The Lyapunov characteristic exponents and their computation

C Skokos - Dynamics of Small Solar System Bodies and …, 2009 - Springer
We present a survey of the theory of the Lyapunov Characteristic Exponents (LCEs) for
dynamical systems, as well as of the numerical techniques developed for the computation of …

[BOOK][B] Extremes and recurrence in dynamical systems

V Lucarini, D Faranda, JMM de Freitas, M Holland… - 2016 - books.google.com
Written by a team of international experts, Extremes and Recurrence in Dynamical Systems
presents a unique point of view on the mathematical theory of extremes and on its …

The Shannon entropy: An efficient indicator of dynamical stability

PM Cincotta, CM Giordano, RA Silva… - Physica D: Nonlinear …, 2021 - Elsevier
In this work it is shown that the Shannon entropy is an efficient dynamical indicator that
provides a direct measure of the diffusion rate and thus a time-scale for the instabilities …

[PDF][PDF] DynamicalSystems. jl: A Julia software library for chaos and nonlinear dynamics

G Datseris - Journal of Open Source Software, 2018 - joss.theoj.org
Chaotic systems are everywhere (Strogatz 1995), from celestial mechanics to biology to
electron transport. Not only do they cover many scales, but the phenomena that fall under …

[BOOK][B] Nonlinear dynamics: a concise introduction interlaced with code

G Datseris, U Parlitz - 2022 - books.google.com
This concise and up-to-date textbook provides an accessible introduction to the core
concepts of nonlinear dynamics as well as its existing and potential applications. The book …

Intramolecular vibrational energy redistribution and the quantum ergodicity transition: a phase space perspective

S Karmakar, S Keshavamurthy - Physical Chemistry Chemical Physics, 2020 - pubs.rsc.org
Intramolecular vibrational energy redistribution (IVR) impacts the dynamics of reactions in a
profound way. Theoretical and experimental studies are increasingly indicating that …

Stickiness in chaos

G Contopoulos, M Harsoula - International Journal of Bifurcation and …, 2008 - World Scientific
We distinguish two types of stickiness in systems of two degrees of freedom:(a) stickiness
around an island of stability, and (b) stickiness in chaos, along the unstable asymptotic …

Phase Transition to Chaos in Complex Ecosystems with Nonreciprocal Species-Resource Interactions

E Blumenthal, JW Rocks, P Mehta - Physical Review Letters, 2024 - APS
Nonreciprocal interactions between microscopic constituents can profoundly shape the
large-scale properties of complex systems. Here, we investigate the effects of nonreciprocity …

Comparative study of variational chaos indicators and ODEs' numerical integrators

LA Darriba, NP Maffione, PM Cincotta… - International Journal of …, 2012 - World Scientific
The reader can find in the literature a lot of different techniques to study the dynamics of a
given system and also, many suitable numerical integrators to compute them …

[HTML][HTML] Performance of chaos diagnostics based on Lagrangian descriptors. Application to the 4D standard map

S Zimper, A Ngapasare, M Hillebrand… - Physica D: Nonlinear …, 2023 - Elsevier
We investigate the ability of simple diagnostics based on Lagrangian descriptor (LD)
computations of initially nearby orbits to detect chaos in conservative dynamical systems …