Herd behavior in a complex adaptive system

Zhao, Liang; Yang, Guang; Wang, W; Chen, Ying; Huang, Jue; Ohashi, Hirotada; Stanley, H. Eugene

doi:10.1073/pnas.1105239108

Cited by 78 publications

(73 citation statements)

References 17 publications

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“…The origin of collective dynamics and LRCCs based on local interactions often appears elusive (20), and is the focus of current research (19, 21). Of particular interest are the rules of interactions of the individuals in a crowd (22, 23) and transitions to synchronized behavior (16,24). We introduce a stochastic model for mutually interacting complex systems (MICS) that generates LRCCs and provides a physiologically motivated explanation for the surprising presence of longterm memory in the cross-correlations of musical performances.…”

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confidence: 99%

Synchronization in human musical rhythms and mutually interacting complex systems

Hennig

2014

Proc. Natl. Acad. Sci. U.S.A.

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Though the music produced by an ensemble is influenced by multiple factors, including musical genre, musician skill, and individual interpretation, rhythmic synchronization is at the foundation of musical interaction. Here, we study the statistical nature of the mutual interaction between two humans synchronizing rhythms. We find that the interbeat intervals of both laypeople and professional musicians exhibit scale-free (power law) cross-correlations. Surprisingly, the next beat to be played by one person is dependent on the entire history of the other person's interbeat intervals on timescales up to several minutes. To understand this finding, we propose a general stochastic model for mutually interacting complex systems, which suggests a physiologically motivated explanation for the occurrence of scale-free cross-correlations. We show that the observed long-term memory phenomenon in rhythmic synchronization can be imitated by fractal coupling of separately recorded or synthesized audio tracks and thus applied in electronic music. Though this study provides an understanding of fundamental characteristics of timing and synchronization at the interbrain level, the mutually interacting complex systems model may also be applied to study the dynamics of other complex systems where scale-free crosscorrelations have been observed, including econophysics, physiological time series, and collective behavior of animal flocks.time series analysis | long-range cross-correlations | anticorrelations | musical coupling | interbrain synchronization I n his book Musicophilia, neurologist Oliver Sacks writes: "In all societies, a primary function of music is collective and communal, to bring and bind people together. People sing together and dance together in every culture, and one can imagine them having done so around the first fires, a hundred thousand years ago" (1). Sacks adds, "In such a situation, there seems to be an actual binding of nervous systems accomplished by rhythm" (2). These thoughts lead to the question: Is there any underlying and quantifiable structure to the subjective experience of "musical binding"? Here, we examine the statistical nature of musical binding (also referred to as musical coupling) when two humans play rhythms in synchrony.Every beat a single (noninteracting) layperson or musician plays is accompanied by small temporal deviations from the exact beat pattern, i.e., even a trained musician will hit a drum beat slightly ahead or behind the metronome (with a SD of typically 5-15 ms). Interestingly, these deviations are statistically dependent and exhibit long-range correlations (LRC) (3, 4). Listeners significantly prefer music mirroring long-range correlated temporal deviations over uncorrelated (white noise) fluctuations (5, 6). LRC are also inherent in the reproduction of both spatial and temporal intervals of single subjects (4, 7-9) and in musical compositions, such as pitch fluctuations (a simple example of pitch fluctuations is a melody) (10, 11) and note lengths (12). The observation of ...

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confidence: 99%

Synchronization in human musical rhythms and mutually interacting complex systems

Hennig

2014

Proc. Natl. Acad. Sci. U.S.A.

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“…Mt, 73.21.Cd Understanding the interplay between the properties of individual objects and their collective behavior is of fundamental interest in many fields [1][2][3][4]. It explains, for example, jamming and pattern formation in granular systems [1,[5][6][7], dynamical heterogeneity in phase transitions [3], tunneling dynamics and quantum phases in cold atoms [8,9], and the synchronization of networks and complex adaptive systems [2,10]. Moreover, interactions between particles play a key role in determining the structures formed when the particles come into contact [4].…”

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Controlling High-Frequency Collective Electron Dynamics via Single-Particle Complexity

et al. 2012

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We demonstrate, through experiment and theory, enhanced high-frequency current oscillations due to magnetically-induced conduction resonances in superlattices. Strong increase in the ac power originates from complex single-electron dynamics, characterized by abrupt resonant transitions between unbound and localized trajectories, which trigger and shape propagating charge domains. Our data demonstrate that external fields can tune the collective behavior of quantum particles by imprinting configurable patterns in the single-particle classical phase space.PACS numbers: 05.45. Mt, 73.21.Cd Understanding the interplay between the properties of individual objects and their collective behavior is of fundamental interest in many fields [1][2][3][4]. It explains, for example, jamming and pattern formation in granular systems [1,[5][6][7], dynamical heterogeneity in phase transitions [3], tunneling dynamics and quantum phases in cold atoms [8,9], and the synchronization of networks and complex adaptive systems [2,10]. Moreover, interactions between particles play a key role in determining the structures formed when the particles come into contact [4]. Consequently, tailoring single-particle dynamics may provide a route to controlling the collective dynamics of many-body systems. This is a major challenge both in fundamental science [11][12][13] and for developing new technologies such as high-frequency electronic devices [14][15][16], whose performance can be greatly enhanced by applied quantizing magnetic fields [17,18].The phase space structure of individual particles, in particular the existence and relative location of regular and chaotic trajectories, critically affects thermalization and diffusion both in classical and quantum systems [19,20]. Therefore, manipulating the single-particle phase space, by generating new chaotic trajectories for example, is a promising strategy in the search for ways to control other collective phenomena.Usually, the transition to chaos in Hamiltonian systems occurs by the gradual destruction of stable orbits, in accordance with the Kolmogorov-Arnold-Moser (KAM) theorem [21]. In far rarer non-KAM chaos, the chaotic orbits become abruptly unbounded when the perturbation frequency attains critical values and map out intricate "stochastic webs" in phase space [19]. Experimental realization of non-KAM classical chaos was recently achieved using a quantum system [22]: a semiconductor superlattice (SL) with a magnetic field, B, tilted relative to an electric field, F, along the SL axis. When the frequency of single-electron Bloch oscillations along the SL axis is commensurate with that for cyclotron motion in the plane of the layers [14,22,23], the orbits map out stochastic webs in phase space, which delocalize the electrons in real space. This delocalization creates multiple resonant peaks in the single-electron drift velocity versus F characteristics, which enhance the measured dc conductivity [22].In this Letter, we show, via experiments and theoretical modeling, that non-KAM single-pa...

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“…And the combination of these two methods to examine the same phenomenon is also shown to be a successful approach [34][35][36][37][38][39][40][41][42]. Thanks to these preceding researches by both economists and econophysicists mentioned above, we are able to raise the inspirations and ideas in combining the two methods to give a new point of view on the effect of leverage.…”

Section: Introductionmentioning

confidence: 96%

Overall fluctuations and fat tails in an artificial financial market: The two-sided impact of leveraged trading

Yang

Zhu

et al. 2015

Physics Letters A

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Herd behavior in a complex adaptive system

Cited by 78 publications

References 17 publications

Synchronization in human musical rhythms and mutually interacting complex systems

Synchronization in human musical rhythms and mutually interacting complex systems

Controlling High-Frequency Collective Electron Dynamics via Single-Particle Complexity

Overall fluctuations and fat tails in an artificial financial market: The two-sided impact of leveraged trading

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