Non-linear dynamics of operant behavior: A new approach via the extended return map

Reviews in the Neurosciences

Volumn 13, Issue 1, 2002, Pages 31-57

  Li, Jay Shake ^a   Huston, Joseph P ^a  

^a HEINRICH HEINE UNIVERSITY   (Germany)

Author keywords

Extended return map; Nonlinear dynamics; Operant; Rat; Reinforcement; Skinner box

Indexed keywords

ANIMAL BEHAVIOR; ANIMAL EXPERIMENT; DYNAMICS; INSTRUMENTAL CONDITIONING; MALE; MATHEMATICAL ANALYSIS; NONHUMAN; NONLINEAR SYSTEM; PRIORITY JOURNAL; RAT; REINFORCEMENT; RESPONSE TIME; REVIEW; SIMULATION;

EID: 0036380679     PISSN: 03341763     EISSN: None     Source Type: Journal    
DOI: 10.1515/REVNEURO.2002.13.1.31     Document Type: Review

References (38)

1. Baker GL, Gollub JP. Chaotic Dynamics - An Introduction. New York: Cambridge University Press, 1990.
2. Bizo LA, Killeen PR. Models of ratio schedule performance. J Exp Psychol-Anim Behav Proc 1997; 23: 351-367.
3. Branch MN, Gollub LR. A detailed analysis of the effects of d-amphetamine on behavior under fixed-interval schedules. J Exp Anal Behav 1974; 21: 519-539.
4. Braun T, Lisbôa JA. Characterization of homoclinic chaos in a glow discharge through return maps. Int J Bifurcation Chaos 1994; 4: 1483-1493.
5. Church RM, Meck WH, Gibbon J. Application of scalar timing theory to individual trials. J Exp Psychol-Anim Behav Proc 1994; 20: 135-155.
6. Dews PB. The theory of fixed-interval responding. In: Schoenfeld WN, ed. The Theory of Reinforcement Schedules. New York: Appleton-Century-Crofts, Educational Division, Meredith Corporation, 1970; 43-61.
7. Dews PB. Studies on responding under fixed-interval schedules of reinforcement: II The scalloped pattern of the cumulative record. J Exp Anal Behav 1978; 29: 67-75.
8. Ferster CB, Skinner BF. Schedules of Reinforcement. New York: Appleton-Centrury-Crofts, 1957.
9. Gentry GD, Weiss B, Laties VG. The microanalysis of fixed-interval responding. J Exp Anal Behav 1983; 39: 327-343.
10. Gibbon J. Scalar expectancy theory and Weber's law in animal timing. Psychol Rev 1977; 84: 279-325.
11. Gleick J. Chaos - Making a New Science. New York: Penguin Books, 1987.
12. Grassberger P. Generalized dimensions of strange attractors. Phys Lett 1983; 97A: 227-230.
13. Guzzetti S, Signorini MG, Cogliati C, Mezzetti S, Porta A, Cerutti S, Malliani A. Non-linear dynamics and chaotic indices in heart rate variability of normal subjects and the heart-transplanted patients. Cardiovasc Res 1996; 31: 441-446.
14. Hentschel HGE, Procaccia 1. The infinite number of generalized dimensions of fractals and strange attractors. Physica D 1983; 8: 435-444.
15. Herrnstein RJ. On the law of effect. J Exp Anal Behav 1970; 13: 243-266.
16. Herrnstein RJ. Formal properties of the matching law. J Exp Anal Behav 1974; 21: 159-164.
17. Hoyert MS. Order and chaos in fixed-interval schedules of reinforcement. J Exp Anal Behav 1992; 57: 339-336.
18. Kantz H, Schreiber T. Nonlinear Time Series Analysis. New York: Cambridge University Press, 1997.
19. Killeen P, Fetterman G. A behavioral theory of timing. Psychol Rev 1988; 95: 274-295.
20. Killeen P. Mathematical principles of reinforcement. Behav Brain Sci 1994; 17: 105-172.
21. Li JS, Huston JP. The extended return map: a new method to analyse the non-linear dynamics of interresponse-intervals in Skinner-box experiments. In: Fourth European Meeting for the Experimental Analysis of Behaviour, Amiens, France, July 9-13, 2000.
22. Li JS. The extended return map: a new method to analyze the nonlinear dynamics of inter-response-intervals in operant conditioning studies. In: Tenth Annual International Conference of the Society For Chaos Theory in Psychology & Life Sciences, University of Pennsylvania, Pennsylvania, PA, July 20-23, 2000.
23. Liebovitch LS. Fractals and Chaos: Simplified for the Life Sciences. New York: Oxford University Press, 1998.
24. Machado A. Learning the temporal dynamics of behavior. Psychol Rev 1997; 104: 241-265.
25. Machado A, Cevik M. Acquisition and extinction under periodic reinforcement. Behav Proc 1998; 44: 237-262.
26. May RM. Simple mathematical models with very complicated dynamics. Nature 1976; 261: 459-467.
27. Nevin JA, Baum WM. Feedback functions for variable-interval reinforcement. J Exp Anal Behav 1980; 34: 207-217.
28. Ott E, Sauer T, Yorke JA. Coping with Chaos: Analysis of Chaotic Data and the Exploitation of Chaotic Systems. New York: John Wiley & Sons, Inc., 1994.
29. Packard NH, Crutchfiel JP, Farmer JD, Shaw RS. Geometry from a time series. Phys Rev Lett 1980; 45: 712-716.
30. Palya WL. Dynamics in the fine structure of schedule-controlled behavior. J Exp Anal Behav 1992; 57: 267-287.
31. Schneider AB. A two-state analysis of fixed-interval responding in the pigeon. J Exp Anal Behav 1969; 12: 677-687.
32. Shaw RS. The Dripping Faucet as a Model Chaotic System. Santa Cruz, CA: Aerial Press, 1984.
33. Skinner BF. The Behavior of Organisms. New York: Appleton-Century-Crofts, 1938.
34. Suzuki H, Aihara K, Murakami J, Shimozawa T. Analysis of neural spike with interspike interval reconstruction. Biol Cybem 2000; 82: 305-311.
35. Takens F. Detecting strange attractors in turbulence. In: Rand DA, Young LS, eds. Lecture Notes in Mathematics: Dynamical Systems and Turbulence 898. Berlin: Springer-Verlag, 1981; 336-381.
36. Takens F. On the numerical determination of the dimension of an attractor. In: Braaksma Boele LJ, ed. Lecture Notes in Mathematics: Dynamical Systems and Bifurcations 1125. Berlin: Springer-Verlag, 1985; 99-106.
37. Theiler J, Eubank S, Longtin A, Garldrikian B, Farmer JD. Testing for nonlinearity in time series: the method of surrogate data. Physica D 1992; 58: 77-94.
38. Weiss B. The fine structure of operant behavior during transition states. In: Schoenfeld WN, ed. The Theory of Reinforcement Schedules. New York: Appleton-Century-Crofts, Educational Division, Meredith Corporation, 1970; 277-311.