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In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…
The aim of this paper is to present a result of discrete approximation of some class of stable self-similar stationary increments processes. The properties of such processes were intensively investigated, but little is known on the context…
We study the emergence of typicality in classical systems with a large number of binary state variables. We show analytically that for sufficiently large subsets of the complete state space, state functions which can be associated with…
We construct a family of chaotic dynamical systems with explicit broad distributions, which always violate the central limit theorem. In particular, we show that the superposition of many statistically independent, identically distributed…
Motivated by data on coauthorships in scientific publications, we analyze a team formation process that generalizes matching models and network formation models, allowing for overlapping teams of heterogeneous size. We apply different…
We study a class of singularly perturbed impulsive linear switched systems exhibiting switching between slow and fast dynamics. To analyze their behavior, we construct auxiliary switched systems evolving in a single time scale. We prove…
We study small random perturbations by additive white-noise of a spatial discretization of a reaction-diffusion equation with a stable equilibrium and solutions that blow up in finite time. We prove that the perturbed system blows up with…
Understanding and predicting how complex systems respond to external perturbations is a central challenge in nonequilibrium statistical physics. Here we consider continuous-time Markov networks, which we subject to perturbations along a…
This paper presents an analysis approach to finite-time attraction in probability concerns with nonlinear systems described by nonlinear random differential equations (RDE). RDE provide meticulous physical interpreted models for some…
Stability is a central property in learning and statistics promising the output of an algorithm $A$ does not change substantially when applied to similar datasets $S$ and $S'$. It is an elementary fact that any sufficiently stable algorithm…
In this paper, we address the problem of robust stability for uncertain sampled-data systems controlled by a discrete-time disturbance observer (DT-DOB). Unlike most of previous works that rely on the small-gain theorem, our approach is to…
Thermodynamic stability of statistical systems requires that susceptibilities be semipositive and finite. Susceptibilities are known to be related to the fluctuations of extensive observable quantities. This relation becomes nontrivial,…
Some aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize how a…
We study random dynamical systems composed of LSV maps with varying parameters, without any mixing assumptions on the base space of random dynamics. We establish a quenched central limit theorem and identify conditions under which the…
For a class of linear switched systems in continuous time a controllability condition implies that state feedbacks allow to achieve almost sure stabilization with arbitrary exponential decay rates. This is based on the Multiplicative…
We investigate the statistical properties of a piecewise smooth dynamical system by studying directly the action of the transfer operator on appropriate spaces of distributions. We accomplish such a program in the case of two-dimensional…
Emerging network scenarios require the development of solid large-scale situated systems. Unfortunately, the diffusion/aggregation computational processes therein often introduce a source of complexity that hampers predictability of the…
We establish sufficient conditions for exponential convergence to a unique quasi-stationary distribution in the total variation norm. These conditions also ensure the existence and exponential ergodicity of the Q-process, the process…
Linear systems with many degrees of freedom containing multiplicative and additive noise are considered. The steady state probability distribution for equations of this kind is examined. With multiplicative white noise it is shown that…
The lifetime of a system of connected units under some natural assumptions can be represented as a random variable Y defined as a weighted lattice polynomial of random lifetimes of its components. As such, the concept of a random variable Y…