Related papers: Generation of random dynamical systems from fracti…
In this paper we present stochastic foundations of fractional dynamics driven by fractional material derivative of distributed order-type. Before stating our main result we present the stochastic scenario which underlies the dynamics given…
Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…
The ability of Gaussian noise to induce ordered states in dynamical systems is here presented in an overview of the main stochastic mechanisms able to generate spatial patterns. These mechanisms involve: (i) a deterministic local dynamics…
We generalize the exact solution to the Bernoulli shift map. Under certain conditions, the generalized functions can produce unpredictable dynamics. We use the properties of the generalized functions to show that certain dynamical systems…
Many physical phenomena occur on domains that grow in time. When the timescales of the phenomena and domain growth are comparable, models must include the dynamics of the domain. A widespread intrinsically slow transport process is…
In this work we present a model for computation of random processes in digital computers which solves the problem of periodic sequences and hidden errors produced by correlations. We show that systems with non-invertible non-linearities can…
The generation of droplets at low Reynolds numbers is driven by non-linear dynamics that give rise to complex patterns concerning both the droplet-to-droplet spacing and the individual droplet sizes. Here we demonstrate an experimental…
We study stochastic resonance in an over-damped approximation of the stochastic Duffing oscillator from a random dynamical systems point of view. We analyse this problem in the general framework of random dynamical systems with a…
We consider a 2-dimensional stochastic differential equation in polar coordinates depending on several parameters. We show that if these parameters belong to a specific regime then the deterministic system explodes in finite time, but the…
In this note, we derive an existence and uniqueness results for delayed backward stochastic differential equation with only integrable data.
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
In this paper, we study random dynamical systems generated by two Allee maps. Two models are considered - with and without small random perturbations. It is shown that the behavior of the systems is very similar to the behavior of the…
The global asymptotic behavior of a stochastic Hopfield neural network model (HNNM) with delays is explored by studying the existence and structure of random attractors. It is first proved that the trajectory field of the stochastic delayed…
Hybrid numerical-experimental testing is a standard approach for complex dynamical structures that are, on the one hand, not easy to model due to complexity and parameter uncertainty and, on the other hand, too expensive for full-scale…
Randomness generation through quantum-chaotic evolution underpins foundational questions in statistical mechanics and applications across quantum information science, including benchmarking, tomography, metrology, and demonstrations of…
The purpose of this paper is to develop a new fractional dynamical approach to superstatistics. Namely, we show that superstatistical distribution functions can be obtained from stationary solutions of the generalized Fokker-Planck equation…
We consider a stable driven degenerate stochastic differential equation, whose coefficients satisfy a kind of weak H{\"o}rmander condition. Under mild smoothness assumptions we prove the uniqueness of the martingale problem for the…
We prove the pathwise well-posedness of stochastic porous media and fast diffusion equations driven by nonlinear, conservative noise. As a consequence, the generation of a random dynamical system is obtained. This extends results of the…
Modelling is an essential procedure in analyzing and controlling a given logical dynamic system (LDS). It has been proved that deterministic LDS can be modeled as a linear-like system using algebraic state space representation. However, due…
This paper develops solutions of fractional Fokker-Planck equations describing subdiffusion of probability densities of stochastic dynamical systems driven by non-Gaussian L\'evy processes, with space-time-dependent drift, diffusion and…