Abstract
The altered feedback technique is very suited to display nonlinearities of the human smooth pursuit system. In fact, when the gain of the retinal feedback path is raised, for the horizontal channel, above its normal unitary negative value, a threshold is met beyond which sustained horizontal self-excited smooth oscillations of the eye can be observed, which point out the existence of a stable limit cycle. Furthermore, the characterizing features of both the transient and steady state show a well defined dependence on the total feedback factor K. In particular, the analytical dependence on K of the amplitude and frequency of limit cycle oscillations can be derived. Implications of the experiment with respect to the mathematical modelling of the system are discussed.
Similar content being viewed by others
References
Bahill, A.T., Iandolo, M.J., Troost, B.T.: Smooth pursuit eye movements in response to unpredictable target waveforms. Vision Res. 20, 923–931 (1980)
Bahill, A.T., McDonald, J.D.: Model emulates human smooth pursuit system producing zero-latency target tracking. Biol. Cybern. 48, 213–222 (1983)
Bekey, G.A., Yamashiro, S.M.: Parameter estimation in mathematical models of biological systems. Adv. Biomed. Eng. 6, 1–43 (1976)
Burford, G.E.: Involuntary eyeball motion during anesthesia and sleep. Relationships to cortica rhythmic potentials. Anesthesia and Analgesia, pp. 191–199 (1941)
Carpenter, R.H.S.: Movements of the eyes. London: Pion Limited 1977
Collins, C.C.: The human oculomotor control system. In: Basic mechanisms of ocular motility and their clinical implications, pp. 145–180. Lennerstrand, G., Bach-y-Rita, P. (eds.) Oxford: Pergamon Press 1975
Dallos, P.J., Jones, R.W.: Learning behavior of the eye fixation control system. IEEE Trans. AC-8, 218–227 (1963)
Deckert, G.H.: Pursuit eye movements in the absence of a moving visual stimulus. Science 143, 1192–1193 (1964)
Dement, W.C.: Eye movements during sleep. In: The oculomotor system, pp. 366–416. Bender, M.B. (ed.). New York: Harper and Row 1964
Dichgans, J., Jung, R.: Attention, eye movements and motion detection; facilitation and selection in optokinetic nystagmus and railway nystagmus. In: Attention in neurophysiology, pp. 348–375. Evans, C.R., Mulholland, T.B. (eds.). London: Butterworths 1969
Fender, D.H., Nye, P.W.: An investigation of the mechanism of eye movement control. Kybernetik 1, 81–88 (1961)
Fleming, D.G., Vossius, G.W., Bowman, G., Johnson, E.L.: Adaptive properties of the eye tracking system as revealed by moving-head and open-loop studies. Ann. Acad. Sci. N.Y. 156, 825–850 (1969)
Gauthier, G.M., Hofferer, J.M.: Eye tracking of self moved targets in teh absence of vision. Exp. Brain Res. 26, 121–139 (1976)
Glenny, G., Heywood, S.: Hans Gertz revisited: the different effects of invisibility and darkness on pursuit eye movements. Perception 8, 31–36 (1979)
Greene, D.E., Ward, F.E.: Human eye tracking as a sequential input adaptive process. Biol. Cybern. 33, 1–7 (1979)
Hedlun, J.M., White, C.T.: Nystagmus induced by visual feedback. J. Opt. Soc. Am. 49, 729–730 (1959)
Henn, V., Cohen, B., Young, L.R.: Visual-vestubular interaction in motion perception and the generation of nystagmus. Neurosci. Res. Program. Bull. 18, 459–651 (1980)
Heywood, S.: Voluntary control of smooth eye movements and their velocity. Nature 238, 408–410 (1972)
Heywood, S.: Pursung stationary dots: smooth eye movements and apparent movement. Perception 2, 181–195 (1973)
Heywood, S., Churcher, J.: Eye movements and the afterimage. I. Tracking the afterimage. Vision Res. 11, 1163–1168 (1971)
Holzman, P.S., Proctor, L.R., Hughes, D.W.: Eye-tracking patterns in schizophrenia. Science 181, 179–181 (1973)
Iacono, W.G., Tuason, V.B., Johnson, R.A.: Dissociation of smooth-pursuit and saccadic eye tracking in remitted schizphrenics. Arch. Gen. Psychiatry 38, 991–996 (1981)
Jacobs, L., Feldman, M., Bender, M.B.: Eye movements during sleep. I. The pattern in the normal human. Arch. Neurol. 25, 151–159 (1981)
Jordan, S.: Ocular pursuit movement as a function of visual and proprioceptive stimulation. Vision Res. 10, 775–780 (1970)
Lackner, J.R.: Pursuit eye movements elicited by muscle afferent information. Neurosci. Letters 1, 25–28 (1975)
Riggs, L.A., Tulunay, S.U.: Visual effects of varying the extent of compensation for eye movements. J. Opt. Soc. Am. 49, 741–745 (1959)
Robinson, D.A.: The mechanics of human smooth pursuit eye movements. J. Physiol. 180, 569–591 (1965)
Robinson, D.A.: The oculomotor control system: a review. Proc. IEEE 56, 1032–1049 (1968)
Robinson, D.A.: Models of the saccadic eye movement control system. Kybernetik 14, 71–83 (1973)
Robinson, D.A.: The physiology of pursuit eye movements. In: Eye movements and psychological processes, pp. 19–31. Monty, R.A., Senders, J.W. (eds.) Hillsdale, NJ: Lawrence Erlbaum 1976
Robinson, D.A.: The use of control systems analysis in the neurophysiology of eye movements. Ann. Rev. Neurosci. 4, 463–503 (1981)
Stark, L.: Neurological control systems. Studies in bioengineering. New York: Plenum Press 1968
Stark, L.: The control system for versional eye movements. In: The control of eye movements, pp. 363–428. Bach-y-Rita, P., Collinc, C.C., Hyde, J.E. (eds.). New York: Academic Press 1971
Stark, L., Vossius, G., Young, R.L.: Predictive control of eye tracking movements. IRE Trans. HFE-3, 52–57 (1962)
Steinbach, M.J.: Eye tracking of self-moved targets: the role of efference. J. Exp. Psych. 82, 366–376 (1969)
Steinbach, M.J.: Pursuing the perceptual rather than the retinal stimulus. Vision Res. 16, 1371–1376 (1976)
Steinback, M.J., Held, R.: Eye tracking of observer-generated target movements. Science 161, 187–188 (1968)
Steinbach, M.J., Pearce, D.G.: Release of pursuit eye movements using after-images. Vision Res. 12, 1307–1311 (1972)
Steinman, R.M., Skavenski, A.A., Sansbury, R.V.: Voluntary control of smooth pursuit velocity. Vision Res. 9, 1167–1171 (1969)
St.-Cyr, G.J., Fender, D.H.: Nonlinearities of the human oculomotor system: gain. Vision Res. 9, 1235–1246 (1969a)
St-Cyr, G.J., Fender, D.H.: Nonlinearities of the human oculomotor system: time delays. Vision Res. 9, 1491–1503 (1969b)
Sugie, N.: A model of predictive control in visual target tracking. IEEE Trans. SMC-1, 2–7 (1971)
Ten Doesschate, J.: A new form of physiological nystagmus. Ophthalmologica 127, 65–73 (1954)
Ward, R.: Perceptual effect of pursuit eye movements in the absence of a target. Nature 274, 158–159 (1978)
Westheimer, G.: Mechanism of saccadic eye movements. A.M.A. Arch. Ophth. 52, 710–723 (1954)
Williams, R.A., Fender, D.H.: Velocity precision in smooth pursuit eye movements. Vision Res. 19, 343–348 (1979)
Winterson, B.J., Steinman, R.M.: The effect of luminance on human smooth pursuit of perifoveal and foveal targets. Vision Res. 18, 1165–1172 (1978)
Wyatt, H.J., Pola, J.: Smooth pursuit eye movements under open-loop and closed-loop conditions. Vision Res. 23, 1121–1131 (1983)
Yasui, S., Young, L.R.: On the predictive control of foveal eye tracking and slow phases of optokinetic and vestibular nystagmus. J. Physiol. 347, 17–33 (1984)
Young, L.R.: Pursuit eye tracking movements. In: The control of eye movements, pp. 429–443. Bach-y-Rita, P., Collins, C.C., Hyde, J.E. (eds.). New York: Academic Press 1971
Young, L.R., Stark, L.: Variable feedback experiments testing a sampled data model for eye tracking movements. IEEE Trans. HFE-4, 38–51 (1963)
Lackner, J.R., Evanoff, J.N.: Smooth pursuit eye movements elicited by somatosensory stimulation. Neurosci. Letters 4, 43–48 (1977)
Lamontagne, C.: A new experimental paradigm for the investigation of the secondary system of human visual motion perception. Perception 2, 167–180 (1973)
Lehmann, D.: EEG, evoked potentials, and eye and image movements. In: The control of eye movements, pp. 149–174, Bach-y-Rita, P., Collins, C.C., Hyde, J.E. (eds.). New York: Academic Press 1971
Leigh, R.J., Newman, S.A., Zee, D.S., Miller, N.R.: Visual following during stimulation of an immobile eye (the open loop condition). Vision Res. 22, 1193–1197 (1982)
Lenox, J.R., Lange, A.F., Graham, K.R.: Eye movement amplitudes in imagined pursuit of a pendulum with eyes closed. Psychophysiology 6, 773–777 (1970)
Levin, S., Lipton, R.B., Holzman, P.S.: Pursuit eye movements in psychopathology: effects of target characteristics. Biol. Psychiatry 16, 255–267 (1981)
Levy, D.L., Lipton, R.B., Holzman, P.S.: Smooth pursuit eye movements: effects of alcohol and chloral hydrate. J. Psych. Res. 16, 1–11 (1981)
Lipton, R.B., Frost, L.A., Holzman, P.S.: Smooth pursuit eye movements, schizophrenia, and distraction. Percept. Motor Skills 50, 159–167 (1980)
Lisberger, S.G., Evinger, C., Johanson, G.W., Fuchs, A.F.: Relationship between eye acceleration and retinal image velocity during foveal smooth pursuit in man and monkey. J. Neurophysiol. 46, 229–249 (1981)
Mack, A., Fendrich, R., Wong, E.: Is perceived motion a stimulus for smooth pursuit. Vision Res. 22, 77–88 (1982)
Mansourian, P.G.: System analysis of the vestibulo-ocular control mechanism. Adv. Ophthalmol. 28, 175–205 (1974)
Michael, J.A., Jones, G.M.: Dependence of visual tracking capability upon stimulus predictability. Vision Res. 6, 707–716 (1966)
Milsum, J.H.: Biological control systems analysis. New York: McGraw-Hill 1966
Minorsky, N.: Introduction to non-linear mechanics. Ann Arbor: Edwards 1947
Morgan, M.J., Turnbull, D.F.: Smooth eye tracking and the perception of motion in the absence of real movement. Vision Res. 18, 1053–1059 (1978)
Netushil, A.: Theory of automatic control. Moscow: MIR 1973
Noorden, G.K. von, Mackensen, G.: Pursuit movements of normal and amblyopic eyes. An electro ophthalmographic study. 1. Physiology of pursuit movements. Am. J. Opth. 53, 325–336 (1962)
Palmieri, G., Oliva, G.A., Scotto, M.: C.R.T. spot-follower device for eye-movements measurements. Kybernetik 8, 23–30 (1971)
Palmieri, G., Scotto, M., Oliva, G.A.: Image-converter pattern tracker for variable retinal feedback experiments. Kybernetik 15, 193–202 (1974)
Pivik, R.T.: Target velocity and smooth pursuit eye movements in psychiatric patients. Psychiatry Res. 1, 313–323 (1979)
Pola, J., Wyatt, H.J.: Target position and velocity: the stimuli for smooth pursuit eye movements. Vision Res. 20, 523–534 (1980)
Raphan, T., Cohen, B.: Brainstem mechanisms for rapid and slow eye movements. Ann. Rev. Physiol. 40, 527–552 (1978)
Rashbass, C.: The relationship between saccadic and smooth tracking eye movements. J. Physiol. 159, 326–338 (1961)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Scotto, M., Oliva, G.A. Limit cycle oscillations of the human eye. Biol. Cybern. 51, 33–44 (1984). https://doi.org/10.1007/BF00336185
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00336185