Related papers: Linear response, and consequences for differentiab…

In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…

It is already well-understood that many delay differential equations with only a single constant delay exhibit a change in stability according to the value of the delay in relation to a critical delay value. Finding a formula for the…

This work is devoted to examining qualitative properties of dynamic systems, in particular, limit cycles of stochastic differential equations with both rapid switching and small diffusion. The systems are featured by multi-scale…

Hamiltonian systems with functionally dependent constraints (irregular systems), for which the standard Dirac procedure is not directly applicable, are discussed. They are classified according to their behavior in the vicinity of the…

Linear response theory asserts that sufficiently small external biases produce currents proportional to the applied force and forms the theoretical foundation of nonequilibrium transport. Here we demonstrate that linear response can break…

For strongly monotone dynamical systems, the dynamics alternative for smooth discrete-time systems turns out to be a perfect analogy of the celebrated Hirsch's limit-set dichotomy for continuous-time semiflows. In this paper, we first…

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…

Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the…

In this article, the historic set is divided into different level sets and we use topological pressure to describe the size of these level sets. We give an application of these results to dimension theory. Especially, we use topological…

In this work, we develop a rigorous theoretical framework for the evolution of linear viscoelastic properties across the sol-gel transition. More specifically, we derive general admissible expressions for the relaxation modulus and dynamic…

An asymptotic analysis for a system with equation and dynamic boundary condition of Cahn-Hilliard type is carried out as the coefficient of the surface diffusion acting on the phase variable tends to 0, thus obtaining a forward-backward…

Starting from a linear fractional representation of a linear system affected by constant parametric uncertainties, we demonstrate how to enhance standard robust analysis tests by taking available (noisy) input-output data of the uncertain…

This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…

We study the number of occurrences of any fixed vincular permutation pattern. We show that this statistics on uniform random permutations is asymptotically normal and describe the speed of convergence. To prove this central limit theorem,…

In this paper, time-dependent dynamical systems given by sequences of maps are studied. For systems built from expanding C^2-maps on a compact Riemannian manifold M with uniform bounds on expansion factors and derivatives, we provide…

We establish an abstract quenched linear response result for random dynamical systems, which we then apply to the case of smooth expanding on average cocycles on the unit circle. In sharp contrast to the existing results in the literature,…

The autocorrelation function in many complex systems shows a crossover in the form of its decay: from stretched exponential relaxation (SER) at short times to power law at long times. Studies of the mechanisms leading to such multiple…

Processes occurring in real open systems are far from equilibrium state and they can lead to synergetic effects, which are caused by coordinated behavior of system units. Traditional methods of analysis often just establish such behavior,…

We consider linear dynamical systems with a structure of a multigraph. The vertices are associated to linear spaces and the edges correspond to linear maps between those spaces. We analyse the asymptotic growth of trajectories (associated…

This paper develops central limit theorems (CLT's) and large deviations results for additive functionals associated with reflecting diffusions in which the functional may include a term associated with the cumulative amount of boundary…