In this work we apply point canonical transformations to solve some classes of nonautonomous, nonlinear Schrödinger equations, namely, those which possess specific cubic and quintic (time- and space-dependent) nonlinearities. In this way we generalize some procedures recently published which resort to an ansatz to the wave function and recover a time- and space-independent nonlinear equation wh...

An SEI autonomous model with logistic growth rate and its corresponding nonautonomous model are investigated. For the autonomous case, we give the attractive regions of equilibria and perform some numerical simulations. Basic demographic reproduction number R d is obtained. Moreover, only the basic reproduction number R 0 cannot ensure the existence of the positive equilibrium, which needs addi...

The dissipative and decoherence properties of the two-level atom interacting with the squeezed vacuum field reservoir are investigated based on the nonautonomous master equation of the atomic density matrix in the framework of algebraic dynamics. The nonautonomous master equation is converted into a Schrödinger-like equations and its dynamical symmetry is found based on the left and right repre...

New theorems of asymptotical stability and uniformly asymptotical stability for nonautonomous difference equations are given in this paper. The classical Liapunov asymptotical stability theorem of nonautonomous difference equations relies on the existence of a positive definite Liapunov function that has an indefinitely small upper bound and whose variation along a given nonautonomous differenc...

Abstract Various inequivalent notions of attraction for autonomous dynamical systems have been proposed, each them useful to understand specific aspects attraction. Milnor’s notion a measure attractor considers invariant sets with positive basin attraction, while Ilyashenko’s weaker statistical points that approach the set in terms averages. In this paper we propose generalisations these nonaut...

We analyze chaos in the well-known nonautonomous Double-Gyre system. A key focus is on folding, which is possibly the less-studied aspect of the “stretching+ folding= chaos” mantra of chaotic dynamics. Despite the Double-Gyre not having the classical homoclinic structure for the usage of the Smale–Birkhoff theorem to establish chaos, we use the concept of folding to prove the existence of an em...

In a real separable Hilbert space, we consider nonautonomous evolution equations including time-dependent subdifferentials and their nonmonotone multivalued perturbations. In this paper, we treat the multivalued dynamical systems associated with time-dependent subdifferentials, in which the solution is not unique for a given initial state. In particular, we discuss the asymptotic behaviour of o...

The effects of perturbation or discretization on a maximal attractor of autonomous dynamical systems is now well understood, with the perturbed or discretized system having a nearby maximal attractor [5, 7, 10]. In contrast, for nonautonomous systems the very concept of a nonautonomous attractor itself is still undergoing intensive development and perturbation or discretization results have bee...

We study Galerkin approximation of pullback attractors for a nonautonomous nonlocal parabolic equation. show that the $ n $th system has attractor in $-dimensional subspace Lebesgue space. then prove sequence is uniformly backward bounded and solutions converges on any set. Using these results, we establish upper semi-convergence towards original infinite-dimensional system.