Systems far from equilibrium approach stability slowly due to "anti-mixing" characterized by regions of the phase-space that remain disconnected after prolonged action of the flow. We introduce the Optimal Growth Mode (OGM) to capture this slow initial relaxation. The OGM is calculated from Markov matrices approximating the action of the Fokker-Planck operator onto the phase space. It is obtained as the mode having the largest growth in energy before decay. Important nuances between the OGM and the more traditional slowest decaying mode are detailed in the case of the Lorenz 63 model. The implications for understanding how complex systems respond to external forces, are discussed.
{"title":"The Optimal Growth Mode in the Relaxation to Statistical Equilibrium","authors":"Manuel Santos Gutiérrez, Mickaël D. Chekroun","doi":"arxiv-2407.02545","DOIUrl":"https://doi.org/arxiv-2407.02545","url":null,"abstract":"Systems far from equilibrium approach stability slowly due to \"anti-mixing\"\u0000characterized by regions of the phase-space that remain disconnected after\u0000prolonged action of the flow. We introduce the Optimal Growth Mode (OGM) to\u0000capture this slow initial relaxation. The OGM is calculated from Markov\u0000matrices approximating the action of the Fokker-Planck operator onto the phase\u0000space. It is obtained as the mode having the largest growth in energy before\u0000decay. Important nuances between the OGM and the more traditional slowest\u0000decaying mode are detailed in the case of the Lorenz 63 model. The implications\u0000for understanding how complex systems respond to external forces, are\u0000discussed.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141550970","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}
The heterogeneity among interacting dynamical systems or in the pattern of interactions observed in real complex systems, often lead to partially synchronized states like chimeras or oscillation suppressed states like inhomogeneous or homogeneous steady states. In such cases, recovering synchronized oscillations back is required in many applications but is a real challenge. We present how synchronized oscillations can be restored by tuning the dynamical time scales of the system. For this we use the model of a multiplex network where first layer of coupled oscillators is multiplexed with an environmental layer that can generate various possible chimera states and suppressed states. We show that by tuning the time scale mismatch between the layers , we can revive synchronized oscillations in both layers from these states. We analyse the nature of the transition to synchronization and the results are verified for two- and three-layer multiplex networks.
{"title":"Recovery of synchronized oscillations on multiplex networks by tuning dynamical time scales","authors":"Aiwin T Vadakkan, Umesh Kumar Verma, G. Ambika","doi":"arxiv-2407.00368","DOIUrl":"https://doi.org/arxiv-2407.00368","url":null,"abstract":"The heterogeneity among interacting dynamical systems or in the pattern of\u0000interactions observed in real complex systems, often lead to partially\u0000synchronized states like chimeras or oscillation suppressed states like\u0000inhomogeneous or homogeneous steady states. In such cases, recovering\u0000synchronized oscillations back is required in many applications but is a real\u0000challenge. We present how synchronized oscillations can be restored by tuning\u0000the dynamical time scales of the system. For this we use the model of a\u0000multiplex network where first layer of coupled oscillators is multiplexed with\u0000an environmental layer that can generate various possible chimera states and\u0000suppressed states. We show that by tuning the time scale mismatch between the\u0000layers , we can revive synchronized oscillations in both layers from these\u0000states. We analyse the nature of the transition to synchronization and the\u0000results are verified for two- and three-layer multiplex networks.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"24 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141515164","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}
Intractable phase dynamics often challenge our understanding of complex oscillatory systems, hindering the exploration of synchronisation, chaos, and emergent phenomena across diverse fields. We introduce a novel conceptual framework for phase analysis, using the osculating circle to construct a co-moving coordinate system, which allows us to define a unique phase of the system. This coordinate independent, geometrical technique allows dissecting intricate local phase dynamics, even in regimes where traditional methods fail. Our methodology enables the analysis of a wider range of complex systems which were previously deemed intractable.
{"title":"Osculatory Dynamics: Framework for the Analysis of Oscillatory Systems","authors":"Marco Thiel","doi":"arxiv-2407.00235","DOIUrl":"https://doi.org/arxiv-2407.00235","url":null,"abstract":"Intractable phase dynamics often challenge our understanding of complex\u0000oscillatory systems, hindering the exploration of synchronisation, chaos, and\u0000emergent phenomena across diverse fields. We introduce a novel conceptual\u0000framework for phase analysis, using the osculating circle to construct a\u0000co-moving coordinate system, which allows us to define a unique phase of the\u0000system. This coordinate independent, geometrical technique allows dissecting\u0000intricate local phase dynamics, even in regimes where traditional methods fail.\u0000Our methodology enables the analysis of a wider range of complex systems which\u0000were previously deemed intractable.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504227","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}
M. Mugnaine, J. D. Szezech Jr., R. L. Viana, I. L. Caldas, P. J. Morrison
For several decades now it has been known that systems with shearless invariant tori, nontwist Hamiltonian systems, possess barriers to chaotic transport. These barriers are resilient to breakage under perturbation and therefore regions where they occur are natural places to look for barriers to transport. We describe a novel kind of effective barrier that persists after the shearless torus is broken. Because phenomena are generic, for convenience we study the Standard Nontwist Map (SNM), an area-preserving map that violates the twist condition locally in the phase space. The novel barrier occurs in nontwist systems when twin even period islands are present, which happens for a broad range of parameter values in the SNM. With a phase space composed of regular and irregular orbits, the movement of chaotic trajectories is hampered by the existence of both shearless curves, total barriers, and a network of partial barriers formed by the stable and unstable manifolds of the hyperbolic points. Being a degenerate system, the SNM has twin islands and, consequently, twin hyperbolic points. We show that the structures formed by the manifolds intrinsically depend on period parity of the twin islands. For this even scenario the novel structure, named a torus free barrier, occurs because the manifolds of different hyperbolic points form an intricate chain atop a dipole configuration and the transport of chaotic trajectories through the chain becomes a rare event. This structure impacts the emergence of transport, the escape basin for chaotic trajectories, the transport mechanism and the chaotic saddle. The case of odd periodic orbits is different: we find for this case the emergence of transport immediately after the breakup of the last invariant curve, and this leads to a scenario of higher transport, with intricate escape basin boundary and a chaotic saddle with non-uniformly distributed points.
{"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}
Amin Alibakhshi, Sasan Rahmanian, Michel Destrade, Giuseppe Zurlo
We investigate the nonlinear vibrations of a functionally graded dielectric elastomer plate subjected to electromechanical loads. We focus on local and global dynamics in the system. We employ the Gent strain energy function to model the dielectric elastomer. The functionally graded parameters are the shear modulus, mass density, and permittivity of the elastomer, which are formulated by a common through-thickness power-law scheme. We derive the equation of motion using the Euler-Lagrange equations and solve it numerically with the Runge-Kutta method and a continuation-based method. We investigate the influence of the functionally graded parameters on equilibrium points, natural frequencies, and static/dynamic instability. We also establish a Hamiltonian energy method to detect safe regions of operating gradient parameters. Furthermore, we explore the effect of the functionally graded parameters on chaos and resonance by plotting several numerical diagrams, including time histories, phase portraits, Poincar'e maps, largest Lyapunov exponent criteria, bifurcation diagram of Poincar'e maps, and frequency-stretch curves. The results provide a benchmark for developing functionally graded soft smart materials.
{"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}
Bharath V Nair, Vismaya V S, Sishu Shankar Muni, Ali Durdu
In this paper, we introduce a novel image encryption and decryption algorithm using hyperchaotic signals from the novel 3D hyperchaotic map, 2D memristor map, Convolutional Neural Network (CNN), and key sensitivity analysis to achieve robust security and high efficiency. The encryption starts with the scrambling of gray images by using a 3D hyperchaotic map to yield complex sequences under disruption of pixel values; the robustness of this original encryption is further reinforced by employing a CNN to learn the intricate patterns and add the safety layer. The robustness of the encryption algorithm is shown by key sensitivity analysis, i.e., the average sensitivity of the algorithm to key elements. The other factors and systems of unauthorized decryption, even with slight variations in the keys, can alter the decryption procedure, resulting in the ineffective recreation of the decrypted image. Statistical analysis includes entropy analysis, correlation analysis, histogram analysis, and other security analyses like anomaly detection, all of which confirm the high security and effectiveness of the proposed encryption method. Testing of the algorithm under various noisy conditions is carried out to test robustness against Gaussian noise. Metrics for differential analysis, such as the NPCR (Number of Pixel Change Rate)and UACI (Unified Average Change Intensity), are also used to determine the strength of encryption. At the same time, the empirical validation was performed on several test images, which showed that the proposed encryption techniques have practical applicability and are robust to noise. Simulation results and comparative analyses illustrate that our encryption scheme possesses excellent visual security, decryption quality, and computational efficiency, and thus, it is efficient for secure image transmission and storage in big data applications.
{"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}
This paper explores the prediction of the dynamics of piecewise smooth maps using various deep learning models. We have shown various novel ways of predicting the dynamics of piecewise smooth maps using deep learning models. Moreover, we have used machine learning models such as Decision Tree Classifier, Logistic Regression, K-Nearest Neighbor, Random Forest, and Support Vector Machine for predicting the border collision bifurcation in the 1D normal form map and the 1D tent map. Further, we classified the regular and chaotic behaviour of the 1D tent map and the 2D Lozi map using deep learning models like Convolutional Neural Network (CNN), ResNet50, and ConvLSTM via cobweb diagram and phase portraits. We also classified the chaotic and hyperchaotic behaviour of the 3D piecewise smooth map using deep learning models such as the Feed Forward Neural Network (FNN), Long Short-Term Memory (LSTM), and Recurrent Neural Network (RNN). Finally, deep learning models such as Long Short-Term Memory (LSTM) and Recurrent Neural Network (RNN) are used for reconstructing the two parametric charts of 2D border collision bifurcation normal form map.
{"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}
When neural networks are trained from data to simulate the dynamics of physical systems, they encounter a persistent challenge: the long-time dynamics they produce are often unphysical or unstable. We analyze the origin of such instabilities when learning linear dynamical systems, focusing on the training dynamics. We make several analytical findings which empirical observations suggest extend to nonlinear dynamical systems. First, the rate of convergence of the training dynamics is uneven and depends on the distribution of energy in the data. As a special case, the dynamics in directions where the data have no energy cannot be learned. Second, in the unlearnable directions, the dynamics produced by the neural network depend on the weight initialization, and common weight initialization schemes can produce unstable dynamics. Third, injecting synthetic noise into the data during training adds damping to the training dynamics and can stabilize the learned simulator, though doing so undesirably biases the learned dynamics. For each contributor to instability, we suggest mitigative strategies. We also highlight important differences between learning discrete-time and continuous-time dynamics, and discuss extensions to nonlinear systems.
{"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}
Yorgos M. Psarellis, Themistoklis P. Sapsis, Ioannis G. Kevrekidis
Bifurcations mark qualitative changes of long-term behavior in dynamical systems and can often signal sudden ("hard") transitions or catastrophic events (divergences). Accurately locating them is critical not just for deeper understanding of observed dynamic behavior, but also for designing efficient interventions. When the dynamical system at hand is complex, possibly noisy, and expensive to sample, standard (e.g. continuation based) numerical methods may become impractical. We propose an active learning framework, where Bayesian Optimization is leveraged to discover saddle-node or Hopf bifurcations, from a judiciously chosen small number of vector field observations. Such an approach becomes especially attractive in systems whose state x parameter space exploration is resource-limited. It also naturally provides a framework for uncertainty quantification (aleatoric and epistemic), useful in systems with inherent stochasticity.
分岔标志着动态系统中长期行为的质变，通常预示着突然（"艰难"）的转变或灾难性事件（分歧）。准确定位分岔不仅对深入理解观察到的动态行为至关重要，而且对设计有效的干预措施也至关重要。当手头的动态系统非常复杂、可能存在噪声、采样成本高昂时，标准（如基于延续的）数值方法可能会变得不切实际。我们提出了一种主动学习框架，利用贝叶斯最优化技术，从明智选择的少量矢量场观测中发现鞍节点或霍普夫分岔。这种方法在资源有限的状态 x 参数空间探索系统中尤其具有吸引力。它还自然而然地提供了一个不确定性量化框架（估计和认识），对固有随机性系统非常有用。
{"title":"Active search for Bifurcations","authors":"Yorgos M. Psarellis, Themistoklis P. Sapsis, Ioannis G. Kevrekidis","doi":"arxiv-2406.11141","DOIUrl":"https://doi.org/arxiv-2406.11141","url":null,"abstract":"Bifurcations mark qualitative changes of long-term behavior in dynamical\u0000systems and can often signal sudden (\"hard\") transitions or catastrophic events\u0000(divergences). Accurately locating them is critical not just for deeper\u0000understanding of observed dynamic behavior, but also for designing efficient\u0000interventions. When the dynamical system at hand is complex, possibly noisy,\u0000and expensive to sample, standard (e.g. continuation based) numerical methods\u0000may become impractical. We propose an active learning framework, where Bayesian\u0000Optimization is leveraged to discover saddle-node or Hopf bifurcations, from a\u0000judiciously chosen small number of vector field observations. Such an approach\u0000becomes especially attractive in systems whose state x parameter space\u0000exploration is resource-limited. It also naturally provides a framework for\u0000uncertainty quantification (aleatoric and epistemic), useful in systems with\u0000inherent stochasticity.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141504257","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}
Recent observations of chaos in nanomagnet suggest a possibility of new spintronics applications such as random-number generator and neuromorphic computing. However, large amount of electric current and/or magnetic field are necessary for the excitation of chaos, which are unsuitable for energy-saving applications. Here, we propose an excitation of chaos in three-terminal spin-torque oscillator (STO). The driving force of the chaos is voltage-controlled magnetic anisotropy (VCMA) effect, which enables us to manipulate magnetization dynamics without spending electric current or magnetic field, and thus, energy efficient. In particular, we focus on the VCMA effect generated by feedback signal from the STO since feedback effect is known to be effective in exciting chaos in dynamical system. Solving the Landau-Lifshitz-Gilbert (LLG) equation numerically and applying temporal and statistical analyses to its solution, the existence of the chaotic and transient-chaotic magnetization dynamics driven by the feedback VCMA effect is identified.
最近在纳米磁体中观察到的混沌现象表明了新闻电子学应用的可能性，如随机数发生器和神经形态计算。然而，激发混沌需要大量的电流和/或磁场，不适合节省能量的应用。在此，我们提出了一种在三端旋扭振荡器（STO）中激发混沌的方法。混沌的驱动力是电压控制磁各向异性效应（VCMA），它能让我们在不消耗电流或磁场的情况下操纵磁化动态，从而实现节能。由于众所周知反馈效应能有效激发动态系统中的混沌，因此我们特别关注由 STO 反馈信号产生的 VCMA 效应。通过数值求解兰道-利夫希茨-吉尔伯特（Landau-Lifshitz-Gilbert，LLG）方程，并对其解法进行时间和统计分析，确定了由反馈 VCMA 效应驱动的混沌和瞬态混沌磁化动力学的存在。
{"title":"Feedback-voltage driven chaos in three-terminal spin-torque oscillator","authors":"Tomohiro Taniguchi","doi":"arxiv-2406.10493","DOIUrl":"https://doi.org/arxiv-2406.10493","url":null,"abstract":"Recent observations of chaos in nanomagnet suggest a possibility of new\u0000spintronics applications such as random-number generator and neuromorphic\u0000computing. However, large amount of electric current and/or magnetic field are\u0000necessary for the excitation of chaos, which are unsuitable for energy-saving\u0000applications. Here, we propose an excitation of chaos in three-terminal\u0000spin-torque oscillator (STO). The driving force of the chaos is\u0000voltage-controlled magnetic anisotropy (VCMA) effect, which enables us to\u0000manipulate magnetization dynamics without spending electric current or magnetic\u0000field, and thus, energy efficient. In particular, we focus on the VCMA effect\u0000generated by feedback signal from the STO since feedback effect is known to be\u0000effective in exciting chaos in dynamical system. Solving the\u0000Landau-Lifshitz-Gilbert (LLG) equation numerically and applying temporal and\u0000statistical analyses to its solution, the existence of the chaotic and\u0000transient-chaotic magnetization dynamics driven by the feedback VCMA effect is\u0000identified.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141515165","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}
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