相关论文: Spijker's example and its extension
This paper presents a new paradigm to stabilize uncertain stochastic linear systems. Herein, second moment polytopic (SMP) systems are proposed that generalize systems with both uncertainty and randomness. The SMP systems are characterized…
A stability criterion is derived in general relativity for self-similar solutions with a scalar field and those with a stiff fluid, which is a perfect fluid with the equation of state $P=\rho$. A wide class of self-similar solutions turn…
A modification of the usual Type-II second-harmonic-generation model is proposed, which includes two additional features: linear conversion and walkoff (group-velocity difference) between two components of the fundamental-frequency (FF)…
The starting assumptions to study the convergence and complexity of gradient-type methods may be the smoothness (also called Lipschitz continuity of gradient) and the strong convexity. In this note, we revisit these two basic properties…
We consider a dynamical system which has a stable attractor and which is perturbed by an additive noise. Under some quite typical conditions, the fluctuations from the attractor are intermittent and have a probability distribution with…
A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by…
A new model for viscoelastic phase separation is proposed, based on a systematically derived conservative two-fluid model. Dissipative effects are included by phenomenological viscoelastic terms. By construction, the model is consistent…
We consider the multiple scattering of a scalar wave in a disordered medium with a weak nonlinearity of Kerr type. The perturbation theory, developed to calculate the temporal autocorrelation function of scattered wave, fails at short…
Two-stroke relaxation oscillations consist of two distinct phases per cycle - one slow and one fast - which distinguishes them from the well-known van der Pol-type 'four-stroke' relaxation oscillations. This type of oscillation can be found…
We consider the problem of embedding a dynamic network, to obtain time-evolving vector representations of each node, which can then be used to describe changes in behaviour of individual nodes, communities, or the entire graph. Given this…
We extend the invariant manifold method for analyzing the asymptotics of dissipative partial differential equations on unbounded spatial domains to treat equations in which the linear part has order greater than two. One important example…
In this paper, we study properties and patterns on permutations of multisets whose multivariate generating functions are symmetric. We interpret this phenomenon through the lens of group actions and define such a property or pattern as…
We consider degenerate porous medium equations with a divergence type of drift terms. We establish the existence of $L^{q}$-weak solutions (satisfying energy estimates or even further with moment and speed estimates in Wasserstein spaces),…
Invariant manifolds are fundamental tools for describing and understanding nonlinear dynamics. In this paper, we present a theory of stable and unstable manifolds for infinite dimensional random dynamical systems generated by a class of…
We consider the set of bimodal linear systems consisting of two linear dynamics acting on each side of a given hyperplane, assuming continuity along the separating hyperplane. Focusing on the unobservable planar ones, we obtain a simple…
We consider bilevel linear problems, where the right-hand side of the lower level problems is stochastic. The leader has to decide in a here-and-now fashion, while the follower has complete information. In this setting, the leader's outcome…
Forced advection of passive scalar by a smooth $d$-dimensional incompressible velocity in the presence of a linear damping is studied. Acting separately advection and dumping do not lead to an essential intermittency of the steady scalar…
In this paper, we study the long-time stability behavior of a class of linear stochastic evolution equations in a Hilbert space with multiplicative noise. Explicit sufficient conditions for $p$-th moment and almost sure exponential…
After having closely re-examined the notion of a L\'evy's stable vector, it is shown that the notion of a stable multivariate distribution is more general than previously defined. Indeed, a more intrinsic vector definition is obtained with…
Consider a multidimensional SDE of the form $X_t = x+\int_{0}^{t} b(X_{s-})ds+\int{0}^{t} f(X_{s-})dZ_s$ where $(Z_s)_{s\ge 0}$ is a symmetric stable process. Under suitable assumptions on the coefficients the unique strong solution of the…