Related papers: Detecting chaos in hurricane intensity
We investigate uncertainty growth and chaotic dynamics in statistically steady, stably stratified three-dimensional turbulence. Using direct numerical simulations of the Boussinesq equations, we quantify the divergence of initially…
Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is…
Temporal evolutions toward thermal equilibria are numerically investigated in a Hamiltonian system with many degrees of freedom which has second order phase transition. Relaxation processes are studied through local order parameter, and…
Engineered injection and extraction systems that create chaotic advection are promising procedures for enhancing mixing between two species. Mixing efficiencies vary considerably, so carefully selecting the design parameters, like pumping…
The efficient detection of chaotic behavior in orbits of a complex dynamical system is an active domain of research. Several indicators have been proposed in the past, and new ones have recently been developed in view of improving the…
We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…
A streamflow time series encompasses a large amount of hidden information and reliable prediction of its behavior in the future remains a challenge. It seems that the use of information measures can significantly contribute to determining…
In quantum/wave systems with chaotic classical analogs, wavefunctions evolve in highly complex, yet deterministic ways. A slight perturbation of the system, though, will cause the evolution to diverge from its original behavior increasingly…
In this article we study a relatively novel way of constructing chaotic sequences of probability measures supported on Kac's sphere, which are obtained as the law of a vector of $N$ i.i.d. variables after it is rescaled to have unit average…
This work proposes an innovative approach using machine learning to predict extreme events in time series of chaotic dynamical systems. The research focuses on the time series of the H\'enon map, a two-dimensional model known for its…
Using the method of symbolic dynamics, we show that a large class of classical chaotic maps exhibit exponential hypersensitivity to perturbation, i.e., a rapid increase with time of the information needed to describe the perturbed time…
During hurricanes, coupled wave-circulation models are critical tools for public safety. The standard approach is to use a high fidelity circulation model coupled with a wave model which uses the most advanced source terms. As a result, the…
An extreme event is a sudden and violent change in the state of a nonlinear system. In fluid dynamics, extreme events can have adverse effects on the system's optimal design and operability, which calls for accurate methods for their…
Via evaluation of the Lyapunov exponent, we report the discovery of three prominent sets of phase space regimes of quasi-periodic orbits of charged particles trapped in a dipole magnetic field. Besides the low energy regime that has been…
In this Letter, we consider a model of dynamical agents coupled through a random connectivity matrix, as introduced in [Sompolinsky et. al, 1988] in the context of random neural networks. It is known that increasing the disorder parameter…
This paper examines discreteness effects in nearly collisionless N-body systems of charged particles interacting via an unscreened r^-2 force, allowing for bulk potentials admitting both regular and chaotic orbits. Both for ensembles and…
The scaling behavior of the maximal Lyapunov exponent in chaotic systems with time-delayed feedback is investigated. For large delay times it has been shown that the delay-dependence of the exponent allows a distinction between strong and…
Despite the prominent importance of the Lyapunov exponents for characterizing chaos, it still remains a challenge to measure them for large experimental systems, mainly because of the lack of recurrences in time series analysis. Here we…
Accurate precipitation nowcasting over extended horizons (0-3 hours) is essential for disaster mitigation and operational decision-making, yet remains a critical challenge in the field. Existing deterministic approaches are predominantly…
We propose a general method for constructing a minimal cover of high-dimensional chaotic attractors by embedded unstable recurrent patterns. By minimal cover we mean a subset of available patterns such that the approximation of chaotic…