Related papers: Spijker's example and its extension
Random walks represent an important tool for probing the structural and dynamical properties of networks and modeling transport and diffusion processes on networks. However, when individuals' movement becomes dictated by more complicated…
Stochastic feedback systems give rise to a variety of notions of stability. The conditions for the stability of the median, mean, and variance stability conditions differ. These conditions can be stated explicitly for scalar discrete-time…
In this paper, a systematic study of the strong metric subregularity property of mappings is carried out by means of a variational tool, called steepest displacement rate. With the aid of this tool, a simple characterization of strong…
In this paper, we discuss some limitations of the modified equations approach as a tool for stability analysis for a class of explicit linear schemes to scalar partial derivative equations. We show that the infinite series obtained by…
Interior stagnation point flows of viscoelastic liquids arise in a wide variety of applications including extensional viscometry, polymer processing and microfluidics. Experimentally, these flows have long been known to exhibit…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
In this paper, we introduce a three-component Gierer-Meinhardt model in the semi-strong interaction regime, characterized by an asymptotically large diffusivity ratio. A key feature of this model is that the interior spike can undergo Hopf…
We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded as from below (the guaranteed dwell-time) as from above. The upper bounds make this…
A robust fixed-lag smoothing approach is proposed in the case there is a mismatch between the nominal model and the actual model. The resulting robust smoother is characterized by a dynamic game between two players: one player selects the…
The May-Leonard model for three competing species, symmetric with respect to cyclic permutation of the variables and extended by diffusive terms, is considered. Exact time-periodic solutions of the system have been found, and their…
Strong Feller property and irreducibility are study for a class of non-linear monotone stochastic partial differential equations with multiplicative noise. H\"older continuity of the associated Markov semigroups are discussed in some…
This article deals with stability of continuous-time switched linear systems under constrained switching. Given a family of linear systems, possibly containing unstable dynamics, we characterize a new class of switching signals under which…
The Faraday problem is an important pattern-forming system that provides some middle ground between systems where the initial instability involves just a single mode and in which complexity then results from mode interactions or secondary…
Piecewise smooth dynamical systems make use of discontinuities to model switching between regions of smooth evolution. This introduces an ambiguity in prescribing dynamics at the discontinuity: should it be given by a limiting value on one…
In this paper, we prove a central limit theorem and estabilish a moderate deviation principle for stochastic models of incompressible second fluids. The weak convergence method inreoduced by [4] plays an important role.
We study the excitation of spatial patterns by resonant, multi-frequency forcing in systems undergoing a Hopf bifurcation to spatially homogeneous oscillations. Using weakly nonlinear analysis we show that for small amplitudes only stripe…
The modulational instability in the class of NLS equations is discussed using a statistical approach. A kinetic equation for the two-point correlation function is studied in a linear approximation, and an integral stability equation is…
The evolution of weak discontinuity is investigated in the flat FRW universe with a single scalar field and with multiple scalar fields. We consider both massless scalar fields and scalar fields with exponential potentials. Then we find…
We show that while individual Riesz transforms are two weight norm stable under biLipschitz change of variables on $A_{\infty}$ weights, they are two weight norm unstable under even rotational change of variables on doubling weights. More…
We analyze the morphological transition of a one-dimensional system described by a scalar field, where a flat state looses its stability. This scalar field may for example account for the position of a crystal growth front, an order…