Related papers: Minimal forward random point attractors need not e…

Recently for a class of critically intermittent random systems a phase transition was found for the finiteness of the absolutely continuous invariant measure. The systems for which this result holds are characterized by the interplay…

We study an infinite dimensional dynamical system that was proposed by J.C. Yoccoz and N.G. Yoccoz for modeling the population dynamics of some small rodents. We show an attractor exist in a large domain of the parameter space. Thanks to…

A mechanical system is presented exhibiting a non-deterministic singularity, that is, a point in an otherwise deterministic system where forward time trajectories become non-unique. A Coulomb friction force applies linear and angular forces…

Reaction systems are discrete dynamical systems that model biochemical processes in living cells using finite sets of reactants, inhibitors, and products. We investigate the computational complexity of a comprehensive set of problems…

We study the dynamics of the periodically-forced May-Leonard system. We extend previous results on the field and we identify different dynamical regimes depending on the strength of attraction $\delta$ of the network and the frequency…

We formulate the problem of finding the probability that the determinant of a matrix undergoes the least change upon perturbation of one of its elements, provided that most or all of the elements of the matrix are chosen at random and that…

We give an abstract framework for studying nonautonomous PDEs, called a generalized evolutionary system. In this setting, we define the notion of a pullback attractor. Moreover, we show that the pullback attractor, in the weak sense, must…

We give a systematic account of iterated function systems (IFS) of weak contractions of different types (Browder, Rakotch, topological). We show that the existence of attractors and asymptotically stable invariant measures, and the validity…

The structure of invariant regions and globally attracting regions is fundamental to understanding the dynamical properties of reaction network models. We describe an explicit construction of the minimal invariant regions and minimal…

We study the stable attractors of a class of continuous dynamical systems that may be idealized as networks of Boolean elements, with the goal of determining which Boolean attractors, if any, are good approximations of the attractors of…

A theory on bi-spatial random attractors developed recently by Li \emph{et al.} is extended to study stochastic Fitzhugh-Nagumo system driven by a non-autonomous term as well as a general multiplicative noise. By using the so-called notions…

Slow parameter drift is common in many systems (e.g., the amount of greenhouse gases in the terrestrial atmosphere is increasing). In such situations, the attractor on which the system trajectory lies can be destroyed, and the trajectory…

In this paper, a continuous approximation to studying a class of PWC systems of fractionalorder is presented. Some known results of set-valued analysis and differential inclusions are utilized. The example of a hyperchaotic PWC system of…

Continuous and discrete time systems possessing strange non-chaotic attractors are under investigation. It is demonstrated that unpredictable trajectories exist in the dynamics. A recent numerical technique, the sequential test, is utilized…

In this paper, we first establish a criterion based on contractive function for the existence of polynomial attractors. This criterion only involves some rather weak compactness associated with the repeated limit inferior and requires no…

Marginal optima are minima or maxima of a function with many nearly flat directions. In settings with many competing optima, marginal ones tend to attract algorithms and physical dynamics. Often, the important family of marginal attractors…

We study proximal random dynamical systems of homeomorphisms of the circle without a common fixed point. We prove the existence of two random points that govern the behavior of the forward and backward orbits of the system. Assuming the…

Let $\beta: S^{2n+1}\to S^{2n+1}$ be a minimal homeomorphism ($n\ge 1$). We show that the crossed product $C(S^{2n+1})\rtimes_{\beta} \Z$ has rational tracial rank at most one. More generally, let $\Omega$ be a connected compact metric…

We consider a random walker in a dynamic random environment given by a system of independent simple symmetric random walks. We obtain ballisticity results under two types of perturbations: low particle density, and strong local drift on…

We discuss the nonlinear phenomena of irreversible tipping for non-autonomous systems where time-varying inputs correspond to a smooth "parameter shift" from one asymptotic value to another. We express tipping in terms of pullback…