Related papers: Multicanonical Sampling of Rare Trajectories in Ch…
In many situations, the statistical properties of wave systems with chaotic classical limits are well-described by random matrix theory. However, applications of random matrix theory to scattering problems require introduction of system…
Polynomial chaos based methods enable the efficient computation of output variability in the presence of input uncertainty in complex models. Consequently, they have been used extensively for propagating uncertainty through a wide variety…
We introduce a new analytical method, which allows to find out chaotic dynamics in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered as an example. The corresponding…
Modern space missions with uncrewed spacecraft require robust trajectory design to connect multiple chaotic orbits by small controls. To address this issue, we propose a control scheme to design robust trajectories by leveraging a…
We present a general mathematical framework for trajectory stratification for simulating rare events. Trajectory stratification involves decomposing trajectories of the underlying process into fragments limited to restricted regions of…
Causal phenomena associated with rare events occur across a wide range of engineering problems, such as risk-sensitive safety analysis, accident analysis and prevention, and extreme value theory. However, current methods for causal…
A procedure to characterize chaotic dynamical systems with concepts of complex networks is pursued, in which a dynamical system is mapped onto a network. The nodes represent the regions of space visited by the system, while edges represent…
We consider the problem of probabilistic quantification of dynamical systems that have heavy-tailed characteristics. These heavy-tailed features are associated with rare transient responses due to the occurrence of internal instabilities.…
In generic Hamiltonian systems tori of regular motion are dynamically separated from regions of chaotic motion in phase space. Quantum mechanically these phase-space regions are coupled by dynamical tunneling. We introduce a semiclassical…
We uncover and characterize different chaotic transport scenarios on perfect periodic surfaces by controlling the chaotic dynamics of particles subjected to periodic external forces in the absence of a ratchet effect. After identifying…
Chaos is an active research subject in the fields of science in recent years. it is a complex and an erratic behavior that is possible in very simple systems. in the present day, the chaotic behavior can be observed in experiments. Many…
The important phenomenon of "stickiness" of chaotic orbits in low dimensional dynamical systems has been investigated for several decades, in view of its applications to various areas of physics, such as classical and statistical mechanics,…
Fundamental problems of periodicity and transient process to periodicity of chaotic trajectories in computer realization with finite computation precision is investigated by taking single and coupled Logistic maps as examples. Empirical…
We describe a method for analyzing the phase space structures of Hamiltonian systems. This method is based on a time-frequency decomposition of a trajectory using wavelets. The ridges of the time-frequency landscape of a trajectory, also…
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 investigate the high dimensional Hamiltonian chaotic dynamics in $N$ coupled area-preserving maps. We show the existence of an enhanced trapping regime caused by trajectories performing a random walk {\em inside} the area corresponding…
When coping with the urgent challenge of locating and rescuing a deep-sea submersible in the event of communication or power failure, environmental uncertainty in the ocean can not be ignored. However, classic physical models are limited to…
Using the tools of Differential Geometry, we define a new <<fast>> chaoticity indicator, able to detect dynamical instability of trajectories much more effectively, (i.e. "quickly") than the usual tools, like Lyapunov Characteristic Numbers…
This paper examines the most probable route to chaos in high-dimensional dynamical systems in a very general computational setting. The most probable route to chaos in high-dimensional, discrete-time maps is observed to be a sequence of…
We use a recently found parametrization of the solutions of the inverse Frobenius-Perron problem within the class of complete unimodal maps to develop a Monte-Carlo approach for the construction of one-dimensional chaotic dynamical laws…