Related papers: Stability and Instability of Equilibria in Age-Str…
In this paper, we consider a stabilization problem of an uncertain system in a networked control setting. Due to the network, the measurements are quantized to finite-bit signals and may be randomly lost in the communication. We study…
We study systems on time scales that are generalizations of classical differential or difference equations. In this paper we consider linear systems and their small nonlinear perturbations. In terms of time scales and of eigenvalues of…
The stability of solutions to evolution equations with respect to small stochastic perturbations is considered. The stability of a stochastic dynamical system is characterized by the local stability index. The limit of this index with…
The stability of the boundary between regenerating tissues is essential to the maintenance of their integrity and biological function. Stress is known to play an important role in the regulation of cell division, cell growth and cell death,…
Understanding the relationship between complexity and stability in large dynamical systems -- such as ecosystems -- remains a key open question in complexity theory which has inspired a rich body of work developed over more than fifty…
Flocculation is the process whereby particles (i.e., flocs) in suspension reversibly combine and separate. The process is widespread in soft matter and aerosol physics as well as environmental science and engineering. We consider a general…
We are concerned with a nonlinear nonautonomous model represented by an equation describing the dynamics of an age-structured population diffusing in a space habitat $O,$ governed by local Lipschitz vital factors and by a stochastic…
In this paper the non-linear wave equation with a spatial inhomogeneity is considered. The inhomogeneity splits the unbounded spatial domain into three or more intervals, on each of which the non-linear wave equation is homogeneous. In such…
In the realm of spatiotemporal chaos, unstable periodic orbits play a major role in understanding the dynamics. Their stability changes and bifurcations in general are thus of central interest. Here, coupled map lattice discretizations of…
We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…
Identification of the parameters of stable linear dynamical systems is a well-studied problem in the literature, both in the low and high-dimensional settings. However, there are hardly any results for the unstable case, especially…
We consider the failure of localized control in a nonlinear spatially extended system caused by extremely small amounts of noise. It is shown that this failure occurs as a result of a nonlinear instability. Nonlinear instabilities can occur…
Quasilinear (and semilinear) parabolic problems of the form $v'=A(v)v+f(v)$ with strict inclusion $\mathrm{dom}(f)\subsetneq \mathrm{dom}(A)$ of the domains of the function $v\mapsto f(v)$ and the quasilinear part $v\mapsto A(v)$ are…
A new approach is developed to understand stability of a population and further understanding of population momentum.
This paper proposes a novel method for determining the number of factors in linear factor models under stability considerations. An instability measure is proposed based on the principal angle between the estimated loading spaces obtained…
To predict allowable time-step size for the fully discretized nonlinear differential equations, a stability theory is developed using exact determination of an infinite perturbation series. Mathematical induction is used to determine the…
The problem of behaviour prediction for linear parameter-varying systems is considered in the interval framework. It is assumed that the system is subject to uncertain inputs and the vector of scheduling parameters is unmeasurable, but all…
How do networks of relationships evolve over time? We analyse a dataset tracking the social interactions of 900 individuals over four years. Despite continuous shifts in individual relationships, the macroscopic structural properties of the…
A wide body of work has applied the concept of critical slowing down to estimate the stability of different Earth system components. Most of them -- such as global vegetation -- are inherently non-stationary, for example due to strong…
We propose an abstract approach to prove local uniqueness and conditional H\"older stability to non-linear inverse problems by linearization. The main condition is that, in addition to the injectivity of the linearization $A$, we need a…