We reprove in an extremely simple way the classical theorem that time periodic dissipative systems imply the existence of harmonic periodic solutions, in the case of uniqueness. We will also show that, in the lack of uniqueness, the existence of harmonics is implied by uniform dissipativity. The localization of starting points and multiplicity of periodic solutions will be established, under su...

In this paper, we study the regularity and long-time behavior of the solutions to the Moore-Greitzer model of an axial-flow compressor. In particular, we prove that this dissipative system of evolution equations possesses a global invariant inertial manifold, and therefore its underlying long-time dynamics reduces to that of an ordinary differential system. Furthermore, we show that the solutio...

We study the lifetime of localized states in a two-level system coupled to a dissipative bath and driven by strong time-periodic monochromatic fields. At high temperature, moderate friction and high frequency driving the dynamics is practically exponential characterized by a rate constant. By mapping the driven dissipative two-level system onto a dissipative multilevel curve-crossing problem an...

We analyze the motion of a pressure control system described by a differential equation with nonlocal dissipative force. This system is composed by an oscillator, a membrane and a constant force. We consider the dissipative memory kernel consisting of two terms. One of them is described by the Dirac delta function which represents a local friction, whereas for the second one we consider two typ...

Three inter-related topics are discussed here. One, the Lindblad dynamics of quantum dissipative systems; two, quantum entanglement in composite systems and its quantification based on the Tsallis entropy; and three, robustness of entanglement under dissipation. After a brief review of the Lindblad theory of quantum dissipative systems and the idea of quantum entanglement in composite quantum s...

The axisymmetric linear stability of dissipative Taylor-Couette flow with an azimuthal magnetic field is considered. The magnetic field can be unstable without a rotation. This is the well-known pinch type instability. The stable rotation stabilizes the unstable azimuthal magnetic field. The dissipative flow stability can be classified according to Michael's stability condition for an ideal flo...

Quantum field theory of a damped vibrating string as the simplest dissipative scalar field investigated by its coupling with an infinit number of Klein-Gordon fields as the environment by introducing a minimal coupling method. Heisenberg equation containing a dissipative term proportional to velocity obtained for a special choice of coupling function and quantum dynamics for such a dissipative ...

This paper is endeavoured to the problem of local feedback dissipativity and the use of feedback dissipativity for stabilization purposes in the nonlinear discretetime setting. Sufficient conditions under which a class of non-affine discrete-time control systems can be rendered locally dissipative are derived. A methodology in order to render nonlinear single-input single-output discrete-time s...