Pub Date : 2019-07-09DOI: 10.1007/978-3-319-58996-1_3
A. Makarenko
{"title":"Multivaluedness Aspects in Self-Organization, Complexity and Computations Investigations by Strong Anticipation","authors":"A. Makarenko","doi":"10.1007/978-3-319-58996-1_3","DOIUrl":"https://doi.org/10.1007/978-3-319-58996-1_3","url":null,"abstract":"","PeriodicalId":139082,"journal":{"name":"arXiv: Adaptation and Self-Organizing Systems","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134265564","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}
Pub Date : 2019-06-06DOI: 10.1103/PHYSREVRESEARCH.2.023183
D. M'etivier, L. Wetzel, Shamik Gupta
We consider the inertial Kuramoto model of $N$ globally coupled oscillators characterized by both their phase and angular velocity, in which there is a time delay in the interaction between the oscillators. Besides the academic interest, we show that the model can be related to a network of phase-locked loops widely used in electronic circuits for generating a stable frequency at multiples of an input frequency. We study the model for a generic choice of the natural frequency distribution of the oscillators, to elucidate how a synchronized phase bifurcates from an incoherent phase as the coupling constant between the oscillators is tuned. We show that in contrast to the case with no delay, here the system in the stationary state may exhibit either a subcritical or a supercritical bifurcation between a synchronized and an incoherent phase, which is dictated by the value of the delay present in the interaction and the precise value of inertia of the oscillators. Our theoretical analysis, performed in the limit $N to infty$, is based on an unstable manifold expansion in the vicinity of the bifurcation, which we apply to the kinetic equation satisfied by the single-oscillator distribution function. We check our results by performing direct numerical integration of the dynamics for large $N$, and highlight the subtleties arising from having a finite number of oscillators.
我们考虑了具有相位和角速度特征的$N$全局耦合振子的惯性Kuramoto模型，其中振子之间的相互作用存在时间延迟。除了学术兴趣之外，我们还表明该模型可以与电子电路中广泛使用的锁相环网络相关，用于在输入频率的倍数下产生稳定的频率。我们研究了振子固有频率分布的一般选择模型，以阐明当振子之间的耦合常数被调谐时，同步相位如何从非相干相位分叉。我们表明，与没有延迟的情况相反，这里的系统在静止状态下可能表现出同步相位和非相干相位之间的亚临界或超临界分岔，这是由相互作用中存在的延迟值和振荡器的精确惯性值决定的。我们在极限$N to infty$中进行的理论分析是基于在分岔附近的不稳定流形展开，我们将其应用于由单振分布函数满足的动力学方程。我们通过对大型$N$的动力学进行直接数值积分来检查我们的结果，并强调具有有限数量的振子所引起的微妙之处。
{"title":"Onset of synchronization in networks of second-order Kuramoto oscillators with delayed coupling: Exact results and application to phase-locked loops","authors":"D. M'etivier, L. Wetzel, Shamik Gupta","doi":"10.1103/PHYSREVRESEARCH.2.023183","DOIUrl":"https://doi.org/10.1103/PHYSREVRESEARCH.2.023183","url":null,"abstract":"We consider the inertial Kuramoto model of $N$ globally coupled oscillators characterized by both their phase and angular velocity, in which there is a time delay in the interaction between the oscillators. Besides the academic interest, we show that the model can be related to a network of phase-locked loops widely used in electronic circuits for generating a stable frequency at multiples of an input frequency. We study the model for a generic choice of the natural frequency distribution of the oscillators, to elucidate how a synchronized phase bifurcates from an incoherent phase as the coupling constant between the oscillators is tuned. We show that in contrast to the case with no delay, here the system in the stationary state may exhibit either a subcritical or a supercritical bifurcation between a synchronized and an incoherent phase, which is dictated by the value of the delay present in the interaction and the precise value of inertia of the oscillators. Our theoretical analysis, performed in the limit $N to infty$, is based on an unstable manifold expansion in the vicinity of the bifurcation, which we apply to the kinetic equation satisfied by the single-oscillator distribution function. We check our results by performing direct numerical integration of the dynamics for large $N$, and highlight the subtleties arising from having a finite number of oscillators.","PeriodicalId":139082,"journal":{"name":"arXiv: Adaptation and Self-Organizing Systems","volume":"92 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128597875","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}
Pub Date : 2017-05-11DOI: 10.29195/iascs.01.01.0019
D. Labavić, H. Meyer-Ortmanns
We study synchronization patterns in repulsively coupled Kuramoto oscillators and focus on the impact of disorder in the natural frequencies. Among other choices we select the grid size and topology in a way that we observe a dynamically induced dimensional reduction with a continuum of attractors as long as the natural frequencies are uniformly chosen. When we introduce disorder in these frequencies, we find limit cycles with periods that are orders of magnitude longer than the natural frequencies of individual oscillators. Moreover we identify sequences of temporary patterns of phase-locked motion, which are self-similar in time and whose periods scale with a power of the inverse width about a uniform frequency distribution. This behavior provides challenges for future research.
{"title":"Temporal self-similar synchronization patterns and scaling in repulsively coupled oscillators","authors":"D. Labavić, H. Meyer-Ortmanns","doi":"10.29195/iascs.01.01.0019","DOIUrl":"https://doi.org/10.29195/iascs.01.01.0019","url":null,"abstract":"We study synchronization patterns in repulsively coupled Kuramoto oscillators and focus on the impact of disorder in the natural frequencies. Among other choices we select the grid size and topology in a way that we observe a dynamically induced dimensional reduction with a continuum of attractors as long as the natural frequencies are uniformly chosen. When we introduce disorder in these frequencies, we find limit cycles with periods that are orders of magnitude longer than the natural frequencies of individual oscillators. Moreover we identify sequences of temporary patterns of phase-locked motion, which are self-similar in time and whose periods scale with a power of the inverse width about a uniform frequency distribution. This behavior provides challenges for future research.","PeriodicalId":139082,"journal":{"name":"arXiv: Adaptation and Self-Organizing Systems","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124314258","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}
Pub Date : 2016-11-03DOI: 10.1103/PhysRevX.7.041044
T. Nishikawa, Jie Sun, A. Motter
The relation between network structure and dynamics is determinant for the behavior of complex systems in numerous domains. An important long-standing problem concerns the properties of the networks that optimize the dynamics with respect to a given performance measure. Here we show that such optimization can lead to sensitive dependence of the dynamics on the structure of the network. Specifically, using diffusively coupled systems as examples, we demonstrate that the stability of a dynamical state can exhibit sensitivity to unweighted structural perturbations (i.e., link removals and node additions) for undirected optimal networks and to weighted perturbations (i.e., small changes in link weights) for directed optimal networks. As mechanisms underlying this sensitivity, we identify discontinuous transitions occurring in the complement of undirected optimal networks and the prevalence of eigenvector degeneracy in directed optimal networks. These findings establish a unified characterization of networks optimized for dynamical stability, which we illustrate using Turing instability in activator-inhibitor systems, synchronization in power-grid networks, network diffusion, and several other network processes. Our results suggest that the network structure of a complex system operating near an optimum can potentially be fine-tuned for a significantly enhanced stability compared to what one might expect from simple extrapolation. On the other hand, they also suggest constraints on how close to the optimum the system can be in practice. Finally, the results have potential implications for biophysical networks, which have evolved under the competing pressures of optimizing fitness while remaining robust against perturbations.
{"title":"Sensitive Dependence of Optimal Network Dynamics on Network Structure","authors":"T. Nishikawa, Jie Sun, A. Motter","doi":"10.1103/PhysRevX.7.041044","DOIUrl":"https://doi.org/10.1103/PhysRevX.7.041044","url":null,"abstract":"The relation between network structure and dynamics is determinant for the behavior of complex systems in numerous domains. An important long-standing problem concerns the properties of the networks that optimize the dynamics with respect to a given performance measure. Here we show that such optimization can lead to sensitive dependence of the dynamics on the structure of the network. Specifically, using diffusively coupled systems as examples, we demonstrate that the stability of a dynamical state can exhibit sensitivity to unweighted structural perturbations (i.e., link removals and node additions) for undirected optimal networks and to weighted perturbations (i.e., small changes in link weights) for directed optimal networks. As mechanisms underlying this sensitivity, we identify discontinuous transitions occurring in the complement of undirected optimal networks and the prevalence of eigenvector degeneracy in directed optimal networks. These findings establish a unified characterization of networks optimized for dynamical stability, which we illustrate using Turing instability in activator-inhibitor systems, synchronization in power-grid networks, network diffusion, and several other network processes. Our results suggest that the network structure of a complex system operating near an optimum can potentially be fine-tuned for a significantly enhanced stability compared to what one might expect from simple extrapolation. On the other hand, they also suggest constraints on how close to the optimum the system can be in practice. Finally, the results have potential implications for biophysical networks, which have evolved under the competing pressures of optimizing fitness while remaining robust against perturbations.","PeriodicalId":139082,"journal":{"name":"arXiv: Adaptation and Self-Organizing Systems","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114208185","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 number $mathcal{N}$ of stable fixed points of locally coupled Kuramoto models depends on the topology of the network on which the model is defined. It has been shown that cycles in meshed networks play a crucial role in determining $mathcal{N}$, because any two different stable fixed points differ by a collection of loop flows on those cycles. Since the number of different loop flows increases with the length of the cycle that carries them, one expects $mathcal{N}$ to be larger in meshed networks with longer cycles. Simultaneously, the existence of more cycles in a network means more freedom to choose the location of loop flows differentiating between two stable fixed points. Therefore, $mathcal{N}$ should also be larger in networks with more cycles. We derive an algebraic upper bound for the number of stable fixed points of the Kuramoto model with identical frequencies, under the assumption that angle differences between connected nodes do not exceed $pi/2$. We obtain $mathcal{N}leqprod_{k=1}^cleft[2cdot{rm Int}(n_k/4)+1right]$, which depends both on the number $c$ of cycles and on the spectrum of their lengths ${n_k}$. We further identify network topologies carrying stable fixed points with angle differences larger than $pi/2$, which leads us to conjecture an upper bound for the number of stable fixed points for Kuramoto models on any planar network. Compared to earlier approaches that give exponential upper bounds in the total number of vertices, our bounds are much lower and therefore much closer to the true number of stable fixed points.
{"title":"Multistability of Phase-Locking in Equal-Frequency Kuramoto Models on Planar Graphs","authors":"R. Delabays, T. Coletta, P. Jacquod","doi":"10.1063/1.4978697","DOIUrl":"https://doi.org/10.1063/1.4978697","url":null,"abstract":"The number $mathcal{N}$ of stable fixed points of locally coupled Kuramoto models depends on the topology of the network on which the model is defined. It has been shown that cycles in meshed networks play a crucial role in determining $mathcal{N}$, because any two different stable fixed points differ by a collection of loop flows on those cycles. Since the number of different loop flows increases with the length of the cycle that carries them, one expects $mathcal{N}$ to be larger in meshed networks with longer cycles. Simultaneously, the existence of more cycles in a network means more freedom to choose the location of loop flows differentiating between two stable fixed points. Therefore, $mathcal{N}$ should also be larger in networks with more cycles. We derive an algebraic upper bound for the number of stable fixed points of the Kuramoto model with identical frequencies, under the assumption that angle differences between connected nodes do not exceed $pi/2$. We obtain $mathcal{N}leqprod_{k=1}^cleft[2cdot{rm Int}(n_k/4)+1right]$, which depends both on the number $c$ of cycles and on the spectrum of their lengths ${n_k}$. We further identify network topologies carrying stable fixed points with angle differences larger than $pi/2$, which leads us to conjecture an upper bound for the number of stable fixed points for Kuramoto models on any planar network. Compared to earlier approaches that give exponential upper bounds in the total number of vertices, our bounds are much lower and therefore much closer to the true number of stable fixed points.","PeriodicalId":139082,"journal":{"name":"arXiv: Adaptation and Self-Organizing Systems","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117124379","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}
Starting from a fine-scale dissipative particle dynamics (DPD) model of self-motile point particles, we derive meso-scale continuum equations by applying a spatial averaging version of the Irving--Kirkwood--Noll procedure. Since the method does not rely on kinetic theory, the derivation is valid for highly concentrated particle systems. Spatial averaging yields a stochastic continuum equations similar to those of Toner and Tu. However, our theory also involves a constitutive equation for the average fluctuation force. According to this equation, both the strength and the probability distribution vary with time and position through the effective mass density. The statistics of the fluctuation force also depend on the fine scale dissipative force equation, the physical temperature, and two additional parameters which characterize fluctuation strengths. Although the self-propulsion force entering our DPD model contains no explicit mechanism for aligning the velocities of neighboring particles, our averaged coarse-scale equations include the commonly encountered cubically nonlinear (internal) body force density.
{"title":"Spatial averaging of a dissipative particle dynamics model for active suspensions","authors":"A. Panchenko, D. F. Hinz, E. Fried","doi":"10.1063/1.5024746","DOIUrl":"https://doi.org/10.1063/1.5024746","url":null,"abstract":"Starting from a fine-scale dissipative particle dynamics (DPD) model of self-motile point particles, we derive meso-scale continuum equations by applying a spatial averaging version of the Irving--Kirkwood--Noll procedure. Since the method does not rely on kinetic theory, the derivation is valid for highly concentrated particle systems. Spatial averaging yields a stochastic continuum equations similar to those of Toner and Tu. However, our theory also involves a constitutive equation for the average fluctuation force. According to this equation, both the strength and the probability distribution vary with time and position through the effective mass density. The statistics of the fluctuation force also depend on the fine scale dissipative force equation, the physical temperature, and two additional parameters which characterize fluctuation strengths. Although the self-propulsion force entering our DPD model contains no explicit mechanism for aligning the velocities of neighboring particles, our averaged coarse-scale equations include the commonly encountered cubically nonlinear (internal) body force density.","PeriodicalId":139082,"journal":{"name":"arXiv: Adaptation and Self-Organizing Systems","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122022468","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 phase reduction method is a dimension reduction method for weakly driven limit-cycle oscillators, which has played an important role in the theoretical analysis of synchro- nization phenomena. Recently, we proposed a generalization of the phase reduction method [W. Kurebayashi et al., Phys. Rev. Lett. 111, 2013]. This generalized phase reduction method can robustly predict the dynamics of strongly driven oscillators, for which the conventional phase reduction method fails. In this generalized method, the external input to the oscillator should be properly decomposed into a slowly varying component and remaining weak fluctua- tions. In this paper, we propose a simple criterion for timescale decomposition of the external input, which gives accurate prediction of the phase dynamics and enables us to systematically apply the generalized phase reduction method to a general class of limit-cycle oscillators. The validity of the criterion is confirmed by numerical simulations.
减相法是弱驱动极限环振荡器的一种降维方法，在同步现象的理论分析中起着重要的作用。最近，我们提出了一种相消减法的推广方法[W]。Kurebayashi et al.，物理学。[j].科学通报，2013。这种广义减相方法可以鲁棒地预测强驱动振子的动力学，而传统的减相方法无法预测强驱动振子的动力学。在这种广义方法中，应适当地将振荡器的外部输入分解为缓慢变化的分量和剩余的弱波动。在本文中，我们提出了一个对外部输入的时间尺度分解的简单准则，它给出了相位动力学的准确预测，并使我们能够系统地将广义相位缩减方法应用于一般类型的极限环振荡器。数值模拟验证了该准则的有效性。
{"title":"A criterion for timescale decomposition of external inputs for generalized phase reduction of limit-cycle oscillators","authors":"W. Kurebayashi, Sho Shirasaka, H. Nakao","doi":"10.1587/nolta.6.171","DOIUrl":"https://doi.org/10.1587/nolta.6.171","url":null,"abstract":"The phase reduction method is a dimension reduction method for weakly driven limit-cycle oscillators, which has played an important role in the theoretical analysis of synchro- nization phenomena. Recently, we proposed a generalization of the phase reduction method [W. Kurebayashi et al., Phys. Rev. Lett. 111, 2013]. This generalized phase reduction method can robustly predict the dynamics of strongly driven oscillators, for which the conventional phase reduction method fails. In this generalized method, the external input to the oscillator should be properly decomposed into a slowly varying component and remaining weak fluctua- tions. In this paper, we propose a simple criterion for timescale decomposition of the external input, which gives accurate prediction of the phase dynamics and enables us to systematically apply the generalized phase reduction method to a general class of limit-cycle oscillators. The validity of the criterion is confirmed by numerical simulations.","PeriodicalId":139082,"journal":{"name":"arXiv: Adaptation and Self-Organizing Systems","volume":"743 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127817879","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}
Pub Date : 2015-07-05DOI: 10.1142/S0218348X15500267
Konstantinos Karamanos, S. Mistakidis, T. Massart, I. Mistakidis
The entropy production and the variational functional of a Laplacian diffusional field around the first four fractal iterations of a linear self-similar tree (von Koch curve) is studied analytically and detailed predictions are stated. In a next stage, these predictions are confronted with results from numerical resolution of the Laplace equation by means of Finite Elements computations. After a brief review of the existing results, the range of distances near the geometric irregularity, the so-called "Near Field", a situation never studied in the past, is treated exhaustively. We notice here that in the Near Field, the usual notion of the active zone approximation introduced by Sapoval et al. is strictly inapplicable. The basic new result is that the validity of the active-zone approximation based on irreversible thermodynamics is confirmed in this limit, and this implies a new interpretation of this notion for Laplacian diffusional fields.
{"title":"Entropy production of entirely diffusional Laplacian transfer and the possible role of fragmentation of the boundaries","authors":"Konstantinos Karamanos, S. Mistakidis, T. Massart, I. Mistakidis","doi":"10.1142/S0218348X15500267","DOIUrl":"https://doi.org/10.1142/S0218348X15500267","url":null,"abstract":"The entropy production and the variational functional of a Laplacian diffusional field around the first four fractal iterations of a linear self-similar tree (von Koch curve) is studied analytically and detailed predictions are stated. In a next stage, these predictions are confronted with results from numerical resolution of the Laplace equation by means of Finite Elements computations. After a brief review of the existing results, the range of distances near the geometric irregularity, the so-called \"Near Field\", a situation never studied in the past, is treated exhaustively. We notice here that in the Near Field, the usual notion of the active zone approximation introduced by Sapoval et al. is strictly inapplicable. The basic new result is that the validity of the active-zone approximation based on irreversible thermodynamics is confirmed in this limit, and this implies a new interpretation of this notion for Laplacian diffusional fields.","PeriodicalId":139082,"journal":{"name":"arXiv: Adaptation and Self-Organizing Systems","volume":"114 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124557166","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}
Hiromasa Ando, I. Lubashevsky, A. Zgonnikov, Yoshiaki Saito
A fair simple car driving simulator was created based on the open source engine TORCS and used in car-following experiments aimed at studying the basic features of human behavior in car driving. Four subjects with different skill in driving real cars participated in these experiments. The subjects were instructed to drive a car without overtaking and losing sight of a lead car driven by computer at a fixed speed. Based on the collected data the distributions of the headway distance, the car velocity, acceleration, and jerk are constructed and compared with the available experimental data for the real traffic flow. A new model for the car-following is proposed to capture the found properties. As the main result, we draw a conclusion that human actions in car driving should be categorized as generalized intermittent control with noise-driven activation. Besides, we hypothesize that the car jerk together with the car acceleration are additional phase variables required for describing the dynamics of car motion governed by human drivers.
{"title":"Statistical Properties of Car Following: Theory and Driving Simulator Experiments","authors":"Hiromasa Ando, I. Lubashevsky, A. Zgonnikov, Yoshiaki Saito","doi":"10.5687/SSS.2015.149","DOIUrl":"https://doi.org/10.5687/SSS.2015.149","url":null,"abstract":"A fair simple car driving simulator was created based on the open source engine TORCS and used in car-following experiments aimed at studying the basic features of human behavior in car driving. Four subjects with different skill in driving real cars participated in these experiments. The subjects were instructed to drive a car without overtaking and losing sight of a lead car driven by computer at a fixed speed. Based on the collected data the distributions of the headway distance, the car velocity, acceleration, and jerk are constructed and compared with the available experimental data for the real traffic flow. A new model for the car-following is proposed to capture the found properties. As the main result, we draw a conclusion that human actions in car driving should be categorized as generalized intermittent control with noise-driven activation. Besides, we hypothesize that the car jerk together with the car acceleration are additional phase variables required for describing the dynamics of car motion governed by human drivers.","PeriodicalId":139082,"journal":{"name":"arXiv: Adaptation and Self-Organizing Systems","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130802119","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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