相关论文: Lyapunov modes in soft-disk systems
We study the existence and property of Fast magnetosonic modes in 3D compressible MHD turbulence by carrying out a number of simulations with compressible and incompressible driving conditions. We use two approaches to determine the…
A method for deriving provably stable low-dimensional Galerkin models of post-transient incompressible flows is introduced. The proposed approach involves an iterative procedure for expansion modes that satisfy Lyapunov stability in the…
The dissipation associated with nonequilibrium flow processes is reflected by the formation of strange attractor distributions in phase space. The information dimension of these attractors is less than that of the equilibrium phase space,…
We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…
Recently, a new algorithm for the computation of covariant Lyapunov vectors and of corresponding local Lyapunov exponents has become available. Here we study the properties of these still unfamiliar quantities for a number of simple models,…
Coupled-mode systems are used in physical literature to simplify the nonlinear Maxwell and Gross-Pitaevskii equations with a small periodic potential and to approximate localized solutions called gap solitons by analytical expressions…
We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…
Switched linear hyperbolic partial differential equations are considered in this paper. They model infinite dimensional systems of conservation laws and balance laws, which are potentially affected by a distributed source or sink term. The…
This article proposes an approach to construct a Lyapunov function for a linear coupled impulsive system consisting of two time-invariant subsystems. In contrast to various variants of small-gain stability conditions for coupled systems,…
This article is devoted to the Relativistic Vlasov-Maxwell system in space dimension three. We prove the local smooth solvability for weak topologies (and its long time version for small data). This result is derived from a representation…
A general stability condition for plasma-vacuum systems with resistive walls is derived by using the Frieman Rotenberg lagrangian stability formulation [Rev. Mod. Phys. 32, 898 (1960)]. It is shown that the Lyapunov stability limit for…
We study a one-dimensional model for heavy particles in a compressible fluid. The fluid-velocity field is modelled by a persistent Gaussian random function, and the particles are assumed to be weakly inertial. Since one-dimensional…
Astrophysical fluids under the influence of magnetic fields are often subjected to single-fluid or two-fluid approximations. In the case of weakly ionized plasmas however, this can be inappropriate due to distinct responses from the…
A two-dimensional system of 10000 hard disks with square periodic boundary conditions, at a density in the middle of the 2-phase region predicted from equation-of-state data, when subjected to a weak external uniform force, is seen to phase…
In this paper, we investigate a class of hybrid stochastic heat equations. By explicit formulae of solutions, we not only reveal the sample Lyapunov exponents but also discuss the $p$th moment Lyapnov exponents. Moreover, several examples…
Fixed-time stable dynamical systems are capable of achieving exact convergence to an equilibrium point within a fixed time that is independent of the initial conditions of the system. This property makes them highly appealing for designing…
The dynamics of the localized region of the Lyapunov vector for the largest Lyapunov exponent is discussed in quasi-one-dimensional hard-disk systems at low density. We introduce a hopping rate to quantitatively describe the movement of the…
A modified method is presented to generate artificial magnetic turbulence that is used for test-particle simulations. Such turbulent fields are obtained from the superposition of a set of wave modes with random polarizations and random…
Finite-time Lyapunov exponents and vectors are used to define and diagnose boundary-layer type, two-timescale behavior in the tangent linear dynamics and to determine the associated manifold structure in the flow of a finite-dimensional…
New estimates and global existence results are provided for a class of systems of cross diffusion equations arising from the modeling of chemotaxis with local sensing, possibly featuring a growth term of logistic-type as well. For sublinear…