相关论文: Averaging, Conley index continuation and recurrent…

We study a class of nonlinear nonparametric inverse problems. Specifically, we propose a nonparametric estimator of the dynamics of a monotonically increasing trajectory defined on a finite time interval. Under suitable regularity…

Several nonlinear stochastic differential equations have been proposed in connection with self-organized critical phenomena. Due to the threshold condition involved in its dynamic evolution an infinite number of nonlinearities arises in a…

The aim of this paper is to explore the relationship between invariant cones and nonlinear normal modes in piecewise linear mechanical systems. As a key result, we extend the invariant cone concept, originally established for homogeneous…

We consider a quasi-linear parabolic equation with nonlinear dynamic boundary conditions occurring as a natural generalization of the semilinear reaction-diffusion equation with dynamic boundary conditions. The corresponding class of…

This paper is concerned with the global dynamics of a hybrid parabolic-hyperbolic model describing populations with distinct dispersal and sedentary stages. We first establish the global well-posedness of solutions, prove a comparison…

Averaging principle for abstract non-autonomous parabolic evolution equations governed by time-dependent family of positive sectorial operators is proved. Apart from linear case also a nonlinear version for continuous perturbations is…

We study linearization models for continuous one-parameter semigroups of parabolic type. In particular, we introduce new limit schemes to obtain solutions of Abel's functional equation and to study asymptotic behavior of such semigroups.…

Peridynamics describes the nonlinear interactions in spatially extended Hamiltonian systems by nonlocal integro-differential equations, which can be regarded as the natural generalization of lattice models. We prove the existence of…

Some properties of random Conley index are obtained and then a sufficient condition for the existence of abstract bifurcation points for both discrete-time and continuous-time random dynamical systems is presented. This stochastic…

In this paper we provide sufficient conditions which guarantee the existence of a system of invariant measures for semigroups associated to systems of parabolic differential equations with unbounded coefficients. We prove that these…

When solitary waves are characterized as homoclinic orbits of a finite-dimensional Hamiltonian system, they have an integer-valued topological invariant, the Maslov index. We are interested in developing a robust numerical algorithm to…

We develop a generalization of correlated trend-cycle decompositions that avoids prior assumptions about the long-run dynamic characteristics by modelling the permanent component as a fractionally integrated process and incorporating a…

It is rigorously proved that quasilinear impulsive systems possess unpredictable solutions when a perturbation generated by an unpredictable sequence is applied. The existence, uniqueness, as well as asymptotic stability of such solutions…

We study a system of parabolic equations consisting of a double nonlinear parabolic equations of Forchheimer type coupled with a semilinear parabolic equations. The system describes a fluid-like driven system for active-passive pedestrian…

This paper concerns spectral stability of nonlinear waves in KdV-type evolution equations. The relevant eigenvalue problem is defined by the composition of an unbounded self-adjoint operator with a finite number of negative eigenvalues and…

We consider asymptotically autonomous semilinear parabolic equations u_t + Au = f(t,u). Suppose that $f(t,.)\to f^\pm$ as $t\to\pm\infty$, where the semiflows induced by \label{eq:140602-1511} u_t + Au = f^\pm(u) \tag{*} are gradient-like.…

We prove that for certain partially hyperbolic skew-products, non-uniform hyperbolicity along the leaves implies existence of a finite number of ergodic absolutely continuous invariant probability measures which describe the asymptotics of…

We address the count of isolated and embedded eigenvalues in a generalized eigenvalue problem defined by two self-adjoint operators with a positive essential spectrum and a finite number of isolated eigenvalues. The generalized eigenvalue…

A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…

In contrast to existing works on stochastic averaging on finite intervals, we establish an averaging principle on the whole real axis, i.e. the so-called second Bogolyubov theorem, for semilinear stochastic ordinary differential equations…