameter may be uncertain. Moreover, we propose a new algorithm for the numerical resolution of...

This paper presents the current possible applications of Dynamical Systems in Engineering. The applications of chaos, fractals have proven to be an exciting and fruitful endeavor. These applications are highly diverse ranging over such fields as Electrical, Electronics and Computer Engineering. Dynamical Systems theory describes general patterns found in the solution of systems of nonlinear equ...

The time-dependent Ginzburg-Landau equations of superconduc-tivity deene a dynamical process when the applied magnetic eld varies with time. Suucient conditions (in terms of the time rate of change of the applied eld) are given that, if satissed, guarantee that this dynamical process is asymptotically autonomous. As time goes to innnity, the dynamical process asymptotically approaches a dynamic...

The gauge independence of the dynamical fermion mass generated through chiral symmetry breaking in QED in a strong, constant external magnetic field is critically examined. We present a (first, to the best of our knowledge) consistent truncation of the Schwinger-Dyson equations in the lowest Landau level approximation. We demonstrate that the dynamical fermion mass, obtained as the solution of ...

Dynamical models based on three steady-state equations for the law of effect were constructed under the assumption that behavior changes in proportion to the difference between current behavior and the equilibrium implied by current reinforcer rates. A comparison of dynamical models showed that a model based on Navakatikyan's (2007) two-component functions law-of-effect equations performed bett...