We numerically investigate the stability of exceptional periodic classical trajectories in rather generic chaotic many-body systems and explore a possible connection between these trajectories and exceptional nonthermal quantum eigenstates known as "quantum many-body scars". The systems considered are chaotic spin chains with short-range interactions, both classical and quantum. On the classical side, the chosen periodic trajectories are such that all spins instantaneously point in the same direction, which evolves as a function of time. We find that the largest Lyapunov exponents characterising the stabillity of these trajectories have surprisingly strong and nontrivial dependencies on the interaction constants and chain lengths. In particular, we identify rather long spin chains, where the above periodic trajectories are Lyapunov-stable on many-body energy shells overwhelmingly dominated by chaotic motion. We also find that instabilities around periodic trajectories in modestly large spin chains develop into a transient nearly quasiperiodic non-ergodic regime. In some cases, the lifetime of this regime is extremely long, which we interpret as a manifestation of Arnold diffusion in the vicinity of integrable dynamics. On the quantum side, we numerically investigate the dynamics of quantum states starting with all spins initially pointing in the same direction: these are the quantum counterparts of the initial conditions for the above periodic classical trajectories. Our investigation reveals the existence of quantum many-body scars for numerically accessible finite chains of spins 3/2 and higher. The dynamic thermalisation process dominated by quantum scars is shown to exhibit a slowdown in comparison with generic thermalisation at the same energy. Finally, we identify quantum signatures of the proximity to a classical separatrix of the periodic motion.
{"title":"Periodic classical trajectories and quantum scars in many-spin systems","authors":"Igor Ermakov, Oleg Lychkovskiy, Boris V. Fine","doi":"arxiv-2409.00258","DOIUrl":"https://doi.org/arxiv-2409.00258","url":null,"abstract":"We numerically investigate the stability of exceptional periodic classical\u0000trajectories in rather generic chaotic many-body systems and explore a possible\u0000connection between these trajectories and exceptional nonthermal quantum\u0000eigenstates known as \"quantum many-body scars\". The systems considered are\u0000chaotic spin chains with short-range interactions, both classical and quantum.\u0000On the classical side, the chosen periodic trajectories are such that all spins\u0000instantaneously point in the same direction, which evolves as a function of\u0000time. We find that the largest Lyapunov exponents characterising the stabillity\u0000of these trajectories have surprisingly strong and nontrivial dependencies on\u0000the interaction constants and chain lengths. In particular, we identify rather\u0000long spin chains, where the above periodic trajectories are Lyapunov-stable on\u0000many-body energy shells overwhelmingly dominated by chaotic motion. We also\u0000find that instabilities around periodic trajectories in modestly large spin\u0000chains develop into a transient nearly quasiperiodic non-ergodic regime. In\u0000some cases, the lifetime of this regime is extremely long, which we interpret\u0000as a manifestation of Arnold diffusion in the vicinity of integrable dynamics.\u0000On the quantum side, we numerically investigate the dynamics of quantum states\u0000starting with all spins initially pointing in the same direction: these are the\u0000quantum counterparts of the initial conditions for the above periodic classical\u0000trajectories. Our investigation reveals the existence of quantum many-body\u0000scars for numerically accessible finite chains of spins 3/2 and higher. The\u0000dynamic thermalisation process dominated by quantum scars is shown to exhibit a\u0000slowdown in comparison with generic thermalisation at the same energy. Finally,\u0000we identify quantum signatures of the proximity to a classical separatrix of\u0000the periodic motion.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"23 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222605","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}
Mauro Di Marco, Mauro Forti, Giacomo Innocenti, Luca Pancioni, Alberto Tesi
In the last few years the literature has witnessed a remarkable surge of interest for maps implemented by discrete-time (DT) memristor circuits. This paper investigates on the reasons underlying this type of complex behavior. To this end, the papers considers the map implemented by the simplest memristor circuit given by a capacitor and an ideal flux-controlled memristor or an inductor and an ideal charge-controlled memristor. In particular, the manuscript uses the DT flux-charge analysis method (FCAM) introduced in a recent paper to ensure that the first integrals and foliation in invariant manifolds of continuous-time (CT) memristor circuits are preserved exactly in the discretization for any step size. DT-FCAM yields a two-dimensional map in the voltage-current domain (VCD) and a manifold-dependent one-dimensional map in the flux-charge domain (FCD), i.e., a one-dimensional map on each invariant manifold. One main result is that, for suitable choices of the circuit parameters and memristor nonlinearities, both DT circuits can exactly embed two classic chaotic maps, i.e., the logistic map and the tent map. Moreover, due to the property of extreme multistability, the DT circuits can simultaneously embed in the manifolds all the dynamics displayed by varying one parameter in the logistic and tent map. The paper then considers a DT memristor Murali-Lakshmanan-Chua circuit and its dual. Via DT-FCAM these circuits implement a three-dimensional map in the VCD and a two-dimensional map on each invariant manifold in the FCD. It is shown that both circuits can simultaneously embed in the manifolds all the dynamics displayed by two other classic chaotic maps, i.e., the Henon map and the Lozi map, when varying one parameter in such maps. In essence, these results provide an explanation of why it is not surprising to observe complex dynamics even in simple DT memristor circuits.
{"title":"Embedding classic chaotic maps in simple discrete-time memristor circuits","authors":"Mauro Di Marco, Mauro Forti, Giacomo Innocenti, Luca Pancioni, Alberto Tesi","doi":"arxiv-2408.16352","DOIUrl":"https://doi.org/arxiv-2408.16352","url":null,"abstract":"In the last few years the literature has witnessed a remarkable surge of\u0000interest for maps implemented by discrete-time (DT) memristor circuits. This\u0000paper investigates on the reasons underlying this type of complex behavior. To\u0000this end, the papers considers the map implemented by the simplest memristor\u0000circuit given by a capacitor and an ideal flux-controlled memristor or an\u0000inductor and an ideal charge-controlled memristor. In particular, the\u0000manuscript uses the DT flux-charge analysis method (FCAM) introduced in a\u0000recent paper to ensure that the first integrals and foliation in invariant\u0000manifolds of continuous-time (CT) memristor circuits are preserved exactly in\u0000the discretization for any step size. DT-FCAM yields a two-dimensional map in\u0000the voltage-current domain (VCD) and a manifold-dependent one-dimensional map\u0000in the flux-charge domain (FCD), i.e., a one-dimensional map on each invariant\u0000manifold. One main result is that, for suitable choices of the circuit\u0000parameters and memristor nonlinearities, both DT circuits can exactly embed two\u0000classic chaotic maps, i.e., the logistic map and the tent map. Moreover, due to\u0000the property of extreme multistability, the DT circuits can simultaneously\u0000embed in the manifolds all the dynamics displayed by varying one parameter in\u0000the logistic and tent map. The paper then considers a DT memristor\u0000Murali-Lakshmanan-Chua circuit and its dual. Via DT-FCAM these circuits\u0000implement a three-dimensional map in the VCD and a two-dimensional map on each\u0000invariant manifold in the FCD. It is shown that both circuits can\u0000simultaneously embed in the manifolds all the dynamics displayed by two other\u0000classic chaotic maps, i.e., the Henon map and the Lozi map, when varying one\u0000parameter in such maps. In essence, these results provide an explanation of why\u0000it is not surprising to observe complex dynamics even in simple DT memristor\u0000circuits.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"9 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222570","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}
Determination of the nature of the dynamical state of a system as a function of its parameters is an important problem in the study of dynamical systems. This problem becomes harder in experimental systems where the obtained data is inadequate (low-res) or has missing values. Recent developments in the field of topological data analysis have given a powerful methodology, viz. persistent homology, that is particularly suited for the study of dynamical systems. Earlier studies have mapped the dynamical features with the topological features of some systems. However, these mappings between the dynamical features and the topological features are notional and inadequate for accurate classification on two counts. First, the methodologies employed by the earlier studies heavily relied on human validation and intervention. Second, this mapping done on the chaotic dynamical regime makes little sense because essentially the topological summaries in this regime are too noisy to extract meaningful features from it. In this paper, we employ Machine Learning (ML) assisted methodology to minimize the human intervention and validation of extracting the topological summaries from the dynamical states of systems. Further, we employ a metric that counts in the noisy topological summaries, which are normally discarded, to characterize the state of the dynamical system as periodic or chaotic. This is surprisingly different from the conventional methodologies wherein only the persisting (long-lived) topological features are taken into consideration while the noisy (short-lived) topological features are neglected. We have demonstrated our ML-assisted method on well-known systems such as the Lorentz, Duffing, and Jerk systems. And we expect that our methodology will be of utility in characterizing other dynamical systems including experimental systems that are constrained with limited data.
确定一个系统的动力学状态作为其参数函数的性质是动力学系统研究中的一个重要问题。在实验系统中，由于获得的数据不充分（低分辨率）或有缺失值，这个问题变得更加困难。拓扑数据分析领域的最新发展提供了一种强大的方法论，即持久本构学，它特别适合研究动力系统。然而，这些动态特征与拓扑特征之间的映射只是名义上的，不足以准确分类，原因有二。首先，早期研究采用的方法严重依赖人工验证和干预。其次，在混沌动力学体系中进行的映射意义不大，因为该体系中的拓扑总结噪声太大，无法从中提取有意义的特征。在本文中，我们采用了机器学习（ML）辅助方法，最大程度地减少了从系统动态状态中提取拓扑总结时的人为干预和验证。这与传统方法大相径庭，传统方法只考虑持久（长寿命）拓扑特征，而忽略噪声（短寿命）拓扑特征。我们已经在洛伦兹系统、达芬系统和杰克系统等著名系统上演示了我们的 ML 辅助方法。我们希望我们的方法能在表征其他动力系统（包括数据有限的实验系统）时发挥作用。
{"title":"Characterization of dynamical systems with scanty data using Persistent Homology and Machine Learning","authors":"Rishab Antosh, Sanjit Das, N. Nirmal Thyagu","doi":"arxiv-2408.15834","DOIUrl":"https://doi.org/arxiv-2408.15834","url":null,"abstract":"Determination of the nature of the dynamical state of a system as a function\u0000of its parameters is an important problem in the study of dynamical systems.\u0000This problem becomes harder in experimental systems where the obtained data is\u0000inadequate (low-res) or has missing values. Recent developments in the field of\u0000topological data analysis have given a powerful methodology, viz. persistent\u0000homology, that is particularly suited for the study of dynamical systems.\u0000Earlier studies have mapped the dynamical features with the topological\u0000features of some systems. However, these mappings between the dynamical\u0000features and the topological features are notional and inadequate for accurate\u0000classification on two counts. First, the methodologies employed by the earlier\u0000studies heavily relied on human validation and intervention. Second, this\u0000mapping done on the chaotic dynamical regime makes little sense because\u0000essentially the topological summaries in this regime are too noisy to extract\u0000meaningful features from it. In this paper, we employ Machine Learning (ML)\u0000assisted methodology to minimize the human intervention and validation of\u0000extracting the topological summaries from the dynamical states of systems.\u0000Further, we employ a metric that counts in the noisy topological summaries,\u0000which are normally discarded, to characterize the state of the dynamical system\u0000as periodic or chaotic. This is surprisingly different from the conventional\u0000methodologies wherein only the persisting (long-lived) topological features are\u0000taken into consideration while the noisy (short-lived) topological features are\u0000neglected. We have demonstrated our ML-assisted method on well-known systems\u0000such as the Lorentz, Duffing, and Jerk systems. And we expect that our\u0000methodology will be of utility in characterizing other dynamical systems\u0000including experimental systems that are constrained with limited data.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"436 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222572","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}
Several authors have reported that the echo state network reproduces bifurcation diagrams of some nonlinear differential equations using the data for a few control parameters. We demonstrate that a simpler feedforward neural network can also reproduce the bifurcation diagram of the logistics map and synchronization transition in globally coupled Stuart-Landau equations.
{"title":"Machine Learning of Nonlinear Dynamical Systems with Control Parameters Using Feedforward Neural Networks","authors":"Hidetsugu Sakaguchi","doi":"arxiv-2409.07468","DOIUrl":"https://doi.org/arxiv-2409.07468","url":null,"abstract":"Several authors have reported that the echo state network reproduces\u0000bifurcation diagrams of some nonlinear differential equations using the data\u0000for a few control parameters. We demonstrate that a simpler feedforward neural\u0000network can also reproduce the bifurcation diagram of the logistics map and\u0000synchronization transition in globally coupled Stuart-Landau equations.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"51 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222571","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 route to chaos and phase dynamics in a rotating shallow-water model were rigorously examined using a five-mode Galerkin truncated system with complex variables. This system is valuable for investigating how large/meso-scales destabilize and evolve into chaos. Two distinct transitions into chaotic behaviour were identified as energy levels increased. The initial transition occurs through bifurcations following the Feigenbaum sequence. The subsequent transition, at higher energy levels, shows a shift from quasi-periodic states to chaotic regimes. The first chaotic state is mainly due to inertial forces governing nonlinear interactions. The second chaotic state arises from the increased significance of free surface elevation in the dynamics. A novel reformulation using phase and amplitude representations for each truncated variable revealed that phase components exhibit a temporal piece-wise locking behaviour, maintaining a constant value for a prolonged interval before an abrupt transition of $pmpi$, while amplitudes remain chaotic. It was observed that phase stability duration decreases with increased energy, leading to chaos in phase components at high energy levels. This is attributed to the nonlinear term in the equations, where phase components are introduced through linear combinations of triads with different modes. When locking durations vary across modes, the dynamics result in a stochastic interplay of multiple $pi$ phase shifts, creating a stochastic dynamic within the coupled phase triads, observable even at minimal energy injections.
{"title":"Route to chaos and resonant triads interaction in a truncated Rotating Nonlinear shallow-water model","authors":"Francesco Carbone, Denys Dutykh","doi":"arxiv-2408.14495","DOIUrl":"https://doi.org/arxiv-2408.14495","url":null,"abstract":"The route to chaos and phase dynamics in a rotating shallow-water model were\u0000rigorously examined using a five-mode Galerkin truncated system with complex\u0000variables. This system is valuable for investigating how large/meso-scales\u0000destabilize and evolve into chaos. Two distinct transitions into chaotic\u0000behaviour were identified as energy levels increased. The initial transition\u0000occurs through bifurcations following the Feigenbaum sequence. The subsequent\u0000transition, at higher energy levels, shows a shift from quasi-periodic states\u0000to chaotic regimes. The first chaotic state is mainly due to inertial forces\u0000governing nonlinear interactions. The second chaotic state arises from the\u0000increased significance of free surface elevation in the dynamics. A novel\u0000reformulation using phase and amplitude representations for each truncated\u0000variable revealed that phase components exhibit a temporal piece-wise locking\u0000behaviour, maintaining a constant value for a prolonged interval before an\u0000abrupt transition of $pmpi$, while amplitudes remain chaotic. It was observed\u0000that phase stability duration decreases with increased energy, leading to chaos\u0000in phase components at high energy levels. This is attributed to the nonlinear\u0000term in the equations, where phase components are introduced through linear\u0000combinations of triads with different modes. When locking durations vary across\u0000modes, the dynamics result in a stochastic interplay of multiple $pi$ phase\u0000shifts, creating a stochastic dynamic within the coupled phase triads,\u0000observable even at minimal energy injections.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"60 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222573","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 study examines the dynamical properties of the Ikeda map, with a focus on bifurcations and chaotic behavior. We investigate how variations in dissipation parameters influence the system, uncovering shrimp-shaped structures that represent intricate transitions between regular and chaotic dynamics. Key findings include the analysis of period-doubling bifurcations and the onset of chaos. We utilize Lyapunov exponents to distinguish between stable and chaotic regions. These insights contribute to a deeper understanding of nonlinear and chaotic dynamics in optical systems.
{"title":"Mapping Chaos: Bifurcation Patterns and Shrimp Structures in the Ikeda Map","authors":"Diego F. M. Oliveira","doi":"arxiv-2408.11254","DOIUrl":"https://doi.org/arxiv-2408.11254","url":null,"abstract":"This study examines the dynamical properties of the Ikeda map, with a focus\u0000on bifurcations and chaotic behavior. We investigate how variations in\u0000dissipation parameters influence the system, uncovering shrimp-shaped\u0000structures that represent intricate transitions between regular and chaotic\u0000dynamics. Key findings include the analysis of period-doubling bifurcations and\u0000the onset of chaos. We utilize Lyapunov exponents to distinguish between stable\u0000and chaotic regions. These insights contribute to a deeper understanding of\u0000nonlinear and chaotic dynamics in optical systems.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222574","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}
Bruno B. Leal, Matheus J. Lazarotto, Michele Mugnaine, Alfredo M. Ozorio de Almeida, Ricardo L. Viana, Iberê L. Caldas
In nontwist systems, primary shearless curves act as barriers to chaotic transport. Surprisingly, the onset of secondary shearless curves has been reported in a few twist systems. Meanwhile, we found that, in twist systems, the onset of these secondary shearless curves is a standard process that may appear as control parameters are varied in situations where there is resonant mode coupling. Namely, we analyze these shearless bifurcations in two-harmonic systems for the standard map, the Ullmann map, and for the Walker-Ford Hamiltonian flow. The onset of shearless curves is related to bifurcations of periodic points. Furthermore, depending on the bifurcation, these shearless curves can emerge alone or in pairs, and in some cases, deform into separatrices.
{"title":"Shearless bifurcations for two isochronous resonant perturbations","authors":"Bruno B. Leal, Matheus J. Lazarotto, Michele Mugnaine, Alfredo M. Ozorio de Almeida, Ricardo L. Viana, Iberê L. Caldas","doi":"arxiv-2408.10930","DOIUrl":"https://doi.org/arxiv-2408.10930","url":null,"abstract":"In nontwist systems, primary shearless curves act as barriers to chaotic\u0000transport. Surprisingly, the onset of secondary shearless curves has been\u0000reported in a few twist systems. Meanwhile, we found that, in twist systems,\u0000the onset of these secondary shearless curves is a standard process that may\u0000appear as control parameters are varied in situations where there is resonant\u0000mode coupling. Namely, we analyze these shearless bifurcations in two-harmonic\u0000systems for the standard map, the Ullmann map, and for the Walker-Ford\u0000Hamiltonian flow. The onset of shearless curves is related to bifurcations of\u0000periodic points. Furthermore, depending on the bifurcation, these shearless\u0000curves can emerge alone or in pairs, and in some cases, deform into\u0000separatrices.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"60 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222576","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}
Biological activities are often seen entrained onto the day-night and other celestial mechanical cycles (e.g., seasonal and lunar), but studies on the origin of life have largely not accounted for such periodic external environmental variations. We argue that this may be an important omission, because the signature replication behaviour of life represents temporal memory in the dynamics of ecosystems, that signifies the absence of mixing properties (i.e., the dynamics are not fully chaotic), and entrainment onto regular, periodic external perturbative influences has been proven capable of suppressing chaos, and thus may bring otherwise unstable chemical reaction sets into viability, as precursors to abiogenesis. As well, external perturbations may be necessary to prevent an open dissipative (bio)chemical system from collapsing into the opposite extreme -- the point attractor of thermal equilibrium. In short, life may precariously rest on the edge of chaos, and open-loop periodic perturbation rooted in celestial mechanics (and should be simulated in laboratory experiments in origin-of-life studies) may help with the balancing. Such considerations, if pertinent, would also be consequential to exobiology, e.g., in regard to tidal-locking properties of potential host worlds.
{"title":"A dynamical systems perspective on the celestial mechanical contribution to the emergence of life","authors":"Fan Zhang","doi":"arxiv-2408.10544","DOIUrl":"https://doi.org/arxiv-2408.10544","url":null,"abstract":"Biological activities are often seen entrained onto the day-night and other\u0000celestial mechanical cycles (e.g., seasonal and lunar), but studies on the\u0000origin of life have largely not accounted for such periodic external\u0000environmental variations. We argue that this may be an important omission,\u0000because the signature replication behaviour of life represents temporal memory\u0000in the dynamics of ecosystems, that signifies the absence of mixing properties\u0000(i.e., the dynamics are not fully chaotic), and entrainment onto regular,\u0000periodic external perturbative influences has been proven capable of\u0000suppressing chaos, and thus may bring otherwise unstable chemical reaction sets\u0000into viability, as precursors to abiogenesis. As well, external perturbations\u0000may be necessary to prevent an open dissipative (bio)chemical system from\u0000collapsing into the opposite extreme -- the point attractor of thermal\u0000equilibrium. In short, life may precariously rest on the edge of chaos, and\u0000open-loop periodic perturbation rooted in celestial mechanics (and should be\u0000simulated in laboratory experiments in origin-of-life studies) may help with\u0000the balancing. Such considerations, if pertinent, would also be consequential\u0000to exobiology, e.g., in regard to tidal-locking properties of potential host\u0000worlds.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"6 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222575","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}
Here we define natural chaotic systems, like the earths weather and climate system, as chaotic systems which are open to the world so have constantly changing boundary conditions, and measurements of their states are subject to errors. In such systems the chaoticity, amplifying error exponentially fast, is so confounded with the boundary condition fluctuations and the measurement error, that it is impossible to consistently estimate the trajectory of the system much less predict it. Although asymptotic theory exists for estimating the conditional predictive distributions, it is hard to find where this theory has been applied. Here the theory is reviewed, and applied to identifying useful predictive variables for simultaneous multiseason prediction of precipitation with potentially useful updating possible. This is done at two locations, one midocean the other landlocked. The method appears to show promise for fast exploration of variables for multiseason prediction.
{"title":"Chaotic uncertainty and statistical inference for natural chaotic systems: Choosing predictors for multiple season ahead prediction of precipitation, Extended and Annotated","authors":"Michael LuValle","doi":"arxiv-2409.00023","DOIUrl":"https://doi.org/arxiv-2409.00023","url":null,"abstract":"Here we define natural chaotic systems, like the earths weather and climate\u0000system, as chaotic systems which are open to the world so have constantly\u0000changing boundary conditions, and measurements of their states are subject to\u0000errors. In such systems the chaoticity, amplifying error exponentially fast, is\u0000so confounded with the boundary condition fluctuations and the measurement\u0000error, that it is impossible to consistently estimate the trajectory of the\u0000system much less predict it. Although asymptotic theory exists for estimating\u0000the conditional predictive distributions, it is hard to find where this theory\u0000has been applied. Here the theory is reviewed, and applied to identifying\u0000useful predictive variables for simultaneous multiseason prediction of\u0000precipitation with potentially useful updating possible. This is done at two\u0000locations, one midocean the other landlocked. The method appears to show\u0000promise for fast exploration of variables for multiseason prediction.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"81 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222581","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}
Cross-Correlation random matrices have emerged as a promising indicator of phase transitions in spin systems. The core concept is that the evolution of magnetization encapsulates thermodynamic information [R. da Silva, Int. J. Mod. Phys. C, 2350061 (2023)], which is directly reflected in the eigenvalues of these matrices. When these evolutions are analyzed in the mean-field regime, an important question arises: Can the Langevin equation, when translated into maps, perform the same function? Some studies suggest that this method may also capture the chaotic behavior of certain systems. In this work, we propose that the spectral properties of random matrices constructed from maps derived from deterministic or stochastic differential equations can indicate the critical or chaotic behavior of such systems. For chaotic systems, we need only the evolution of iterated Hamiltonian equations, and for spin systems, the Langevin maps obtained from mean-field equations suffice, thus avoiding the need for Monte Carlo (MC) simulations or other techniques.
交叉相关随机矩阵已成为自旋系统相变的一个有前途的指标。其核心概念是磁化演化包含热力学信息[R. da Silva，Int. J. Mod.Phys. C，2350061 (2023)]，这些信息直接反映在这些矩阵的特征值中。在均场机制中分析这些演化时，出现了一个重要问题：朗之文方程在转化为映射时，能否执行相同的功能？一些研究表明，这种方法也可以捕捉某些系统的混沌行为。在这项工作中，我们提出，由确定性或随机微分方程导出的映射构建的随机矩阵的谱特性可以指示这类系统的临界或混沌行为。对于混沌系统，我们只需要迭代哈密顿方程的演化，而对于自旋系统，从均值场方程得到的朗格文映射就足够了，从而避免了蒙特卡罗（MC）模拟或其他技术的需要。
{"title":"Identifying Patterns Using Cross-Correlation Random Matrices Derived from Deterministic and Stochastic Differential Equations","authors":"Roberto da Silva, Sandra D. Prado","doi":"arxiv-2408.08237","DOIUrl":"https://doi.org/arxiv-2408.08237","url":null,"abstract":"Cross-Correlation random matrices have emerged as a promising indicator of\u0000phase transitions in spin systems. The core concept is that the evolution of\u0000magnetization encapsulates thermodynamic information [R. da Silva, Int. J. Mod.\u0000Phys. C, 2350061 (2023)], which is directly reflected in the eigenvalues of\u0000these matrices. When these evolutions are analyzed in the mean-field regime, an\u0000important question arises: Can the Langevin equation, when translated into\u0000maps, perform the same function? Some studies suggest that this method may also\u0000capture the chaotic behavior of certain systems. In this work, we propose that\u0000the spectral properties of random matrices constructed from maps derived from\u0000deterministic or stochastic differential equations can indicate the critical or\u0000chaotic behavior of such systems. For chaotic systems, we need only the\u0000evolution of iterated Hamiltonian equations, and for spin systems, the Langevin\u0000maps obtained from mean-field equations suffice, thus avoiding the need for\u0000Monte Carlo (MC) simulations or other techniques.","PeriodicalId":501167,"journal":{"name":"arXiv - PHYS - Chaotic Dynamics","volume":"62 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142222577","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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