相关论文: The Necessity for a Time Local Dimension in System…

In this paper we establish the existence and uniqueness of global solutions (in time), as well as the existence, regularity and stability (upper semicontinuity) of the attractor for the semigroup generated by the solutions of a…

We consider a nonlocal nonlinear model with fractional diffusion motivated by studies of electroconvection phenomena in incompressible viscous fluids. We address the global well-posedness, global regularity and long time dynamics of the…

Recently new solvable systems of nonlinear evolution equations -- including ODEs, PDEs and systems with discrete time -- have been introduced. These findings are based on certain convenient formulas expressing the $k$-th time-derivative of…

Space-time dependence of the anomalous exponent of electric transport in the disorder model is presented. We show that the anomalous exponent depends on time, according to the time-evolution of the number of the effective neighbouring…

We study the behavior of dynamical systems under time reparameterizations, which is important not only to characterize chaos in relativistic systems but also to probe the invariance of dynamical quantities. We first show that time…

We prove the existence of a compact, finite dimensional, global attractor for a coupled PDE system comprising a nonlinearly damped semilinear wave equation and a nonlinear system of thermoelastic plate equations, without any mechanical…

We investigate the long term behavior in terms of global attractors, as time goes to infinity, of solutions to a continuum model for biological aggregations in which individuals experience long-range social attraction and short range…

We consider dynamical behavior of non-autonomous wave-type evolutionary equations with nonlinear damping, critical nonlinearity, and time-dependent external forcing which is translation bounded but not translation compact (i.e., external…

This paper studies the contraction property of time-varying differential-algebraic equation (DAE) systems by embedding them to higher-dimension ordinary differential equation (ODE) systems. The first result pertains to the equivalence of…

We study some aspects when one consider the existence of one extra-dimension in addition to a non-commutative space-time. We present here two different examples, where the first one provides a scenario were it is possible to relate the…

Using the relativistic concept of time dilation we show that a superposition of gravitational potentials can lead to nonunitary time evolution. For sufficiently weak gravitational potentials one can still define, for all intents and…

This paper reports the 3D planetary geostrophic viscous model has the exponential ergodicity and global attractor if this model is driven by an additive random noise, which results in the support of the integration of invariant measure for…

This paper is concerned with pullback dynamics of 3D Navier-Stokes equations with variable viscosity and subject to time-dependent external forces. Our main result establishes the existence of finite-dimensional pullback attractors in a…

During the last decade, possibilities to realize new phenomena and create new applications by varying system properties in time have gained increasing attention in many research fields, spanning a wide range from acoustics to optics. While…

We show that there is a mildly nonlinear three-dimensional system of ordinary differential equations - realizable by a rather simple electronic circuit - capable of producing a generalized attracting horseshoe map. A system specifically…

The quantum measurement axiom dictates that physical observables and in particular the Hamiltonian must be diagonalizable and have a real spectrum. For a time-independent Hamiltonian (with a discrete spectrum) these conditions ensure the…

We present a nonparametric way to retrieve a system of differential equations in embedding space from a single time series. These equations can be treated with dynamical systems theory and allow for long term predictions. We demonstrate the…

The aim of this paper is to find an upper bound for the box-counting dimension of uniform attractors for non-autonomous dynamical systems. Contrary to the results in literature, we do not ask the symbol space to have finite box-counting…

We consider a Nicholson's equation with multiple pairs of time-varying delays and nonlinear terms given by mixed monotone functions. Sufficient conditions for the permanence, local stability and global attractivity of its positive…

We investigate whether early and late time attractors for non-conformal kinetic theories exist by computing the time-evolution of a large set of moments of the one-particle distribution function. For this purpose we make use of a previously…