Low-dimensional dynamics in sensory biology. 2: Facial cold receptors of the rat

Journal of Computational Neuroscience

Volumn 7, Issue 1, 1999, Pages 17-32

  Braun, Hans A ^a   Dewald, Mathias ^a   Schäfer, Klaus ^a   Voigt, Karlheinz ^a   Pei, Xing ^b   Dolan, Kevin ^b   Moss, Frank ^b  

^a PHILIPPS UNIVERSITY MARBURG   (Germany)

^b UNIVERSITY OF MISSOURI ST LOUIS   (United States)

Author keywords

Internal oscillator; Low dimensional dynamics; Temperature sensitive neurons; Unstable periodic orbits

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); DYNAMICS;

ACTION-POTENTIALS; DIMENSIONAL DYNAMICS; FIRING PATTERNS; INTERNAL OSCILLATORS; LOW DIMENSIONAL; LOW-DIMENSIONAL DYNAMIC; SENSORY AFFERENTS; TEMPERATURE SENSITIVE; TEMPERATURE SENSITIVE NEURON; UNSTABLE PERIODIC ORBITS;

RATS;

ACTION POTENTIAL; ANIMAL EXPERIMENT; ARTICLE; CELL MEMBRANE POTENTIAL; CONTROLLED STUDY; DYNAMICS; FACE; NONHUMAN; OSCILLATOR; PRIORITY JOURNAL; RAT; SENSORY NERVE; TEMPERATURE; THERMORECEPTOR;

EID: 0032874691     PISSN: 09295313     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008911409355     Document Type: Article

References (35)

1. Badii R, Brun E, Finardi M, Flepp L, Holzer R, Parisi J, Reyl C, Simonet J (1994) Progress in the analysis of experimental chaos through periodic orbits. Rev. Mod. Phys. 66:1389-1415.
2. Bevington PR (1969) Data Reduction and Error Analysis. McGraw-Hill, New York, pp. 48-49.
3. Braun HA, Schäfer K, Voigt K, Peters R, Bretschneider F, Pei X, Wilkens L, Moss F (1997) Low-dimensional dynamics in sensory biology 1: Thermally sensitive electroreceptors of the catfish. J. Comp. Neurosci. 4:335-347.
4. Braun HA, Wissing H, Schäfer K, Hirsch MC (1994) Oscillation and noise determine signal transduction in shark multimodal sensory cells. Nature 367:270-273.
5. Christini D, Collins J (1995) Controlling nonchaotic neuronal noise using chaos control techniques. Phys. Rev. Lett. 75:2782-2785.
6. Cvitanovic P (1991) Periodic orbits as the skeleton of classical and quantum chaos. Physica D 51:138-152.
7. Dolan K (1997) The statistical occurrence of unstable periodic orbits in noisy chaotic and random systems. Bull. Am. Phys. Soc. 42:815.
8. Faure P, Korn H (1997) A nonrandom dynamic component in the synaptic noise of a central neuron. Proc. Natl. Acad. Sci. USA 94:6506-6511.
9. Gluckman BJ, Spano ML, Yang W, Ding M, In V, Ditto WL (1997) Tracking unstable periodic orbits in nonstationary high-dimensional chaotic systems: Method and experiment. Phys. Rev. E. 55:4935-4942.
10. Grassberger P, Procaccia I (1983) Measuring the strangeness of strange attractors. Physica D 9:189-208.
11. Hall H, Christini D, Tremblay M, Collins J, Glass L, Billette J (1997) Dynamic control of cardiac alternans. Phys. Rev. Lett. 78:4518-4521.
12. Heinz M, Schäfer K, Braun HA (1990) Analysis of facial cold receptor activity in the rat. Brain Res. 521:289-295.
13. Jung P (1994) Threshold devices: Fractal noise and neural talk. Phys. Rev. E 50:2513-2522.
14. Le Van Quyen M, Martinerie J, Adam C, Varela F (1997) Unstable periodic orbits in human epileptic activity. Phys. Rev. E 56:3401-3411.
15. Longtin A, Hinzer K (1996) Encoding with bursting, subthreshold oscillations and noise in mammalian cold receptors. Neural Comp. 8:217-257.
16. Menendez de la Prida L, Stollenwerk N, Sanchez-Andres JV (1997) Bursting as a source for predictability in biological neural networks activity. Physica D 110:323-331.
17. Narayanan K, Govindan R, Gopinathan M (1998) Unstable periodic orbits in human caridac rhythms. Phys. Rev. E 57:4594-4603.
18. Neiman A, Schimansky-Geier L (1994) Stochastic resonance in bistable systems driven by harmonic noise. Phys. Rev. Lett. 72:2988-2991.
19. Pei X, Dolan K, Moss F, Lai Y-C (1998) Counting unstable periodic orbits in noisy chaotic systems: A scaling relation connecting experiment with theory. Chaos 8:853-860.
20. Pei X, Moss F (1996a) Detecting low-dimensional dynamics in biological experiments. Intern. J. Neural Syst. 7:429-435.
21. Pei X, Moss F (1996b) A statistical measure of unstable periodic orbits in the crayfish caudal photoreceptor. Nature 379:618-621.
22. Pierson D, Moss F (1995) Detecting periodic unstable points in noisy chaotic and limit cycle attractors with applications to biology. Phys. Rev. Lett. 75:2124-2127.
23. Sauer T (1994) Reconstruction of dynamical systems from interspike intervals. Phys. Rev. Lett. 72:3811-3814.
24. Sauer T (1995) Interspike interval embedding of chaotic signals. Chaos 5:127-132.
25. Schäfer K, Braun HA, Bretschneider F, Teunis PFM, Peters RC (1990) Ampullary electroreceptors in catfish (Teleostei): Temperature dependence of stimulus transduction. Pflügers Arch. Eur. J. Physiol. 429:378-385.
26. Schiff S, Jerger K, Duong D, Chang T, Spano M, Ditto W (1994) Controlling chaos in the brain. Nature 370:615-620.
27. Schmelcher P, Diakonos FK (1997) Detecting unstable periodic orbits of chaotic dynamical systems. Phys. Rev. Lett. 78:4733-4736.
28. Schmelcher P, Diakonos FK (1998) General approach to the localization of unstable periodic orbits in chaotic dynamical systems. Phys. Rev. E 57:2739-2746.
29. Schreiber T (1998) Constrained randomization of time series data. Phys. Rev. Lett. 80:2105-2108.
30. So P, Francis J, Netoff T, Gluckman B, Schiff S (1998) Periodic orbits: A new language for neuronal dynamics. Biophys. J. 74: 2776-2785.
31. So P, Ott E, Sauer T, Gluckman BJ, Grebogi C, Schiff SJ (1997) Extracting unstable periodic orbits from chaotic time-series data. Phys. Rev. E. 55:5398-5417.
32. So P, Ott E, Schiff SJ, Kaplan DT, Sauer T, Grebogi C (1996) Detecting unstable periodic orbits in chaotic experimental data. Phys. Rev. Lett. 76:4705-4708.
33. Strogatz SH (1994) Nonlinear Dynamics and Chaos. Addison-Wesley, Reading, MA.
34. Theiler J, Eubank S, Longtin A, Galdrikian B, Farmer JD (1992) Testing for nonlinearity in time series: The method of surrogate data. Physica D 58:77-94.
35. Uhlenbeck GE, Ornstein LS (1930) On the theory of the Brownian motion. Phys. Rev. 36:823-841.