Delay equations in biology

[1]  U. an der Heiden,et al.  Delays in physiological systems , 1979 .

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

[3]  Delay-Induced Biochemical Oscillations , 1979 .

[4]  K. Hadeler.  Periodic solutions of ẋ(t) = –f(x(t), x(t – 1)) , 1979 .

[5]  Solutions of x'(t) = f(x(t),x(t − L) have limits when f is an order relation , 1979 .

[6]  J. Hale,et al.  Periodic solutions of autonomous equations , 1978 .

[7]  Hans-Otto Walther,et al.  A theorem on the amplitudes of periodic solutions of differential delay equations with applications to bifurcation , 1978 .

[8]  W. Alt.  Some periodicity criteria for functional differential equations , 1978 .

[9]  J. Cushing.  Bifurcation of periodic oscillations due to delays in single species growth models , 1978 .

[10]  A. Wörz-Busekros,et al.  Global Stability in Ecological Systems with Continuous Time Delay , 1978 .

[11]  N. D. Kazarinoff,et al.  Hopf Bifurcation and Stability of Periodic Solutions of Differential-difference and Integro-differential Equations , 1978 .

[12]  Harlan W. Stech,et al.  The effect of time lags on the stability of the equilibrium state of a population growth equation , 1978 .

[13]  C P Malta,et al.  Qualitative analysis of oscillations in isolated populations of flies. , 1978, Journal of theoretical biology.

[14]  B. Hassard,et al.  Bifurcation formulae derived from center manifold theory , 1978 .

[15]  A. Somolinos,et al.  Periodic solutions of the sunflower equation: +(/)+(/)sin(-)=0 , 1978 .

[16]  Jim M Cushing,et al.  Integrodifferential Equations and Delay Models in Population Dynamics , 1977 .

[17]  N. Macdonald,et al.  Time lag in a model of a biochemical reaction sequence with end product inhibition. , 1977, Journal of theoretical biology.

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

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

[20]  K. Hadeler.  Some Aspects of the Mathematics of Limulus , 1977 .

[21]  Harvey Thomas Banks,et al.  DELAY SYSTEMS IN BIOLOGICAL MODELS: APPROXIMATION TECHNIQUES , 1977 .

[22]  B. D. Coleman,et al.  Periodic Solutions of Certain Nonlinear Integral Equations with a Time Lag , 1976 .

[23]  H. Walther.  On a transcendental equation in the stability analysis of a population growth model , 1976, Journal of mathematical biology.

[24]  B. D. Coleman,et al.  Theory of the response of the limulus retina to periodic excitation , 1976, Journal of Mathematical Biology.

[25]  K. Hadeler.  On the stability of the stationary state of a population growth equation with time-lag , 1976, Journal of mathematical biology.

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

[27]  C. WEHRHAHN,et al.  Real-time delayed tracking in flies , 1976, Nature.

[28]  R M May,et al.  A note on difference-delay equations. , 1976, Theoretical population biology.

[29]  U. Heiden.  Stability properties of neural and cellular control systems , 1976 .

[30]  N. Macdonald,et al.  Time delay in prey-predator models , 1976 .

[31]  J. Cushing.  Periodic solutions of two species interaction models with lags , 1976 .

[32]  J. Yorke,et al.  Existence and Stability of Periodic Solutions of x′(t) = —f(x(t), x(t — 1)) , 1976 .

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

[34]  Roger D. Nussbaum,et al.  A global bifurcation theorem with applications to functional differential equations , 1975 .

[35]  B. D. Coleman.  Consequences of delayed lateral inhibition in the retina of Limulus. I. Elementary theory of spatially uniform fields. , 1975, Journal of theoretical biology.

[36]  B. D. Coleman.  Consequences of delayed lateral inhibition in the retina of Limulus. II. Theory of spatially uniform fields, assuming the four-point property. , 1975, Journal of Theoretical Biology.

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

[38]  A. Johnsson.  Gravitational Stimulations Inhibit Oscillatory Growth Movements of Plants , 1974 .

[39]  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.

[40]  John Maynard Smith,et al.  Models in ecology , 1974 .

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

[42]  Robert M. May,et al.  Time delays, density-dependence and single-species oscillations , 1974 .

[43]  Roger D. Nussbaum,et al.  Periodic solutions of some nonlinear, autonomous functional differential equations. II , 1973 .

[44]  R. Grafton.  Periodic solutions of certain Lie´nard equations with delay , 1972 .

[45]  Entrainment of Geotropic Oscillations in Hypocotyls of Heliunthus annuus - An Experimental and Theoretical Investigation. I. The Geotropic Movement Initiated by one Single Geotropic Stimulation , 1972 .

[46]  Entrainment of Geotropic Oscillations in Hypocotyls of Helianthus annuus– An Experimental and Theoretical Investigation , 1972 .

[47]  A. Johnsson.  Geotropic Responses in Helianthus and their Dependence on the Auxin Ratio. – With a Refined Mathematical Description of the Course of Geotropic Movements , 1971 .

[48]  R. B. Grafton,et al.  A periodicity theorem for autonomous functional differential equations , 1969 .

[49]  Phase-shift in Geotropical Oscillations - A Theoretical and Experimental Study. , 1969, Physiologia plantarum.

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

[51]  Anders Johnsson,et al.  Application of a Theory for Circumnutations to Geotropic Movements , 1968 .

[52]  Gregory Dunkel.  Single species model for population growth depending on past history , 1968 .

[53]  F. Browder.  A new generalization of the Schauder fixed point theorem , 1967 .

[54]  Richard Bellman,et al.  Differential-Difference Equations , 1967 .

[55]  A. Johnsson,et al.  A Theory for Circumnutations in Helianthus annuus , 1967 .

[56]  P J Wangersky,et al.  ON TIME LAGS IN EQUATIONS OF GROWTH. , 1956, Proceedings of the National Academy of Sciences of the United States of America.

[57]  W J Cunningham,et al.  A NONLINEAR DIFFERENTIAL-DIFFERENCE EQUATION OF GROWTH. , 1954, Proceedings of the National Academy of Sciences of the United States of America.

[58]  Fritz Schürer.  Zur Theorie des Balancierens , 1948 .