Chaotic Dynamics

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New submissions for Fri, 10 May 24

[1]  arXiv:2405.05783 [pdf, other]

Title: Intermediate spectral statistics of rational triangular quantum billiards

Authors: Črt Lozej, Eugene Bogomolny

Comments: 14 pages, 11 figures

Subjects: Chaotic Dynamics (nlin.CD); Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)

Triangular billiards whose angles are rational multiples of $\pi$ are one of the simplest examples of pseudo-integrable models with intriguing classical and quantum properties. We perform an extensive numerical study of spectral statistics of eight quantized rational triangles, six belonging to the family of right-angled Veech triangles and two obtuse rational triangles. Large spectral samples of up to one million energy levels were calculated for each triangle which permits to determine their spectral statistics with great accuracy. It is demonstrated that they are of the intermediate type, sharing some features with chaotic systems, like level repulsion and some with integrable systems, like exponential tails of the level spacing distributions. Another distinctive feature of intermediate spectral statistics is a finite value of the level compressibility.
The short range statistics such as the level spacing distributions, and long-range statistics such as the number variance and spectral form factors were analyzed in detail. An excellent agreement between the numerical data and the model of gamma distributions is revealed.

Cross-lists for Fri, 10 May 24

[2]  arXiv:2405.05675 (cross-list from nlin.AO) [pdf, other]

Title: Dynamical properties of a small heterogeneous chain network of neurons in discrete time

Authors: Indranil Ghosh, Anjana S. Nair, Hammed Olawale Fatoyinbo, Sishu Shankar Muni

Comments: 39 pages, 15 figures

Subjects: Adaptation and Self-Organizing Systems (nlin.AO); Chaotic Dynamics (nlin.CD)

We propose a novel nonlinear bidirectionally coupled heterogeneous chain network whose dynamics evolve in discrete time. The backbone of the model is a pair of popular map-based neuron models, the Chialvo and the Rulkov maps. This model is assumed to proximate the intricate dynamical properties of neurons in the widely complex nervous system. The model is first realized via various nonlinear analysis techniques: fixed point analysis, phase portraits, Jacobian matrix, and bifurcation diagrams. We observe the coexistence of chaotic and period-4 attractors. Various codimension-1 and -2 patterns for example saddle-node, period-doubling, Neimark-Sacker, double Neimark-Sacker, flip- and fold-Neimark Sacker, and 1:1 and 1:2 resonance are also explored. Furthermore, the study employs two synchronization measures to quantify how the oscillators in the network behave in tandem with each other over a long number of iterations. Finally, a time series analysis of the model is performed to investigate its complexity in terms of sample entropy.

[3]  arXiv:2405.05804 (cross-list from physics.class-ph) [pdf, other]

Title: Attochaos I: The classically chaotic postcursor of high harmonic generation

Authors: Jonathan Berkheim, David J. Tannor

Subjects: Classical Physics (physics.class-ph); Chaotic Dynamics (nlin.CD)

Attosecond physics provides unique insights into light-matter interaction on ultrafast time scales. Its core phenomenon, High Harmonic Generation (HHG), is often described by a classical recollision model, the simple-man or three-step model, where the atomic potential is disregarded. Many features are already well explained using this model; however, the simplicity of the model does not allow the possibility of classical chaotic motion. We show that beyond this model, classical chaotic motion does exist albeit on timescales that are generally longer than the first recollision time. Chaos is analyzed using tools from the theory of dynamical systems, such as Lyapunov exponents and stroboscopic maps. The calculations are done for a one-dimensional Coulomb potential subjected to a linearly polarized electric field.

Replacements for Fri, 10 May 24

[4]  arXiv:2405.04556 (replaced) [pdf, other]

Title: Energy-based theory of autoresonance in chains of coupled damped-driven generic oscillators

Authors: Ricardo Chacón, Faustino Palmero, Pedro J. Martínez, Somnath Roy

Comments: 5 pages, 4 figures

Subjects: Chaotic Dynamics (nlin.CD); Pattern Formation and Solitons (nlin.PS)

[5]  arXiv:2401.09438 (replaced) [pdf, other]

Title: Recurrence analysis of meteorological data from climate zones in India

Authors: Joshin John Bejoy, G. Ambika

Comments: 11 pages, 11 figures: supplement-5 pages, 6 figures. arXiv admin note: text overlap with arXiv:2307.01165

Subjects: Atmospheric and Oceanic Physics (physics.ao-ph); Chaotic Dynamics (nlin.CD); Physics and Society (physics.soc-ph)

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