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Consider a chaotic dynamical system generating Brownian motion-like diffusion. Consider a second, non-chaotic system in which all particles localize. Let a particle experience a random combination of both systems by sampling between them in…
The impact of quenched disorder on deterministic diffusion in chaotic dynamical systems is studied. As a simple example, we consider piecewise linear maps on the line. In computer simulations we find a complicated scenario of multiple…
Describing the evolution of quantum systems by means of non-Hermitian generators opens a new avenue to explore the dynamical properties naturally emerging in such a picture, e.g. operation at the so-called exceptional points, preservation…
A mechanism of excitation of the large-scale inertial waves in a rotating inhomogeneous turbulence due to an excitation of a large-scale instability is found. This instability is caused by a combined effect of the inhomogeneity of the…
We develop perturbative methods to study and control dynamical phenomena related to exceptional points in Non-Hermitian systems. In particular, we show how to find perturbative solutions based on the Magnus expansion that accurately…
We develop a theory for the emergence of global firings in non-identical excitable systems subject to noise. Three different dynamical regimes arise: sub-threshold motion, where all elements remain confined near the fixed point; coherent…
Disordered and amorphous materials often retain memories of perturbations they have experienced since preparation. Studying such memories is a gateway to understanding this challenging class of systems, yet it often requires the ability to…
The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, e.g., the number of random components of a system, the time over which a stochastic…
A local quantum phenomenon that gives rise to generic for all surface reactions macroscopic fluctuations is studied. The issue is viewed with respect to the necessary conditions for a long-term stable evolution of any natural and artificial…
Large assemblies of nonlinear dynamical units driven by a long-wave fluctuating external field are found to generate strong turbulence with scaling properties. This type of turbulence is so robust that it persists over a finite parameter…
Driven diffusive systems may undergo phase transitions to sustain atypical values of the current. This leads in some cases to symmetry-broken space-time trajectories which enhance the probability of such fluctuations. Here we shed light on…
We consider the asymptotic behaviour of the fluctuation process for large stochastic systems of interacting particles driven by both idiosyncratic and common noise with an interaction kernel \(k \in L^2(\R^d) \cap L^\infty(\R^d)\). Our…
Neural dynamics is triggered by discrete synaptic inputs of finite amplitude. However, the neural response is usually obtained within the diffusion approximation (DA) representing the synaptic inputs as Gaussian noise. We derive a…
We consider a stochastic perturbation of a FitzHugh-Nagumo system. We show that it is possible to generate oscillations for values of parameters which do not allow oscillations for the deterministic system. We also study the appearance of a…
We have developed the {\it general method} for the description of {\it separatrix chaos}, basing on the analysis of the separatrix map dynamics. Matching it with the resonant Hamiltonian analysis, we show that, for a given amplitude of…
We revisit the problem of diffusion in a driven system consisting of an inertial Brownian particle moving in a symmetric periodic potential and subjected to a symmetric time-periodic force. We reveal parameter domains in which diffusion is…
A natural phenomenon occurring in a living system is an outcome of the dynamics of the specific biological network underlying the phenomenon. The collective dynamics have both deterministic and stochastic components. The stochastic nature…
Crackling noise is observed in many disordered non-equilibrium systems in response to slowly changing external conditions. Examples range from Barkhausen noise in magnets to acoustic emission in martensites to earthquakes. Using the…
The emergence of exceptional points in non-Hermitian systems represents an intriguing phenomenon characterized by the coalescence of eigenenergies and eigenstates. When a system approaches an exceptional point, it exhibits a heightened…
We introduce and analyze a model for the transport of particles or energy in extended lattice systems. The dynamics of the model acts on a discrete phase space at discrete times but has nonetheless some of the characteristic properties of…