arXiv - PHYS - Chaotic Dynamics最新文献_第6页

The Optimal Growth Mode in the Relaxation to Statistical Equilibrium 弛豫统计平衡中的最佳增长模式

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-07-02 DOI: arxiv-2407.02545

Manuel Santos Gutiérrez, Mickaël D. Chekroun

引用次数: 0

Recovery of synchronized oscillations on multiplex networks by tuning dynamical time scales 通过调整动态时间尺度恢复多路复用网络上的同步振荡

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-06-29 DOI: arxiv-2407.00368

Aiwin T Vadakkan, Umesh Kumar Verma, G. Ambika

引用次数: 0

Osculatory Dynamics: Framework for the Analysis of Oscillatory Systems 振荡动力学：振荡系统分析框架

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-06-28 DOI: arxiv-2407.00235

Marco Thiel

引用次数: 0

Shearless effective barriers to chaotic transport induced by even twin islands in nontwist systems 非扭曲系统中偶数孪生岛诱导的无剪切力有效混乱传输障碍

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-06-28 DOI: arxiv-2406.19947

M. Mugnaine, J. D. Szezech Jr., R. L. Viana, I. L. Caldas, P. J. Morrison

{"title":"Shearless effective barriers to chaotic transport induced by even twin islands in nontwist systems","authors":"M. Mugnaine, J. D. Szezech Jr., R. L. Viana, I. L. Caldas, P. J. Morrison","doi":"arxiv-2406.19947","DOIUrl":"https://doi.org/arxiv-2406.19947","url":null,"abstract":"For several decades now it has been known that systems with shearless\u0000invariant tori, nontwist Hamiltonian systems, possess barriers to chaotic\u0000transport. These barriers are resilient to breakage under perturbation and\u0000therefore regions where they occur are natural places to look for barriers to\u0000transport. We describe a novel kind of effective barrier that persists after\u0000the shearless torus is broken. Because phenomena are generic, for convenience\u0000we study the Standard Nontwist Map (SNM), an area-preserving map that violates\u0000the twist condition locally in the phase space. The novel barrier occurs in\u0000nontwist systems when twin even period islands are present, which happens for a\u0000broad range of parameter values in the SNM. With a phase space composed of\u0000regular and irregular orbits, the movement of chaotic trajectories is hampered\u0000by the existence of both shearless curves, total barriers, and a network of\u0000partial barriers formed by the stable and unstable manifolds of the hyperbolic\u0000points. Being a degenerate system, the SNM has twin islands and, consequently,\u0000twin hyperbolic points. We show that the structures formed by the manifolds\u0000intrinsically depend on period parity of the twin islands. For this even\u0000scenario the novel structure, named a torus free barrier, occurs because the\u0000manifolds of different hyperbolic points form an intricate chain atop a dipole\u0000configuration and the transport of chaotic trajectories through the chain\u0000becomes a rare event. This structure impacts the emergence of transport, the\u0000escape basin for chaotic trajectories, the transport mechanism and the chaotic\u0000saddle. The case of odd periodic orbits is different: we find for this case the\u0000emergence of transport immediately after the breakup of the last invariant\u0000curve, and this leads to a scenario of higher transport, with intricate escape\u0000basin boundary and a chaotic saddle with non-uniformly distributed points.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"173 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141515168","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

Local and Global Dynamics of a Functionally Graded Dielectric Elastomer Plate 功能分级介电弹性体板的局部和全局动力学

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-06-27 DOI: arxiv-2406.19145

Amin Alibakhshi, Sasan Rahmanian, Michel Destrade, Giuseppe Zurlo

{"title":"Local and Global Dynamics of a Functionally Graded Dielectric Elastomer Plate","authors":"Amin Alibakhshi, Sasan Rahmanian, Michel Destrade, Giuseppe Zurlo","doi":"arxiv-2406.19145","DOIUrl":"https://doi.org/arxiv-2406.19145","url":null,"abstract":"We investigate the nonlinear vibrations of a functionally graded dielectric\u0000elastomer plate subjected to electromechanical loads. We focus on local and\u0000global dynamics in the system. We employ the Gent strain energy function to\u0000model the dielectric elastomer. The functionally graded parameters are the\u0000shear modulus, mass density, and permittivity of the elastomer, which are\u0000formulated by a common through-thickness power-law scheme. We derive the\u0000equation of motion using the Euler-Lagrange equations and solve it numerically\u0000with the Runge-Kutta method and a continuation-based method. We investigate the\u0000influence of the functionally graded parameters on equilibrium points, natural\u0000frequencies, and static/dynamic instability. We also establish a Hamiltonian\u0000energy method to detect safe regions of operating gradient parameters.\u0000Furthermore, we explore the effect of the functionally graded parameters on\u0000chaos and resonance by plotting several numerical diagrams, including time\u0000histories, phase portraits, Poincar'e maps, largest Lyapunov exponent\u0000criteria, bifurcation diagram of Poincar'e maps, and frequency-stretch curves.\u0000The results provide a benchmark for developing functionally graded soft smart\u0000materials.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504228","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

Deep Learning and Chaos: A combined Approach To Image Encryption and Decryption 深度学习与混沌：图像加密和解密的组合方法

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-06-24 DOI: arxiv-2406.16792

Bharath V Nair, Vismaya V S, Sishu Shankar Muni, Ali Durdu

{"title":"Deep Learning and Chaos: A combined Approach To Image Encryption and Decryption","authors":"Bharath V Nair, Vismaya V S, Sishu Shankar Muni, Ali Durdu","doi":"arxiv-2406.16792","DOIUrl":"https://doi.org/arxiv-2406.16792","url":null,"abstract":"In this paper, we introduce a novel image encryption and decryption algorithm\u0000using hyperchaotic signals from the novel 3D hyperchaotic map, 2D memristor\u0000map, Convolutional Neural Network (CNN), and key sensitivity analysis to\u0000achieve robust security and high efficiency. The encryption starts with the\u0000scrambling of gray images by using a 3D hyperchaotic map to yield complex\u0000sequences under disruption of pixel values; the robustness of this original\u0000encryption is further reinforced by employing a CNN to learn the intricate\u0000patterns and add the safety layer. The robustness of the encryption algorithm\u0000is shown by key sensitivity analysis, i.e., the average sensitivity of the\u0000algorithm to key elements. The other factors and systems of unauthorized\u0000decryption, even with slight variations in the keys, can alter the decryption\u0000procedure, resulting in the ineffective recreation of the decrypted image.\u0000Statistical analysis includes entropy analysis, correlation analysis, histogram\u0000analysis, and other security analyses like anomaly detection, all of which\u0000confirm the high security and effectiveness of the proposed encryption method.\u0000Testing of the algorithm under various noisy conditions is carried out to test\u0000robustness against Gaussian noise. Metrics for differential analysis, such as\u0000the NPCR (Number of Pixel Change Rate)and UACI (Unified Average Change\u0000Intensity), are also used to determine the strength of encryption. At the same\u0000time, the empirical validation was performed on several test images, which\u0000showed that the proposed encryption techniques have practical applicability and\u0000are robust to noise. Simulation results and comparative analyses illustrate\u0000that our encryption scheme possesses excellent visual security, decryption\u0000quality, and computational efficiency, and thus, it is efficient for secure\u0000image transmission and storage in big data applications.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"38 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504253","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

Deep Learning for Prediction and Classifying the Dynamical behaviour of Piecewise Smooth Maps 深度学习用于预测和分类片状平滑地图的动态行为

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-06-24 DOI: arxiv-2406.17001

Vismaya V S, Bharath V Nair, Sishu Shankar Muni

{"title":"Deep Learning for Prediction and Classifying the Dynamical behaviour of Piecewise Smooth Maps","authors":"Vismaya V S, Bharath V Nair, Sishu Shankar Muni","doi":"arxiv-2406.17001","DOIUrl":"https://doi.org/arxiv-2406.17001","url":null,"abstract":"This paper explores the prediction of the dynamics of piecewise smooth maps\u0000using various deep learning models. We have shown various novel ways of\u0000predicting the dynamics of piecewise smooth maps using deep learning models.\u0000Moreover, we have used machine learning models such as Decision Tree\u0000Classifier, Logistic Regression, K-Nearest Neighbor, Random Forest, and Support\u0000Vector Machine for predicting the border collision bifurcation in the 1D normal\u0000form map and the 1D tent map. Further, we classified the regular and chaotic\u0000behaviour of the 1D tent map and the 2D Lozi map using deep learning models\u0000like Convolutional Neural Network (CNN), ResNet50, and ConvLSTM via cobweb\u0000diagram and phase portraits. We also classified the chaotic and hyperchaotic\u0000behaviour of the 3D piecewise smooth map using deep learning models such as the\u0000Feed Forward Neural Network (FNN), Long Short-Term Memory (LSTM), and Recurrent\u0000Neural Network (RNN). Finally, deep learning models such as Long Short-Term\u0000Memory (LSTM) and Recurrent Neural Network (RNN) are used for reconstructing\u0000the two parametric charts of 2D border collision bifurcation normal form map.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"75 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504229","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 instabilities in neural network-based physics simulators 论基于神经网络的物理模拟器的不稳定性

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-06-18 DOI: arxiv-2406.13101

Daniel Floryan

{"title":"On instabilities in neural network-based physics simulators","authors":"Daniel Floryan","doi":"arxiv-2406.13101","DOIUrl":"https://doi.org/arxiv-2406.13101","url":null,"abstract":"When neural networks are trained from data to simulate the dynamics of\u0000physical systems, they encounter a persistent challenge: the long-time dynamics\u0000they produce are often unphysical or unstable. We analyze the origin of such\u0000instabilities when learning linear dynamical systems, focusing on the training\u0000dynamics. We make several analytical findings which empirical observations\u0000suggest extend to nonlinear dynamical systems. First, the rate of convergence\u0000of the training dynamics is uneven and depends on the distribution of energy in\u0000the data. As a special case, the dynamics in directions where the data have no\u0000energy cannot be learned. Second, in the unlearnable directions, the dynamics\u0000produced by the neural network depend on the weight initialization, and common\u0000weight initialization schemes can produce unstable dynamics. Third, injecting\u0000synthetic noise into the data during training adds damping to the training\u0000dynamics and can stabilize the learned simulator, though doing so undesirably\u0000biases the learned dynamics. For each contributor to instability, we suggest\u0000mitigative strategies. We also highlight important differences between learning\u0000discrete-time and continuous-time dynamics, and discuss extensions to nonlinear\u0000systems.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"85 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504254","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

Active search for Bifurcations 主动搜索分岔

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-06-17 DOI: arxiv-2406.11141

Yorgos M. Psarellis, Themistoklis P. Sapsis, Ioannis G. Kevrekidis

引用次数: 0

Feedback-voltage driven chaos in three-terminal spin-torque oscillator 三端自旋扭矩振荡器中的反馈-电压驱动混沌

arXiv - PHYS - Chaotic Dynamics Pub Date : 2024-06-15 DOI: arxiv-2406.10493

Tomohiro Taniguchi

引用次数: 0