AI Article Synopsis
- Dynamical systems with symmetries contain invariant manifolds that influence nearby trajectories, causing them to linger around these structures until they suddenly enter chaotic bursts before returning to stable behavior.
- The onset of chaos is linked to the loss of stability in periodic orbits within the invariant manifold, leading to unpredictable changes in trajectory behavior, measured by fluctuating finite-time Lyapunov exponents.
- A two-dimensional map and a stochastic model are employed to analyze the properties of these chaotic bursts and the relationship between shadowability and Lyapunov exponents.
Article Abstract
Dynamical systems possessing symmetries have invariant manifolds. According to the transversal stability properties of this invariant manifold, nearby trajectories may spend long stretches of time in its vicinity before being repelled from it as a chaotic burst, after which the trajectories return to their original laminar behavior. The onset of chaotic bursting is determined by the loss of transversal stability of low-period periodic orbits embedded in the invariant manifold, in such a way that the shadowability of chaotic orbits is broken due to unstable dimension variability, characterized by finite-time Lyapunov exponents fluctuating about zero. We use a two-dimensional map with an invariant subspace to estimate shadowing distances and times from the statistical properties of the bursts in the transversal direction. A stochastic model (biased random walk with reflecting barrier) is used to relate the shadowability properties to the distribution of the finite-time Lyapunov exponents.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1103/PhysRevE.66.046213 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Difficulties faced by three hospitals evacuated from the urgent protective action planning zone after the 2011 Fukushima Daiichi Nuclear power plant accident.
J Radiat Res
December 2024
Department of Radiation Health Management, Fukushima Medical University, School of Medicine, 1 Hikarigaoka, Fukushima-shi, Fukushima 960-1295, Japan.
In radiological disasters, evacuating institutionalized individuals such as hospitalized patients and nursing home residents presents complex challenges. The Fukushima Daiichi Nuclear power plant (FDNPP) accident, triggered by the Great East Japan Earthquake (GEJE), exposed critical issues in evacuation planning. This case series investigates the evacuation difficulties encountered by three hospitals situated 20 to 30 km from the FDNPP following the GEJE and FDNPP accident.
View Article and Find Full Text PDFUnderstanding perspectives for mixed mode oscillations of the fractional neural network approaches to the analysis of neurophysiological data from the perspective of the observability of complex networks.
Heliyon
December 2024
Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia.
Using discrete fractional calculus, a wide variety of physiological phenomena with various time scales have been productively investigated. In order to comprehend the intricate dynamics and activity of neuronal processing, we investigate the behavior of a slow-fast FitzHugh-Rinzel (FH-R) simulation neuron that is driven by physiological considerations via the Caputo fractional difference scheme. Taking into account the discrete fractional commensurate and incommensurate mechanisms, we speculate on the numerical representations of various excitabilities and persistent activation reactions brought about by the administered stimulation.
View Article and Find Full Text PDFStern-Brocot arithmetic in dynamics of a biochemical reaction model.
Chaos
December 2024
PhyLife, Institute of Biochemistry and Molecular Biology, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark.
A simple almost fifty year old four-variable model of the peroxidase-oxidase reaction has been studied using 2D isospike stability diagrams, 2D maximum Lyapunov exponent diagrams, and other nonlinear numerical methods. The model contains two positive feedback loops. For slightly different sets of parameters, compared to the original parameters, the model reveals a wealth of dynamic behaviors, not previously reported for this model.
View Article and Find Full Text PDFArticle Synopsis
- Intermittency is a phenomenon observed in nonlinear dynamical systems, and this study explores its presence within soliton molecules in ultrafast lasers.
- Using advanced techniques for measuring pulse separation, the researchers identify bursts of variations that challenge traditional patterns in soliton dynamics.
- This research provides new insights into chaotic behavior in soliton molecules, revealing potential connections between optical solitons and molecular dynamics in other contexts.
Firing dynamics and coupling synchronization of memristive EMR-based Chaivlo neuron utilizing equivalent energy approach.
Chaos
November 2024
School of Computer Science and School of Cyberspace Science, Xiangtan University, Xiangtan 411105, China.
Firing dynamics and its energy property of neuron are crucial for exploring the mechanism of intricate information processing within the nervous system. However, the energy analysis of discrete neuron is significantly lacking in comparison to the vast literature and mature theory available on continuous neuron, thereby necessitating a focused effort in this underexplored realm. In this paper, we introduce a Chaivlo neuron map by employing a flux-controlled memristor to simulate electromagnetic radiation (EMR), and a detailed analysis of its firing dynamics is conducted based on an equivalent Hamiltonian energy approach.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!