Related papers: Herding model and 1/f noise
Herding defines a deterministic dynamical system at the edge of chaos. It generates a sequence of model states and parameters by alternating parameter perturbations with state maximizations, where the sequence of states can be interpreted…
We present preliminary results on the problem of driving the dynamics of a group of agents, the herders, so as to steer the collective behaviour of another group of agents, the targets, interacting with them. We define this problem as the…
Simple analytically solvable model of 1/f noise is proposed. The model consists of one or few particles moving in the closed contour. The drift period of the particle round the contour fluctuates about some average value, e.g. due to the…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
We examine characteristic properties of deterministic and stochastic diffusion in low-dimensional chaotic dynamical systems. As an example, we consider a periodic array of scatterers defined by a simple chaotic map on the line. Adding…
Learning the parameters of a (potentially partially observable) random field model is intractable in general. Instead of focussing on a single optimal parameter value we propose to treat parameters as dynamical quantities. We introduce an…
We consider the Robin Hood dynamics, a one-dimensional extremal self-organized critical model that describes the evolution of low-temperature creep. One of the key quantities is the time evolution of the state variable (force noise). To…
Power laws, that is, power spectral densities (PSDs) exhibiting 1/f^alpha behavior for large frequencies f, have commonly been observed in neural recordings. Power laws in noise spectra have not only been observed in microscopic recordings…
The effect of demographic stochasticity, in the form of Gaussian white noise, in a predator-prey model with one fast and two slow variables is studied. We derive the stochastic differential equations (SDEs) from a discrete model. For…
Single species population models and discrete stochastic gene frequency models are two standards of mathematical biology important for the evolution of populations. An agent based model is presented which reproduces these models and then…
The spectral statistic $\delta_n$ measures the fluctuations of the number of energy levels around its mean value. It has been shown that chaotic quantum systems display $1/f$ noise (pink noise) in the power spectrum $S(f)$ of the $\delta_n$…
This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…
We show how one may analytically compute the stationary density of the distribution of molecular constituents in populations of cells in the presence of noise arising from either bursting transcription or translation, or noise in…
Order statistics of periodic, Gaussian noise with 1/f^{\alpha} power spectrum is investigated. Using simulations and phenomenological arguments, we find three scaling regimes for the average gap d_k=<x_k-x_{k+1}> between the k-th and…
The transient behavior of an ecosystem with N random interacting species in the presence of a multiplicative noise is analyzed. The multiplicative noise mimics the interaction with the environment. We investigate different asymptotic…
We propose a model for stochastic formation of opinion clusters, modelled by an evolving network, and herd behaviour to account for the observed fat-tail distribution in returns of financial-price data. The only parameter of the model is h,…
Power spectrum estimation is an important tool in many applications, such as the whitening of noise. The popular multitaper method enjoys significant success, but fails for short signals with few samples. We propose a statistical model…
Agent-based models are a natural choice for modeling complex social systems. In such models simple stochastic interaction rules for a large population of individuals can lead to emergent dynamics on the macroscopic scale, for instance a…
Stochasticity in gene expression can give rise to fluctuations in protein levels and lead to phenotypic variation across a population of genetically identical cells. Recent experiments indicate that bursting and feedback mechanisms play…
Quantum chaotic and integrable systems are known to exhibit a characteristic $1/f$ and $1/f^{2}$ noise, respectively, in the power spectrum associated to their spectral fluctuations. A recent work [R. Riser, V. A. Osipov, and E. Kanzieper,…