Oscillatory modes in a nonlinear second-order differential equation with delay

[1]  Matthew Mark Thomas,et al.  Application of artificial neural networks (ANNs) to complex oscillations in the human pupil light reflex , 1992, [1992] Proceedings Fifth Annual IEEE Symposium on Computer-Based Medical Systems.

[2]  L Glass,et al.  Complex oscillations in a human motor system. , 1989, Journal of motor behavior.

[3]  Michael C. Mackey,et al.  Commodity price fluctuations: Price dependent delays and nonlinearities as explanatory factors , 1989 .

[4]  L Glass,et al.  Complex dynamics and bifurcations in neurology. , 1989, Journal of theoretical biology.

[5]  K. Ukai Irregular pupil cycling as a characteristic abnormality in patients with demyelinative optic neuropathy. , 1988, American journal of ophthalmology.

[6]  André Longtin,et al.  Complex oscillations in the human pupil light reflex with “mixed” and delayed feedback , 1988 .

[7]  Leon Glass,et al.  Time delays, oscillations, and chaos in physiological control systems , 1988 .

[8]  Delisle,et al.  Second-order differential-delay equation to describe a hybrid bistable device. , 1987, Physical review. A, General physics.

[9]  H. Walther,et al.  Existence of chaos in control systems with delayed feedback , 1983 .

[10]  Michael C. Mackey,et al.  The dynamics of production and destruction: Analytic insight into complex behavior , 1982 .

[11]  William Gurney,et al.  Instability and complex dynamic behaviour in population models with long time delays , 1982 .

[12]  Hans-Otto Walther,et al.  Homoclinic solution and chaos in , 1981 .

[13]  H. Gibbs,et al.  Observation of chaos in optical bistability (A) , 1981 .

[14]  K. P. Hadeler,et al.  Effective computation of periodic orbits and bifurcation diagrams in delay equations , 1980 .

[15]  S. P. Blythe,et al.  Nicholson's blowflies revisited , 1980, Nature.

[16]  K. Ikeda,et al.  Optical Turbulence: Chaotic Behavior of Transmitted Light from a Ring Cavity , 1980 .

[17]  U. Heiden Periodic solutions of a nonlinear second order differential equation with delay , 1979 .

[18]  L. Glass,et al.  PATHOLOGICAL CONDITIONS RESULTING FROM INSTABILITIES IN PHYSIOLOGICAL CONTROL SYSTEMS * , 1979, Annals of the New York Academy of Sciences.

[19]  Michael C. Mackey,et al.  Unified hypothesis for the origin of aplastic anemia and periodic hematopoiesis , 1978 .

[20]  L. Glass,et al.  Oscillation and chaos in physiological control systems. , 1977, Science.

[21]  K. P. Hadeler,et al.  Periodic solutions of difference-differential equations , 1977 .

[22]  古用 哲夫 Existence of Periodic Solutions of One-Dimensional Differential-Delay Equations (函数微分方程式の解の定性的研究) , 1977 .

[23]  James A. Yorke,et al.  On the nonlinear differential delay equation x′(t) = −f(x(t), x(t − 1)) , 1977 .

[24]  R. Sokal,et al.  Oscillations in Housefly Population Sizes Due to Time Lags , 1976 .

[25]  W Reichardt,et al.  Visual control of orientation behaviour in the fly: Part I. A quantitative analysis , 1976, Quarterly Reviews of Biophysics.

[26]  Robert M. May,et al.  Simple mathematical models with very complicated dynamics , 1976, Nature.

[27]  J. Yorke,et al.  Period Three Implies Chaos , 1975 .

[28]  Roger D. Nussbaum,et al.  Periodic solutions of some nonlinear autonomous functional differential equations , 1974 .

[29]  B. D. Coleman,et al.  Theory of delayed lateral inhibition in the compound eye of limulus. , 1974, Proceedings of the National Academy of Sciences of the United States of America.

[30]  Shui-Nee Chow,et al.  Existence of periodic solutions of autonomous functional differential equations , 1974 .

[31]  Nicholas C. Metropolis,et al.  On Finite Limit Sets for Transformations on the Unit Interval , 1973, J. Comb. Theory A.

[32]  W. R. Utz,et al.  Periodic Solutions of a Nonlinear Second Order Differential Equation , 1970 .

[33]  J. Maynard Smith,et al.  Mathematical Ideas in Biology , 1968 .

[34]  Lawrence Stark,et al.  Stability, Oscillations, and Noise in the Human Pupil Servomechanism , 1959, Proceedings of the IRE.

[35]  G. E. Hutchinson,et al.  CIRCULAR CAUSAL SYSTEMS IN ECOLOGY , 1948, Annals of the New York Academy of Sciences.

[36]  R. Westervelt,et al.  Stability of analog neural networks with delay. , 1989, Physical review. A, General physics.

[37]  A Longtin,et al.  Modelling autonomous oscillations in the human pupil light reflex using non-linear delay-differential equations. , 1989, Bulletin of Mathematical Biology.

[38]  C A Phillips,et al.  Sensory feedback control of upper- and lower-extremity motor prostheses. , 1988, Critical reviews in biomedical engineering.

[39]  U. Heiden Stochastic Properties of Simple Differential — Delay Equations , 1985 .

[40]  U. an der Heiden,et al.  The dynamics of recurrent inhibition , 1984, Journal of mathematical biology.

[41]  H. Walther Density of slowly oscillating solutions of ẋ(t) = −f(x(t − 1)) , 1981 .

[42]  M. Misiurewicz,et al.  Entropy of piecewise monotone mappings , 1980 .

[43]  M C Mackey,et al.  Periodic auto-immune hemolytic anemia: an induced dynamical disease. , 1979, Bulletin of mathematical biology.

[44]  U. an der Heiden Delays in physiological systems. , 1979, Journal of mathematical biology.

[45]  M C Mackey,et al.  Unified hypothesis for the origin of aplastic anemia and periodic hematopoiesis. , 1978, Blood.

[46]  Robert M. May,et al.  Dynamical diseases , 1978, Nature.

[47]  J. M. Smith Regulation and control , 1968 .