相关论文: The Necessity for a Time Local Dimension in System…
Many natural systems show emergent phenomena at different scales, leading to scaling regimes with signatures of chaos at large scales and an apparently random behavior at small scales. These features are usually investigated quantitatively…
We consider iterated function systems on the real line that consist of continuous, piecewise linear functions. We show that typically the natural dimension of these systems changes continuously with respect to the parameters that define the…
The paper deals with the observer design problem for a wide class of triangular nonlinear time-varying systems. The results of the present work generalize previous results in the literature dealing with the observer design problem for…
The aim of this paper is to describe the structure of global attractors for non-autonomous difference systems of equations with recurrent (in particular, almost periodic) coefficients. We consider a special class of this type of systems…
The cause for first and second order electromagnetic equivalency of inertial systems is approached from a different point of view than that of special relativity. While special relativity applies dilatation to time and contraction to space…
Many measurements on soft condensed matter (e.g., biological and materials) systems track low-dimensional observables projected from the full system phase space as a function of time. Examples are dynamic structure factors, spectroscopic…
The main objective of this paper is to study the existence of a finite dimension global attractor for the three dimensional viscous primitive equations of large-scale atmosphere. Thanks to the shortage of the uniqueness of weak solutions,…
We consider spacetime to be a 4-dimensional differentiable manifold that can be split locally into time and space. No metric, no linear connection are assumed. Matter is described by classical fields/fluids. We distinguish electrically…
We present a procedure to build a single time model for the equations of motion of relativistic retarded systems composed of several particles; at any desired level of accuracy. We treat the especial case of a binary system. We apply this…
Parametric modulation in nonlinear dynamical systems can give rise to attractors on which the dynamics is aperiodic and nonchaotic, namely with largest Lyapunov exponent being nonpositive. We describe a procedure for creating such…
We show that for any fixed accuracy and time length $T$, a {\it finite} number of $T$-time length pieces of the complete trajectories on the global attractor are capable of uniformly approximating all trajectories within the accuracy in the…
We consider the problem of adaptive observer design in the settings when the system is allowed to be nonlinear in the parameters, and furthermore they are to satisfy additional feasibility constraints. A solution to the problem is proposed…
We consider a class of differential equations, $\ddot x + \gamma \dot x + g(x) = f(\omega t)$, with $\omega \in {\bf R}^{d}$, describing one-dimensional dissipative systems subject to a periodic or quasi-periodic (Diophantine) forcing. We…
A proposal for the issue of time and observables in any parameterized theory such as general relativity is addressed. Introduction of a gauge potential 3-form A in the theory of relativity enables us to define a gauge-invariant quantity…
We discuss how to characterize the behavior of a chaotic dynamical system depending on a parameter that varies periodically in time. In particular, we study the predictability time, the correlations and the mean responses, by defining a…
We present a general theory of exceptional points of degeneracy (EPD) in periodically time-variant systems that do not necessarily require the presence of loss or gain, and we show that even a single resonator with a time-periodic component…
The paper is concerned with the exponential attractors for the viscoelastic wave model in $\Omega\subset \mathbb R^3$: $$u_{tt}-h_t(0)\Delta u-\int_0^\infty\partial_sh_t(s)\Delta u(t-s)\mathrm ds+f(u)=h,$$ with time-dependent memory kernel…
In an ordinary time-varying capacitor, there is debate whether a time-domain multiplication or a time-domain convolution of capacitance and voltage determines charge. A time-varying capacitor in parallel with a resistor was implemented by a…
The key questions of uniqueness and existence in time-dependent density functional theory are usually formulated only for potentials and densities that are analytic in time. Simple examples, standard in quantum mechanics, lead however to…
We discuss a one-dimensional version of the Landau-Pekar equations, which are a system of coupled differential equations with two different time scales. We derive an approximation on the slow time scale in the spirit of a non-linear…