Related papers: Conditional mixing in deterministic chaos
Coarse-grained models of chaotic systems neglect unresolved degrees of freedom, inducing structured model error that limits predictability and distorts long-term statistics. Typical data-driven closures are trained to minimize error over a…
We consider the stability of synchronized chaos in coupled map lattices and in coupled ordinary differential equations. Applying the theory of Hermitian and positive semidefinite matrices we prove two results that give simple bounds on…
The logistic map is a nonlinear difference equation well studied in the literature, used to model self-limiting growth in certain populations. It is known that, under certain regularity conditions, the stochastic logistic map, where the…
We consider a family of singular maps as an example of a simple model of dynamical systems exhibiting the property of robust chaos on a well defined range of parameters. Critical boundaries separating the region of robust chaos from the…
We prove global-local mixing for a large class of dynamical systems with infinite invariant measure. In particular, we treat intermittent maps including maps with multiple neutral fixed points, nonMarkovian intermittent maps, and…
The phenomenon of Stochastic Resonance (SR) is reported in a completely noise-free situation, with the role of thermal noise being taken by low-dimensional chaos. A one-dimensional, piecewise linear map and a pair of coupled…
We propose a mechanism which produces periodic variations of the degree of predictability in dynamical systems. It is shown that even in the absence of noise when the control parameter changes periodically in time, below and above the…
Discrete-time stochastic systems are an essential modelling tool for many engineering systems. We consider stochastic control systems that are evolving over continuous spaces. For this class of models, methods for the formal verification…
Conformal prediction is a non-parametric technique for constructing prediction intervals or sets from arbitrary predictive models under the assumption that the data is exchangeable. It is popular as it comes with theoretical guarantees on…
The problem is that of sequential probability forecasting for finite-valued time series. The data is generated by an unknown probability distribution over the space of all one-way infinite sequences. It is known that this measure belongs to…
We investigate the effects of random perturbations on fully chaotic open systems. Perturbations can be applied to each trajectory independently (white noise) or simultaneously to all trajectories (random map). We compare these two scenarios…
In many real world chaotic systems, the interest is typically in determining when the system will behave in an extreme manner. Flooding and drought, extreme heatwaves, large earthquakes, and large drops in the stock market are examples of…
Chaotic dynamics, commonly seen in weather systems and fluid turbulence, are characterized by their sensitivity to initial conditions, which makes accurate prediction challenging. Recent approaches have focused on developing data-driven…
The phase ordering properties of lattices of band-chaotic maps coupled diffusively with some coupling strength $g$ are studied in order to determine the limit value $g_e$ beyond which multistability disappears and non-trivial collective…
We prove that the statistical properties of random perturbations of a nonuniformly hyperbolic diffeomorphism are described by a finite number of stationary measures. We also give necessary and sufficient conditions for the stochastic…
A type of chaos called laminar chaos was found in singularly perturbed dynamical systems with periodically [Phys. Rev. Lett. 120, 084102 (2018)] and quasiperiodically [Phys. Rev. E 107, 014205 (2023)] time-varying delay. Compared to…
We show that the threshold of complete synchronization in a lattice of coupled non-smooth chaotic maps is determined by linear stability along the directions transversal to the synchronization subspace. We examine carefully the…
We study the completely synchronized states (CSSs) of a system of coupled logistic maps as a function of three parameters: interaction strength ($\varepsilon$), range of the interaction ($\alpha$), that can vary from first-neighbors to…
We investigate coupled circle maps in presence of feedback and explore various dynamical phases observed in this system of coupled high dimensional maps. We observe an interesting transition from localized chaos to spatiotemporal chaos. We…
We give conditions under which a Markov chain constructed via parallel or simulated tempering is guaranteed to be rapidly mixing, which are applicable to a wide range of multimodal distributions arising in Bayesian statistical inference and…