Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1806.07766

Resonant behavior and unpredictability in forced chaotic scattering

Alexandre R. Nieto·Jesús M. Seoane·J. E. Alvarellos·Miguel A. F. Sanjuán
View original source ↗Read source document ↗Export metadata ↓

Abstract

Chaotic scattering in open Hamiltonian systems is a topic of fundamental interest in physics, which has been mainly studied in the purely conservative case. However, the effect of weak perturbations in this kind of systems has been an important focus of interest in the last decade. In a previous work, the authors studied the effects of a periodic forcing in the decay law of the survival probability, and they characterized the global properties of escape dynamics. In the present paper, we add two important issues in the effects of periodic forcing: the fractal dimension of the set of singularities in the scattering function, and the unpredictability of the exit basins, which is estimated by using the concept of basin entropy. Both the fractal dimension and the basin entropy exhibit a resonant-like decrease as the forcing frequency increases. We provide a theoretical reasoning, which could justify this decreasing in the fractality near the main resonant frequency, that appears for $ω\approx 1$. We attribute the decrease in the basin entropy to the reduction of the area occupied by the KAM islands and the basin boundaries when the frequency is close to the resonance. Finally, the decay rate of the exponential decay law shows a minimum value of the amplitude, $A_c$, which reflects the complete destruction of the KAM islands in the resonance. We expect that this work could be potentially useful in research fields related to chaotic Hamiltonian pumps, oscillations in chemical reactions and companion galaxies, among others.

Explore related subjects

nlin.CD

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Alexandre R. Nieto, Jesús M. Seoane, J. E. Alvarellos, Miguel A. F. Sanjuán. 2018-06-20. Resonant behavior and unpredictability in forced chaotic scattering. https://doi.org/10.1103/physreve.98.062206

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Linear Response Predicts Cusp-Pair Births in Networks with a Localized Cubic

Linear response is cheap to measure; the bistability boundaries it organizes are not. For a passive network with one localized cubic, the driving-point receptance $G$ fixes the period-one cusp set at fundamental-harmonic order: cusps lie on a fixed phase contour of $G$, a tangency of that contour under parameter variation creates a pair, and its curvature separates a gap opening from an isolated loop. For a two-mode absorber the linear prediction locates a benchmark birth coupling to $0.3\%$, and to $0.03\%$ once a third-harmonic correction of scale $|G(3\Omega)/G(\Omega)|$ is included.

nlin.CD↗
arXiv2026

Dynamics Creation through Neural Dynamical Transfer Learning

Data-driven machine learning has established a robust foundation for reconstructing nonlinear dynamical systems from observations, primarily for the purposes of forecasting and control. However, most existing efforts focus on recovering specific observed dynamics rather than the generative synthesis of new ones. Inspired by image fusion and style transfer, we introduce a neural network framework termed Neural Dynamical Transfer Learning (NDTL) to create new systems with prescribed dynamics from pairs of parent nonlinear dynamical systems. By computing fundamental dynamical signatures, including the intrinsic dimension, the Kaplan-Yorke dimension, the invariant measure statistics, and the Lyapunov spectrum, we demonstrate that NDTL preserves key features inherited from the parent models while simultaneously generating novel dynamics. Beyond these validation examples, NDTL induces a criterion for dynamics classification, creates stable oscillatory coexistence in the Hastings-Powell food chain model, produces interpretable epidemiological models, and provides a chaotic source for image encryption.

nlin.CD↗
arXiv2026

The Spectral Skeleton of Chaos: Koopman Wave Packets on Poincar\'e Sections

A Poincar\'e section replaces a flow by a return map, but for a chaotic system this map is usually known only from sampled crossings. We show that coarse transport can be read directly from Koopman spectral data, without fitting the map. Measure-preserving EDMD retains the isometric structure; riggedDMD then approximates spectral measures and constructs finite regularized wave packets. Packet phase supplies a finite-resolution transport coordinate; low modulus marks a singular skeleton where the phase becomes ill-conditioned. We demonstrate the idea on the R\"ossler system, a 32-mode Kuramoto--Sivashinsky Galerkin system, and the forced Duffing oscillator. The packets yield coarse symbolic models on sections ranging from an almost one-dimensional curve to a visibly thick set. Their graphs organize observed low-period orbits and guide targeted searches for others. In Duffing Regime~II, a seven-region rule accounts for $91\%$--$94\%$ of filtered one-step transitions, while failures in the lowest retained modulus decile occur at $5.08$--$5.20$ times the overall rate. The packets are not Koopman eigenfunctions, nor are the regions exact Markov partitions. Together these computations show how spectral information beyond isolated eigenpairs can expose chaotic transport directly from trajectories.

nlin.CD↗