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Recurrence plots of neuronal spike trains

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Abstract

The recently developed qualitative method of diagnosis of dynamical systems — recurrence plots has been applied to the analysis of dynamics of neuronal spike trains recorded from cerebellum and red nucleus of anesthetized cats. Recurrence plots revealed robust and common changes in the similarity structure of interspike interval sequences as well as significant deviations from randomness in serial ordering of intervals. Recurring episodes of alike, quasi-deterministic firing patterns suggest the spontaneous modulation of the dynamical complexity of the trajectories of observed neurons. These modulations are associated with changing dynamical properties of a neuronal spike-train-generating system. Their existence is compatible with the information processing paradigm of attractor neural networks.

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References

  • Aikara K, Matsumoto G (1986) Chaotic oscillations and bifurcations in squid giant axons. In: Holden AV (eds) Chaos. Manchester University Press, Manchester, pp 257–269

    Google Scholar 

  • Albano AM, Mees AI, de Guzman GC, Rapp PE (1987) Data requirements for reliable estimation of correlation dimensions. In: Degn H, Holden AV, Olsen LF (eds) Chaos in biological systems. Plenum, New York, pp 207–220

    Google Scholar 

  • Albus JS (1971) A theory of cerebellar function. Math Biosci 10:25–61

    Google Scholar 

  • Amit DJ, Treves A (1989) Associative memory neural networks with low temporal spiking rates. Proc Natl Acad Sci USA 86:7871–7876

    Google Scholar 

  • Babloyantz A, Nicolis C, Salazar M (1985) Evidence of chaotic dynamics of brain activity during the sleep cycle. Phys Lett 111A:152–156

    Google Scholar 

  • Basar E, Bullock TH (eds) (1989) Brain dynamics. Springer, Berlin Heidelberg New York

    Google Scholar 

  • Braitenberg V (1987) The cerebellum and the physics of movement: some speculations. In: Glickstein M, Stein J, Yeo C (eds) Cerebellum and neuronal plasticity. Plenum, New York, pp193–207

    Google Scholar 

  • Brooks VB, Thach WT (1981) Cerebellar control of posture and movement. In: Brooks VB (eds) Handbook of physiology, sect 1, The nervous system, vol II, Motor control. American Physiological Society, Bethesda, pp 877–946

    Google Scholar 

  • Chapeau-Blondeau F, Chauvet G (1991) A neural network model of the cerebellar cortex performing dynamic associations. Biol Cybern 65:267–279

    Google Scholar 

  • Chay TR (1984) Abnormal discharges and chaos in a neural model. Biol Cybern 50:301–311

    Google Scholar 

  • Dayhoff J, Gerstein GL (1983) Favored patterns in spike trains. I. Detection. J Neurophysiol 49:1334–1348

    Google Scholar 

  • Ebner TJ, Bloedel JR (1981) Temporal patterning in simple spike discharge of Purkinje cells and its relationship to climbing fiber activity. J Neurophysiol 45:933–947

    Google Scholar 

  • Eckmann J-P, Kamphorst Oliffson S, Ruelle D (1987) Recurrence plots of dynamical systems. Europhys Lett 4:973–977

    Google Scholar 

  • Farmer JD, Sidorowich JJ (1987) Predicting chaotic time series. Phys Rev Lett 59:845–848

    Google Scholar 

  • Gahwiller BH, Mamoon AM, Tobias CA (1973) Spontaneous bioelectrical activity of cultured cerebellar Purkinje cells during exposure to agents that prevent synaptic transmission. Brain Res 53:71–79

    Google Scholar 

  • Gallez D, Babloyantz A (1991) Predictability of human EEG: a dynamical approach. Biol Cybern 64:381–391

    Google Scholar 

  • Glass L, Mackey MC (1988) From clocks to chaos: the rhythms of life. Princeton University Press, Princeton

    Google Scholar 

  • Ito M (1984) The cerebellum and neural control. Raven Press, New York

    Google Scholar 

  • Keeler JD (1990) A dynamical system view of cerebellar function. Physica D 42:396–410

    Google Scholar 

  • Klemm WR, Sherry CJ (1981) Serial ordering in spike trains: “What's it trying to tell us?” Int J Neurosci 14:15–33

    Google Scholar 

  • Landolt JP, Correia MJ (1978) Neuromathematical concepts of point process theory. IEEE Trans Biomed Eng 25:1–12

    Google Scholar 

  • MacGregor RJ (1991) Sequential configuration model for firing patterns in local neural networks. Biol Cybern 65:339–349

    Google Scholar 

  • Marczynski TJ, Burns LL, Monley C (1992) Empirically derived model of the role of sleep in associative learning and recuperative processes. Neural Networks 5:371–402

    Google Scholar 

  • Marr D (1969) A theory of cerebellar cortex. J Physiol (Lond) 202:437–470

    Google Scholar 

  • Mayer-Kress G, Yates FE, Benton L, Keidel M, Tirsh W, Poppl SJ, Geist K (1988) Dimensional analysis of nonlinear oscillations in brain, heart, and muscle. Math Biosci 90:49–70

    Google Scholar 

  • Mood AM (1940) Distribution theory of runs. Ann Math Stat 11:367–392

    Google Scholar 

  • Mpitsos GJ, Burton RM, Creech HC, Soinila SO (1988a) Evidence for chaos in spike trains of neurons that generate rhythmic motor patterns. Brain Res Bull 21:529–538

    Google Scholar 

  • Mpitsos GJ, Creech HC, Cohan CS, Medelson M (1988b) Variability and chaos: Neurointegrative principles in self-organization of motor patterns. In: Kelso JAS, Mandell AJ, Schlesinger MF (eds) Dynamic patterns in complex systems. World Scientific, Teaneck, NJ, pp 162–190

    Google Scholar 

  • Murphy JT, Sabah NH (1970) Spontaneous firing of cerebellar Purkinje cells in decerebrate and barbiturate anesthetized cats. Brain Res 17:515–519

    Google Scholar 

  • Nakahama H, Ishii N, Yamamoto M, Saito H (1971) Stochastic properties of spontaneous impulse activity in central single neurons. Tohoku J Exp Med 104:373–409

    Google Scholar 

  • Nicolis JS (1986) Chaotic dynamics applied to information processing. Rep Progr Phys 49:1109–1196

    Google Scholar 

  • Rapp PE, Zimmermann ID, Albano AM, de Guzman GC, Greenbaum NN (1985) Dynamics of spontaneous neural activity in the simian motor cortex. Phys Lett 110A:335–338

    Google Scholar 

  • Roschke J, Basar E (1989) Correlation dimensions in various parts of cat and human brain. In: Basar E, Bullock TH (eds) Brain dynamics. Springer, Berlin Heidelberg New York, pp 131–148

    Google Scholar 

  • Sherry JC, Barlow DI, Klemm WR (1982) Serial dependencies and Markov properties of neuronal interspike intervals from rat cerebellum. Brain Res Bull 8:163–169

    Google Scholar 

  • Tarnecki R (1988) Functional connections between neurons of interpositus nucleus of cerebellum and the red nucleus. Behav Brain Res 28:117–125

    Google Scholar 

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Kałużny, P., Tarnecki, R. Recurrence plots of neuronal spike trains. Biol. Cybern. 68, 527–534 (1993). https://doi.org/10.1007/BF00200812

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  • DOI: https://doi.org/10.1007/BF00200812

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