We investigate the synchronization behavior and the emergence of chimera states in a system of two interacting populations of maps possessing chaotic neural-like dynamics. We characterize four collective states on the space of coupling parameters of the system: complete synchronization, generalized synchronization, chimera states, and incoherence. We quantify the information exchange between the two neuron populations in chimera states. We have found a well-defined direction of the flow of information in chimera states, from the desynchronized population to the synchronized one. The incoherent population functions as a driver of the coherent neuron population in a chimera state. This feature is independent of the population sizes or population partitions. Our results yield insight into the communication mechanisms arising in brain processes such as unihemispheric sleep and epileptic seizures that have been associated to chimera states.
{"title":"Chimera states and information transfer in interacting populations of map-based neurons","authors":"V. J. Márquez-Rodríguez, K. Tucci, M. G. Cosenza","doi":"arxiv-2407.20289","DOIUrl":"https://doi.org/arxiv-2407.20289","url":null,"abstract":"We investigate the synchronization behavior and the emergence of chimera\u0000states in a system of two interacting populations of maps possessing chaotic\u0000neural-like dynamics. We characterize four collective states on the space of\u0000coupling parameters of the system: complete synchronization, generalized\u0000synchronization, chimera states, and incoherence. We quantify the information\u0000exchange between the two neuron populations in chimera states. We have found a\u0000well-defined direction of the flow of information in chimera states, from the\u0000desynchronized population to the synchronized one. The incoherent population\u0000functions as a driver of the coherent neuron population in a chimera state.\u0000This feature is independent of the population sizes or population partitions.\u0000Our results yield insight into the communication mechanisms arising in brain\u0000processes such as unihemispheric sleep and epileptic seizures that have been\u0000associated to chimera states.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"56 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141870883","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}
Systems of oscillators subject to time-dependent noise typically achieve synchronization for long times when their mutual coupling is sufficiently strong. The dynamical process whereby synchronization is reached can be thought of as a growth process in which an interface formed by the local phase field gradually roughens and eventually saturates. Such a process is here shown to display the generic scale invariance of the one-dimensional Kardar-Parisi-Zhang universality class, including a Tracy-Widom probability distribution for phase fluctuations around their mean. This is revealed by numerical explorations of a variety of oscillator systems: rings of generic phase oscillators and rings of paradigmatic limit-cycle oscillators, like Stuart-Landau and van der Pol. It also agrees with analytical expectations derived under conditions of strong mutual coupling. The nonequilibrium critical behavior that we find is robust and transcends the details of the oscillators considered. Hence, it may well be accessible to experimental ensembles of oscillators in the presence of e.g. thermal noise.
{"title":"Kardar-Parisi-Zhang universality class in the synchronization of oscillator lattices with time-dependent noise","authors":"Ricardo Gutierrez, Rodolfo Cuerno","doi":"arxiv-2407.15634","DOIUrl":"https://doi.org/arxiv-2407.15634","url":null,"abstract":"Systems of oscillators subject to time-dependent noise typically achieve\u0000synchronization for long times when their mutual coupling is sufficiently\u0000strong. The dynamical process whereby synchronization is reached can be thought\u0000of as a growth process in which an interface formed by the local phase field\u0000gradually roughens and eventually saturates. Such a process is here shown to\u0000display the generic scale invariance of the one-dimensional Kardar-Parisi-Zhang\u0000universality class, including a Tracy-Widom probability distribution for phase\u0000fluctuations around their mean. This is revealed by numerical explorations of a\u0000variety of oscillator systems: rings of generic phase oscillators and rings of\u0000paradigmatic limit-cycle oscillators, like Stuart-Landau and van der Pol. It\u0000also agrees with analytical expectations derived under conditions of strong\u0000mutual coupling. The nonequilibrium critical behavior that we find is robust\u0000and transcends the details of the oscillators considered. Hence, it may well be\u0000accessible to experimental ensembles of oscillators in the presence of e.g.\u0000thermal noise.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775079","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}
Impact of noise in coupled oscillators with pairwise interactions has been extensively explored. Here, we study stochastic second-order coupled Kuramoto oscillators with higher-order interactions, and show that as noise strength increases the critical points associated with synchronization transitions shift toward higher coupling values. By employing the perturbation analysis, we obtain an expression for the forward critical point as a function of inertia and noise strength. Further, for overdamped systems we show that as noise strength increases, the first-order transition switches to second-order even for higher-order couplings. We include a discussion on nature of critical points obtained through Ott-Antonsen ansatz.
{"title":"Stochastic Kuramoto oscillators with inertia and higher-order interactions","authors":"Priyanka Rajwani, Sarika Jalan","doi":"arxiv-2407.14874","DOIUrl":"https://doi.org/arxiv-2407.14874","url":null,"abstract":"Impact of noise in coupled oscillators with pairwise interactions has been\u0000extensively explored. Here, we study stochastic second-order coupled Kuramoto\u0000oscillators with higher-order interactions, and show that as noise strength\u0000increases the critical points associated with synchronization transitions shift\u0000toward higher coupling values. By employing the perturbation analysis, we\u0000obtain an expression for the forward critical point as a function of inertia\u0000and noise strength. Further, for overdamped systems we show that as noise\u0000strength increases, the first-order transition switches to second-order even\u0000for higher-order couplings. We include a discussion on nature of critical\u0000points obtained through Ott-Antonsen ansatz.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"72 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775078","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}
Interacting individuals in complex systems often give rise to coherent motion exhibiting coordinated global structures. Such phenomena are ubiquitously observed in nature, from cell migration, bacterial swarms, animal and insect groups, and even human societies. Primary mechanisms responsible for the emergence of collective behavior have been extensively identified, including local alignments based on average or relative velocity, non-local pairwise repulsive-attractive interactions such as distance-based potentials, interplay between local and non-local interactions, and cognitive-based inhomogeneous interactions. However, discovering how to adapt these mechanisms to modulate emergent behaviours remains elusive. Here, we demonstrate that it is possible to generate coordinated structures in collective behavior at desired moments with intended global patterns by fine-tuning an inter-agent interaction rule. Our strategy employs deep neural networks, obeying the laws of dynamics, to find interaction rules that command desired collective structures. The decomposition of interaction rules into distancing and aligning forces, expressed by polynomial series, facilitates the training of neural networks to propose desired interaction models. Presented examples include altering the mean radius and size of clusters in vortical swarms, timing of transitions from random to ordered states, and continuously shifting between typical modes of collective motions. This strategy can even be leveraged to superimpose collective modes, resulting in hitherto unexplored but highly practical hybrid collective patterns, such as protective security formations. Our findings reveal innovative strategies for creating and controlling collective motion, paving the way for new applications in robotic swarm operations, active matter organisation, and for the uncovering of obscure interaction rules in biological systems.
{"title":"Navigating the swarm: Deep neural networks command emergent behaviours","authors":"Dongjo Kim, Jeongsu Lee, Ho-Young Kim","doi":"arxiv-2407.11330","DOIUrl":"https://doi.org/arxiv-2407.11330","url":null,"abstract":"Interacting individuals in complex systems often give rise to coherent motion\u0000exhibiting coordinated global structures. Such phenomena are ubiquitously\u0000observed in nature, from cell migration, bacterial swarms, animal and insect\u0000groups, and even human societies. Primary mechanisms responsible for the\u0000emergence of collective behavior have been extensively identified, including\u0000local alignments based on average or relative velocity, non-local pairwise\u0000repulsive-attractive interactions such as distance-based potentials, interplay\u0000between local and non-local interactions, and cognitive-based inhomogeneous\u0000interactions. However, discovering how to adapt these mechanisms to modulate\u0000emergent behaviours remains elusive. Here, we demonstrate that it is possible\u0000to generate coordinated structures in collective behavior at desired moments\u0000with intended global patterns by fine-tuning an inter-agent interaction rule.\u0000Our strategy employs deep neural networks, obeying the laws of dynamics, to\u0000find interaction rules that command desired collective structures. The\u0000decomposition of interaction rules into distancing and aligning forces,\u0000expressed by polynomial series, facilitates the training of neural networks to\u0000propose desired interaction models. Presented examples include altering the\u0000mean radius and size of clusters in vortical swarms, timing of transitions from\u0000random to ordered states, and continuously shifting between typical modes of\u0000collective motions. This strategy can even be leveraged to superimpose\u0000collective modes, resulting in hitherto unexplored but highly practical hybrid\u0000collective patterns, such as protective security formations. Our findings\u0000reveal innovative strategies for creating and controlling collective motion,\u0000paving the way for new applications in robotic swarm operations, active matter\u0000organisation, and for the uncovering of obscure interaction rules in biological\u0000systems.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"46 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141718432","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}
Felix MaurerExperimental Physics, Saarland University, Saarbruecken, Germany, Camila RomeroExperimental Physics, Saarland University, Saarbruecken, Germany, Nikolas LerchExperimental Physics, Saarland University, Saarbruecken, Germany, Thomas JohnExperimental Physics, Saarland University, Saarbruecken, Germany, Lars KaestnerExperimental Physics, Saarland University, Saarbruecken, GermanyDepartment of Theoretical Medicine and Biosciences, Saarland University, Homburg, Germany, Christian WagnerExperimental Physics, Saarland University, Saarbruecken, GermanyPhysics and Materials Science Research Unit, University of Luxembourg, Luxembourg, Alexis DarrasExperimental Physics, Saarland University, Saarbruecken, Germany
Centrifugation of erythrocytes (aka Red Blood Cells, RBCs) in a self-forming Percoll gradient is a protocol often used as a way to sort RBCs by age. However, a pattern formation of discrete bands is systematically observed along the continuous density gradient. Although early studies mentioned that aggregation between cells might modify their spatial distribution, it is debated whether a population with continuous density distribution can form discrete bands. Here, we develop a continuity equation, considering the aggregation of cells with a continuous density distribution, which describes the macroscopic evolution of the RBC volume concentration in a density gradient. The numerical solutions demonstrate that the competition between iso-density distribution and aggregation is sufficient to create band patterns. Our model reproduces the temporal evolution observed in the conventional experimental protocol, but also predicts several types of bifurcation-like behaviors for the steady-state patterns in constant gradients, when the volume fraction and aggregation energy of the cells are varied. We threrefore discovered that the competition between RBC aggregation and iso-density distribution is a novel physical mechanism leading to pattern formation.
{"title":"Competing aggregation and iso-density equilibrium lead to band pattern formation in density gradients","authors":"Felix MaurerExperimental Physics, Saarland University, Saarbruecken, Germany, Camila RomeroExperimental Physics, Saarland University, Saarbruecken, Germany, Nikolas LerchExperimental Physics, Saarland University, Saarbruecken, Germany, Thomas JohnExperimental Physics, Saarland University, Saarbruecken, Germany, Lars KaestnerExperimental Physics, Saarland University, Saarbruecken, GermanyDepartment of Theoretical Medicine and Biosciences, Saarland University, Homburg, Germany, Christian WagnerExperimental Physics, Saarland University, Saarbruecken, GermanyPhysics and Materials Science Research Unit, University of Luxembourg, Luxembourg, Alexis DarrasExperimental Physics, Saarland University, Saarbruecken, Germany","doi":"arxiv-2407.07676","DOIUrl":"https://doi.org/arxiv-2407.07676","url":null,"abstract":"Centrifugation of erythrocytes (aka Red Blood Cells, RBCs) in a self-forming\u0000Percoll gradient is a protocol often used as a way to sort RBCs by age.\u0000However, a pattern formation of discrete bands is systematically observed along\u0000the continuous density gradient. Although early studies mentioned that\u0000aggregation between cells might modify their spatial distribution, it is\u0000debated whether a population with continuous density distribution can form\u0000discrete bands. Here, we develop a continuity equation, considering the\u0000aggregation of cells with a continuous density distribution, which describes\u0000the macroscopic evolution of the RBC volume concentration in a density\u0000gradient. The numerical solutions demonstrate that the competition between\u0000iso-density distribution and aggregation is sufficient to create band patterns.\u0000Our model reproduces the temporal evolution observed in the conventional\u0000experimental protocol, but also predicts several types of bifurcation-like\u0000behaviors for the steady-state patterns in constant gradients, when the volume\u0000fraction and aggregation energy of the cells are varied. We threrefore\u0000discovered that the competition between RBC aggregation and iso-density\u0000distribution is a novel physical mechanism leading to pattern formation.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"36 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141587369","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}
I introduce a new approach to semantic information based upon the influence of erasure operations (interventions) upon distributions of a system's future trajectories through its phase space. Semantic (meaningful) information is distinguished from syntactic information by the property of having some intrinsic causal power on the future of a given system. As Shannon famously stated, syntactic information is a simple property of probability distributions (the elementary Shannon expression), or correlations between two subsystems and thus does not tell us anything about the meaning of a given message. Kolchinsky & Wolpert (2018) introduced a powerful framework for computing semantic information, which employs interventions upon the state of a system (either initial or dynamic) to erase syntactic information that might influence the viability of a subsystem (such as an organism in an environment). In this work I adapt this framework such that rather than using the viability of a subsystem, we simply observe the changes in future trajectories through a system's phase space as a result of informational interventions (erasures or scrambling). This allows for a more general formalisation of semantic information that does not assume a primary role for the viability of a subsystem (to use examples from Kolchinsky & Wolpert (2018), a rock, a hurricane, or a cell). Many systems of interest have a semantic component, such as a neural network, but may not have such an intrinsic connection to viability as living organisms or dissipative structures. Hence this simple approach to semantic information could be applied to any living, non-living or technological system in order to quantify whether a given quantity of syntactic information within it also has semantic or causal power.
{"title":"Causal Leverage Density: A General Approach to Semantic Information","authors":"Stuart J Bartlett","doi":"arxiv-2407.07335","DOIUrl":"https://doi.org/arxiv-2407.07335","url":null,"abstract":"I introduce a new approach to semantic information based upon the influence\u0000of erasure operations (interventions) upon distributions of a system's future\u0000trajectories through its phase space. Semantic (meaningful) information is\u0000distinguished from syntactic information by the property of having some\u0000intrinsic causal power on the future of a given system. As Shannon famously\u0000stated, syntactic information is a simple property of probability distributions\u0000(the elementary Shannon expression), or correlations between two subsystems and\u0000thus does not tell us anything about the meaning of a given message. Kolchinsky\u0000& Wolpert (2018) introduced a powerful framework for computing semantic\u0000information, which employs interventions upon the state of a system (either\u0000initial or dynamic) to erase syntactic information that might influence the\u0000viability of a subsystem (such as an organism in an environment). In this work\u0000I adapt this framework such that rather than using the viability of a\u0000subsystem, we simply observe the changes in future trajectories through a\u0000system's phase space as a result of informational interventions (erasures or\u0000scrambling). This allows for a more general formalisation of semantic\u0000information that does not assume a primary role for the viability of a\u0000subsystem (to use examples from Kolchinsky & Wolpert (2018), a rock, a\u0000hurricane, or a cell). Many systems of interest have a semantic component, such\u0000as a neural network, but may not have such an intrinsic connection to viability\u0000as living organisms or dissipative structures. Hence this simple approach to\u0000semantic information could be applied to any living, non-living or\u0000technological system in order to quantify whether a given quantity of syntactic\u0000information within it also has semantic or causal power.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"25 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141587370","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}
For real-world complex system constantly enduring perturbation, to achieve survival goal in changing yet unknown environments, the central problem is designing a self-adaptation strategy instead of fixed control strategies, which enables system to adjust its internal multi-scale structure according to environmental feedback. Inspired by thermodynamics, we develop a self-adaptive network utilizing only macroscopic information to achieve desired landscape through reconfiguring itself in unknown environments. By continuously estimating environment entropy, our designed self-adaptive network can adaptively realize desired landscape represented by topological measures. The adaptability of this network is achieved under several scenarios, including confinement on phase space and geographic constraint. The adaptation process is described by relative entropy corresponding to the Boltzmann H function, which decreases with time following unique power law distinguishing our self-adaptive network from memoryless systems. Moreover, we demonstrate the transformability of our self-adaptive network, as a critical mechanism of complex system resilience, allowing for transitions from one target landscape to another. Compared to data-driven methods, our self-adaptive network is understandable without careful choice of learning architecture and parameters. Our designed self-adaptive network could help to understand system intelligence through the lens of thermodynamics.
对于现实世界中不断经受扰动的复杂系统来说，要在不断变化的未知环境中实现生存目标，核心问题是设计一种自适应策略，而不是固定的控制策略，使系统能够根据环境反馈调整其内部多尺度结构。受热力学的启发，我们开发了一种自适应网络，它只利用宏观信息，通过在未知环境中重新配置自身来实现理想的景观。通过不断估计环境熵，我们设计的自适应网络可以自适应地实现以拓扑测量为代表的理想景观。该网络的适应性是在多种情况下实现的，包括对相空间的限制和地理限制。适应过程由与波尔兹曼 H 函数相对应的相对熵来描述，该熵随时间降低，遵循独特的幂律，将我们的自适应网络与无记忆系统区分开来。此外，我们还展示了自适应网络的可转换性，这是复杂系统复原力的关键机制，允许从一个目标景观转换到另一个目标景观。我们设计的自适应网络有助于从热力学的角度理解系统智能。
{"title":"Designing self-adaptive network with thermodynamics","authors":"Mingyang Bai, Daqing Li","doi":"arxiv-2407.04930","DOIUrl":"https://doi.org/arxiv-2407.04930","url":null,"abstract":"For real-world complex system constantly enduring perturbation, to achieve\u0000survival goal in changing yet unknown environments, the central problem is\u0000designing a self-adaptation strategy instead of fixed control strategies, which\u0000enables system to adjust its internal multi-scale structure according to\u0000environmental feedback. Inspired by thermodynamics, we develop a self-adaptive\u0000network utilizing only macroscopic information to achieve desired landscape\u0000through reconfiguring itself in unknown environments. By continuously\u0000estimating environment entropy, our designed self-adaptive network can\u0000adaptively realize desired landscape represented by topological measures. The\u0000adaptability of this network is achieved under several scenarios, including\u0000confinement on phase space and geographic constraint. The adaptation process is\u0000described by relative entropy corresponding to the Boltzmann H function, which\u0000decreases with time following unique power law distinguishing our self-adaptive\u0000network from memoryless systems. Moreover, we demonstrate the transformability\u0000of our self-adaptive network, as a critical mechanism of complex system\u0000resilience, allowing for transitions from one target landscape to another.\u0000Compared to data-driven methods, our self-adaptive network is understandable\u0000without careful choice of learning architecture and parameters. Our designed\u0000self-adaptive network could help to understand system intelligence through the\u0000lens of thermodynamics.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"32 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573464","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 model by Hu and Cai [Phys. Rev. Lett., Vol. 111(13) (2013)1 ] describes the self-organization of vascular networks for transport of fluids from source to sinks. Diameters, and thereby conductances, of vessel segments evolve so as to minimize a cost functional E. The cost is the trade-off between the power required for pumping the fluid and the energy consumption for vessel maintenance. The model has been used to show emergence of cyclic structures in the presence of locally fluctuating demand, i.e. non-constant net flow at sink nodes. Under rapid and sufficiently large fluctuations, the dynamics exhibits bistability of tree-like and cyclic network structures. We compare these solutions in terms of the cost functional E. Close to the saddle-node bifurcation giving rise to the cyclic solutions, we find a parameter regime where the tree-like solution rather than the cyclic solution is cost-optimal. Further increase of fluctuation amplitude then leads to an additional transition at which the cyclic solution becomes optimal. The findings hold both in a small system of one source and two sinks and in an empirical vascular network with hundreds of sinks. In the small system, we further analyze the case of slower fluctuations, i.e., on the same time scale as network adaptation. We find that the noisy dynamics settles around the cyclic structures even when these structures are not cost-optimal.
Hu 和 Cai [Phys. Rev. Lett.该成本是泵送流体所需的功率与血管维护所消耗的能量之间的权衡。该模型已被用于显示局部波动需求（即下沉节点处的非恒定净流量）情况下出现的循环结构。在快速和足够大的波动条件下，动力学表现出树状和循环网络结构的稳定性。在接近产生循环解的鞍节点分叉处，我们发现了一个参数体系，在该体系中，树状解而不是循环解是成本最优的。这些发现在由一个源和两个汇组成的小型系统和由数百个汇组成的经验血管网络中都成立。在小型系统中，我们进一步分析了波动较慢的情况，即与网络适应的时间尺度相同。我们发现，即使循环结构不是成本最优的，噪声动态也会在这些结构周围稳定下来。
{"title":"Optimization dynamics and fluctuations in the self-organization of vascular networks","authors":"Konstantin Klemm, Erik Andreas Martens","doi":"arxiv-2407.04120","DOIUrl":"https://doi.org/arxiv-2407.04120","url":null,"abstract":"The model by Hu and Cai [Phys. Rev. Lett., Vol. 111(13) (2013)1 ] describes\u0000the self-organization of vascular networks for transport of fluids from source\u0000to sinks. Diameters, and thereby conductances, of vessel segments evolve so as\u0000to minimize a cost functional E. The cost is the trade-off between the power\u0000required for pumping the fluid and the energy consumption for vessel\u0000maintenance. The model has been used to show emergence of cyclic structures in\u0000the presence of locally fluctuating demand, i.e. non-constant net flow at sink\u0000nodes. Under rapid and sufficiently large fluctuations, the dynamics exhibits\u0000bistability of tree-like and cyclic network structures. We compare these\u0000solutions in terms of the cost functional E. Close to the saddle-node\u0000bifurcation giving rise to the cyclic solutions, we find a parameter regime\u0000where the tree-like solution rather than the cyclic solution is cost-optimal.\u0000Further increase of fluctuation amplitude then leads to an additional\u0000transition at which the cyclic solution becomes optimal. The findings hold both\u0000in a small system of one source and two sinks and in an empirical vascular\u0000network with hundreds of sinks. In the small system, we further analyze the\u0000case of slower fluctuations, i.e., on the same time scale as network\u0000adaptation. We find that the noisy dynamics settles around the cyclic\u0000structures even when these structures are not cost-optimal.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"31 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573440","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}
We investigate the dynamics of the adaptive Kuramoto model in the continuum limit with slow adaptation. This model is distinguished by dense multistability, where multiple states coexist for the same system parameters. The underlying cause of this multistability is that some oscillators can lock at different phases or switch between locking and drifting depending on their initial conditions. We identify new states, such as two-cluster states. To simplify the analysis we introduce an approximate reduction of the model via row-averaging of the coupling matrix. We derive a self-consistency equation for the reduced model and present a stability diagram illustrating the effects of positive and negative adaptation. Our theoretical findings are validated through numerical simulations of a large finite system. Comparisons to previous work highlight the significant influence of adaptation on synchronization behavior.
{"title":"Continuum limit of the adaptive Kuramoto model","authors":"Rok Cestnik, Erik A. Martens","doi":"arxiv-2407.03433","DOIUrl":"https://doi.org/arxiv-2407.03433","url":null,"abstract":"We investigate the dynamics of the adaptive Kuramoto model in the continuum\u0000limit with slow adaptation. This model is distinguished by dense\u0000multistability, where multiple states coexist for the same system parameters.\u0000The underlying cause of this multistability is that some oscillators can lock\u0000at different phases or switch between locking and drifting depending on their\u0000initial conditions. We identify new states, such as two-cluster states. To\u0000simplify the analysis we introduce an approximate reduction of the model via\u0000row-averaging of the coupling matrix. We derive a self-consistency equation for\u0000the reduced model and present a stability diagram illustrating the effects of\u0000positive and negative adaptation. Our theoretical findings are validated\u0000through numerical simulations of a large finite system. Comparisons to previous\u0000work highlight the significant influence of adaptation on synchronization\u0000behavior.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"28 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141573441","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}
I formulate the theory of three dimensional "Malthusian flocks" -- i.e., coherently moving collections of self-propelled entities (such as living creatures) which are being "born" and "dying" during their motion -- whose constituents all have a preference for having their velocity vectors lie parallel to the same two-dimensional plane. I determine the universal scaling exponents characterizing such systems exactly, finding that the dynamical exponent $z=3/2$, the "anisotropy" exponent $zeta=3/4$, and the "roughness" exponent $chi=-1/2$. I also give the scaling laws implied by these exponents.
{"title":"Birth, Death, and Horizontal Flight: Malthusian flocks with an easy plane in three dimensions","authors":"John Toner","doi":"arxiv-2407.03071","DOIUrl":"https://doi.org/arxiv-2407.03071","url":null,"abstract":"I formulate the theory of three dimensional \"Malthusian flocks\" -- i.e.,\u0000coherently moving collections of self-propelled entities (such as living\u0000creatures) which are being \"born\" and \"dying\" during their motion -- whose\u0000constituents all have a preference for having their velocity vectors lie\u0000parallel to the same two-dimensional plane. I determine the universal scaling\u0000exponents characterizing such systems exactly, finding that the dynamical\u0000exponent $z=3/2$, the \"anisotropy\" exponent $zeta=3/4$, and the \"roughness\"\u0000exponent $chi=-1/2$. I also give the scaling laws implied by these exponents.","PeriodicalId":501305,"journal":{"name":"arXiv - PHYS - Adaptation and Self-Organizing Systems","volume":"76 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141547940","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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