arXiv - PHYS - Chaotic Dynamics最新文献_第9页

Near-horizon chaos beyond Einstein gravity 超越爱因斯坦引力的近地平线混沌

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-05-16 DOI: arxiv-2405.09945

Surajit Das, Surojit Dalui, Rickmoy Samanta

{"title":"Near-horizon chaos beyond Einstein gravity","authors":"Surajit Das, Surojit Dalui, Rickmoy Samanta","doi":"arxiv-2405.09945","DOIUrl":"https://doi.org/arxiv-2405.09945","url":null,"abstract":"We investigate chaos in the dynamics of outgoing massless particles near the\u0000horizon of static spherically symmetric (SSS) black holes in two well-motivated\u0000models of $f(R)$ gravity. In both these models, we probe chaos in the particle\u0000trajectories (under suitable harmonic confinement) in the vicinity of the black\u0000hole horizons, for a set of initial conditions. The particle trajectories,\u0000associated Poincar$acute{e}$ sections, and Lyapunov exponents clearly\u0000illustrate the role played by the black hole horizon in the growth of chaos\u0000within a specific energy range. We demonstrate how this energy range is\u0000controlled by the parameters of the modified gravity theory under\u0000consideration. The growth of chaos in such a classical setting is known to\u0000respect a surface gravity bound arising from universal aspects of particle\u0000dynamics close to the black hole horizon [K. Hashimoto and N. Tanahashi, Phys.\u0000Rev. D 95, 024007 (2017)], analogous to the quantum MSS bound [J. Maldacena,\u0000S.H. Shenker and D. Stanford, JHEP 08 (2016) 106]. Interestingly, both models\u0000studied in our work respect the bound, in contrast to some of the other models\u0000of $f(R)$ gravity in the existing literature. The work serves as a motivation\u0000to use chaos as an additional tool to probe Einstein gravity in the strong\u0000gravity regime in the vicinity of black hole horizons.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"52 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141062344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Comparative Analysis of Predicting Subsequent Steps in Hénon Map 预测赫农图谱后续步骤的比较分析

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-05-15 DOI: arxiv-2405.10190

Vismaya V S, Alok Hareendran, Bharath V Nair, Sishu Shankar Muni, Martin Lellep

{"title":"Comparative Analysis of Predicting Subsequent Steps in Hénon Map","authors":"Vismaya V S, Alok Hareendran, Bharath V Nair, Sishu Shankar Muni, Martin Lellep","doi":"arxiv-2405.10190","DOIUrl":"https://doi.org/arxiv-2405.10190","url":null,"abstract":"This paper explores the prediction of subsequent steps in H'enon Map using\u0000various machine learning techniques. The H'enon map, well known for its\u0000chaotic behaviour, finds applications in various fields including cryptography,\u0000image encryption, and pattern recognition. Machine learning methods,\u0000particularly deep learning, are increasingly essential for understanding and\u0000predicting chaotic phenomena. This study evaluates the performance of different\u0000machine learning models including Random Forest, Recurrent Neural Network\u0000(RNN), Long Short-Term Memory (LSTM) networks, Support Vector Machines (SVM),\u0000and Feed Forward Neural Networks (FNN) in predicting the evolution of the\u0000H'enon map. Results indicate that LSTM network demonstrate superior predictive\u0000accuracy, particularly in extreme event prediction. Furthermore, a comparison\u0000between LSTM and FNN models reveals the LSTM's advantage, especially for longer\u0000prediction horizons and larger datasets. This research underscores the\u0000significance of machine learning in elucidating chaotic dynamics and highlights\u0000the importance of model selection and dataset size in forecasting subsequent\u0000steps in chaotic systems.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"19 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141062373","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Approximation and decomposition of attractors of a Hopfield neural network system Hopfield 神经网络系统吸引子的逼近与分解

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-05-13 DOI: arxiv-2405.07567

Marius-F. Danca, Guanrong Chen

引用次数: 0

Particle transport in open polygonal billiards: a scattering map 开放多边形台球中的粒子传输：散射图

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-05-12 DOI: arxiv-2405.07179

Jordan Orchard, Federico Frascoli, Lamberto Rondoni, Carlos Mejía-Monasterio

{"title":"Particle transport in open polygonal billiards: a scattering map","authors":"Jordan Orchard, Federico Frascoli, Lamberto Rondoni, Carlos Mejía-Monasterio","doi":"arxiv-2405.07179","DOIUrl":"https://doi.org/arxiv-2405.07179","url":null,"abstract":"Polygonal billiards exhibit a rich and complex dynamical behavior. In recent\u0000years polygonal billiards have attracted great attention due to their\u0000application in the understanding of anomalous transport, but also at the\u0000fundamental level, due to its connections with diverse fields in mathematics.\u0000We explore this complexity and its consequences on the properties of particle\u0000transport in infinitely long channels made of the repetitions of an elementary\u0000open polygonal cell. Borrowing ideas from the Zemlyakov-Katok construction, we\u0000construct an interval exchange transformation classified by the singular\u0000directions of the discontinuities of the billiard flow over the translation\u0000surface associated to the elementary cell. From this, we derive an exact\u0000expression of a scattering map of the cell connecting the outgoing flow of\u0000trajectories with the unconstrained incoming flow. The scattering map is\u0000defined over a partition of the coordinate space, characterized by different\u0000families of trajectories. Furthermore, we obtain an analytical expression for\u0000the average speed of propagation of ballistic modes, describing with high\u0000accuracy the speed of propagation of ballistic fronts appearing in the tails of\u0000the distribution of the particle displacement. The symbolic hierarchy of the\u0000trajectories forming these ballistic fronts is also discussed.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"48 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140937731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On the higher-order smallest ring star network of Chialvo neurons under diffusive couplings 论扩散耦合下的奇亚尔沃神经元高阶最小环星网络

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-05-09 DOI: arxiv-2405.06000

Anjana S. Nair, Indranil Ghosh, Hammed O. Fatoyinbo, Sishu S. Muni

{"title":"On the higher-order smallest ring star network of Chialvo neurons under diffusive couplings","authors":"Anjana S. Nair, Indranil Ghosh, Hammed O. Fatoyinbo, Sishu S. Muni","doi":"arxiv-2405.06000","DOIUrl":"https://doi.org/arxiv-2405.06000","url":null,"abstract":"We put forward the dynamical study of a novel higher-order small network of\u0000Chialvo neurons arranged in a ring-star topology, with the neurons interacting\u0000via linear diffusive couplings. This model is perceived to imitate the\u0000nonlinear dynamical properties exhibited by a realistic nervous system where\u0000the neurons transfer information through higher-order multi-body interactions.\u0000We first analyze our model using the tools from nonlinear dynamics literature:\u0000fixed point analysis, Jacobian matrix, and bifurcation patterns. We observe the\u0000coexistence of chaotic attractors, and also an intriguing route to chaos\u0000starting from a fixed point, to period-doubling, to cyclic quasiperiodic closed\u0000invariant curves, to ultimately chaos. We numerically observe the existence of\u0000codimension-1 bifurcation patterns: saddle-node, period-doubling, and Neimark\u0000Sacker. We also qualitatively study the typical phase portraits of the system\u0000and numerically quantify chaos and complexity using the 0-1 test and sample\u0000entropy measure respectively. Finally, we study the collective behavior of the\u0000neurons in terms of two synchronization measures: the cross-correlation\u0000coefficient, and the Kuramoto order parameter.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140937613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Dynamical properties of a small heterogeneous chain network of neurons in discrete time 离散时间小型异质神经元链网络的动态特性

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-05-09 DOI: arxiv-2405.05675

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

引用次数: 0

Mitigation of extreme events in an excitable system 缓解可激系统中的极端事件

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-05-09 DOI: arxiv-2405.05994

R. Shashangan, S. Sudharsan, A. Venkatesan, M. Senthilvelan

引用次数: 0

Trapping and extreme clustering of finitely-dense inertial particles near a rotating vortex pair 旋转涡对附近有限致密惯性粒子的捕获和极端聚类

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-05-08 DOI: arxiv-2405.04949

Saumav Kapoor, Divya Jaganathan, Rama Govindarajan

{"title":"Trapping and extreme clustering of finitely-dense inertial particles near a rotating vortex pair","authors":"Saumav Kapoor, Divya Jaganathan, Rama Govindarajan","doi":"arxiv-2405.04949","DOIUrl":"https://doi.org/arxiv-2405.04949","url":null,"abstract":"Small heavy particles cannot get attracted into a region of closed\u0000streamlines in a non-accelerating frame (Sapsis & Haller 2010). In a rotating\u0000system, however, particles can get trapped (Angilella 2010) near vortices. We\u0000perform numerical simulations examining trapping of inertial particles in a\u0000prototypical rotating flow: an identical pair of rotating Lamb-Oseen vortices,\u0000without gravity. Our parameter space includes the particle Stokes number $St$,\u0000measuring the particle's inertia, and a density parameter $R$, measuring the\u0000particle-to-fluid relative density. We focus on inertial particles that are\u0000finitely denser than the fluid. Particles can get indefinitely trapped near the\u0000vortices and display extreme clustering into smaller dimensional objects:\u0000attracting fixed-points, limit cycles and chaotic attractors. As $St$ increases\u0000for a given $R$, we may have an incomplete or complete period-doubling route to\u0000chaos, as well as an unusual period-halving route back to a fixed-point\u0000attractor. The fraction of trapped particles can vary non-monotonically with\u0000$St$. We may even have windows in $St$ for which no particle trapping occurs.\u0000At $St$ larger than a critical value, beyond no trapping occurs, significant\u0000fractions of particles can spend long but finite times in the vortex vicinity.\u0000The inclusion of the Basset-Boussinesq history (BBH) force is imperative in our\u0000study due to particle's finite density. BBH force significantly increases the\u0000basin of attraction as well as the range of $St$ where trapping can occur.\u0000Extreme clustering can be physically significant in planetesimal formation by\u0000dust aggregation in protoplanetary disks, phytoplankton aggregation in oceans,\u0000etc.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"137 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140937733","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Spiral Attractors in a Reduced Mean-Field Model of Neuron-Glial Interaction 神经元与神经胶质相互作用的缩小平均场模型中的螺旋吸引子

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-05-07 DOI: arxiv-2405.04291

Sergey Olenin, Sergey Stasenko, Tatiana Levanova

{"title":"Spiral Attractors in a Reduced Mean-Field Model of Neuron-Glial Interaction","authors":"Sergey Olenin, Sergey Stasenko, Tatiana Levanova","doi":"arxiv-2405.04291","DOIUrl":"https://doi.org/arxiv-2405.04291","url":null,"abstract":"It is well known that bursting activity plays an important role in the\u0000processes of transmission of neural signals. In terms of population dynamics,\u0000macroscopic bursting can be described using a mean-field approach. Mean field\u0000theory provides a useful tool for analysis of collective behavior of a large\u0000populations of interacting units, allowing to reduce the description of\u0000corresponding dynamics to just a few equations. Recently a new phenomenological\u0000model was proposed that describes bursting population activity of a big group\u0000of excitatory neurons, taking into account short-term synaptic plasticity and\u0000the astrocytic modulation of the synaptic dynamics [1]. The purpose of the\u0000present study is to investigate various bifurcation scenarios of the appearance\u0000of bursting activity in the phenomenological model. We show that the birth of\u0000bursting population pattern can be connected both with the cascade of period\u0000doubling bifurcations and further development of chaos according to the\u0000Shilnikov scenario, which leads to the appearance of a homoclinic attractor\u0000containing a homoclinic loop of a saddle-focus equilibrium with the\u0000two-dimensional unstable invariant manifold. We also show that the homoclinic\u0000spiral attractors observed in the system under study generate several types of\u0000bursting activity with different properties.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140937673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

On the weight dynamics of learning networks 论学习网络的权重动态

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-04-30 DOI: arxiv-2405.00743

Nahal Sharafi, Christoph Martin, Sarah Hallerberg

引用次数: 0