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Delay equations in biology
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What this work says
Outgoing claims: the papers this work cites, builds on, or argues with.
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Zur Theorie des Balancierens
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Periodic solutions of ẋ(t) = –f(x(t), x(t – 1))
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Period Three Implies Chaos
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Some Aspects of the Mathematics of Limulus
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Delay-Induced Biochemical Oscillations
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Integrodifferential Equations and Delay Models in Population Dynamics
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The effect of time lags on the stability of the equilibrium state of a population growth equation
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Theory of the response of the limulus retina to periodic excitation
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On a transcendental equation in the stability analysis of a population growth model
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On the stability of the stationary state of a population growth equation with time-lag
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Periodic solutions of difference-differential equations
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Some periodicity criteria for functional differential equations
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Periodic solutions of some nonlinear autonomous functional differential equations
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Bifurcation of periodic oscillations due to delays in single species growth models
inferredcites →https://doi.org/10.1007/bfb0077132openalex-snapshot
Single species model for population growth depending on past history
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A periodicity theorem for autonomous functional differential equations
inferredcites →https://doi.org/10.1016/0022-0396(72)90064-2openalex-snapshot
Periodic solutions of certain Lie´nard equations with delay
inferredcites →https://doi.org/10.1016/0022-0396(73)90053-3openalex-snapshot
Periodic solutions of some nonlinear, autonomous functional differential equations. II
inferredcites →https://doi.org/10.1016/0022-0396(74)90084-9openalex-snapshot
Existence of periodic solutions of autonomous functional differential equations
inferredcites →https://doi.org/10.1016/0022-0396(78)90049-9openalex-snapshot
A theorem on the amplitudes of periodic solutions of differential delay equations with applications to bifurcation
inferredcites →https://doi.org/10.1016/0022-1236(75)90061-0openalex-snapshot
A global bifurcation theorem with applications to functional differential equations
inferredcites →https://doi.org/10.1016/0022-247x(78)90120-8openalex-snapshot
Bifurcation formulae derived from center manifold theory
inferredcites →https://doi.org/10.1016/0022-247x(78)90250-0openalex-snapshot
Periodic solutions of autonomous equations
inferredcites →https://doi.org/10.1016/0022-247x(79)90068-4openalex-snapshot
Periodic solutions of a nonlinear second order differential equation with delay
inferredcites →https://doi.org/10.1016/0022-5193(75)90058-2openalex-snapshot
Consequences of delayed lateral inhibition in the retina of Limulus I. elementary theory of spatially uniform fields
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Consequences of delayed lateral inhibition in the retina of Limulus II. theory of spatially uniform fields, assuming the four-point property
inferredcites →https://doi.org/10.1016/0022-5193(77)90056-xopenalex-snapshot
Time lag in a model of a biochemical reaction sequence with end product inhibition
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Qualitative analysis of oscillations in isolated populations of flies
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Periodic solutions of two species interaction models with lags
inferredcites →https://doi.org/10.1016/0025-5564(76)90085-7openalex-snapshot
Stability properties of neural and cellular control systems
inferredcites →https://doi.org/10.1016/0025-5564(76)90130-9openalex-snapshot
Time delay in prey-predator models
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A note on difference-delay equations
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Solutions of x'(t) = f(x(t),x(t − L) have limits when f is an order relation
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Existence and Stability of Periodic Solutions of x′(t) = —f(x(t), x(t — 1))
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DELAY SYSTEMS IN BIOLOGICAL MODELS: APPROXIMATION TECHNIQUES**Invited lecture, International Conference on Nonlinear Systems and Applications, July 19-23, Arlington, Texas.
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Nonlinear Systems and Applications
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Differential-Difference Equations
inferredcites →https://doi.org/10.1017/cbo9780511565144openalex-snapshot
Mathematical Ideas in Biology
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Simple mathematical models with very complicated dynamics
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A NONLINEAR DIFFERENTIAL-DIFFERENCE EQUATION OF GROWTH
inferredcites →https://doi.org/10.1073/pnas.42.9.699openalex-snapshot
ON TIME LAGS IN EQUATIONS OF GROWTH
inferredcites →https://doi.org/10.1073/pnas.71.7.2887openalex-snapshot
Theory of Delayed Lateral Inhibition in the Compound Eye of Limulus
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Periodic solutions of the sunflower equation: 𝑥+(𝑎/𝑟)𝑥+(𝑏/𝑟)sin𝑥(𝑡-𝑟)=0
inferredcites →https://doi.org/10.1093/imamat/21.4.461openalex-snapshot
Hopf Bifurcation and Stability of Periodic Solutions of Differential-difference and Integro-differential Equations
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A Theory for Circumnutations in Helianthus annuus
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Application of a Theory for Circumnutations to Geotropic Movements
inferredcites →https://doi.org/10.1111/j.1399-3054.1969.tb09113.xopenalex-snapshot
Phase‐shift in Geotropical Oscillations – A Theoretical and Experimental Study
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Geotropic Responses in Helianthus and their Dependence on the Auxin Ratio. – With a Refined Mathematical Description of the Course of Geotropic Movements
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Entrainment of Geotropic Oscillations in Hypocotyls of Heliunthus annuus– An Experimental and Theoretical Investigation
inferredcites →https://doi.org/10.1111/j.1399-3054.1972.tb03545.xopenalex-snapshot
Entrainment of Geotropic Oscillations in Hypocotyls of Helianthus annuus– An Experimental and Theoretical Investigation
inferredcites →https://doi.org/10.1126/science.267326openalex-snapshot
Oscillation and Chaos in Physiological Control Systems
inferredcites →https://doi.org/10.1137/0131012openalex-snapshot
Periodic Solutions of Certain Nonlinear Integral Equations with a Time Lag
inferredcites →https://doi.org/10.1137/0135011openalex-snapshot
Global Stability in Ecological Systems with Continuous Time Delay
inferredcites →https://doi.org/10.1142/9789814368605_0003openalex-snapshot
DIFFERENTIAL-DIFFERENCE EQUATIONS
inferredcites →https://doi.org/10.1215/s0012-7094-59-02629-8openalex-snapshot
On a generalization of the Schauder fixed point theorem
inferredcites →https://doi.org/10.1215/s0012-7094-65-03261-8openalex-snapshot
A further generalization of the Schauder fixed point theorem
inferredcites →https://doi.org/10.1515/znc-1974-11-1212openalex-snapshot
Gravitational Stimulations Inhibit Oscillatory Growth Movements of Plants
inferredcites →https://doi.org/10.2307/2344498openalex-snapshot
Integrodifferential Equations and Delay Models in Population Dynamics.
inferredcites →https://doi.org/10.2307/3535openalex-snapshot
Time Delays, Density-Dependence and Single-Species Oscillations
What points at this work
Incoming claims: where this work appears in other papers’ reference lists and arguments.
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State‐structure models of microbial growth
inferred← citeshttps://doi.org/10.1002/cplx.10087openalex-snapshot
Complex dynamics is abolished in delayed recurrent systems with distributed feedback times
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Structured Population Models, Conservation Laws, and Delay Equations
inferred← citeshttps://doi.org/10.1007/978-1-4612-0039-0openalex-snapshot
Stability of Time-Delay Systems
inferred← citeshttps://doi.org/10.1007/978-3-030-63591-6_6openalex-snapshot
Oscillations and Periodic Solutions in a Two-Dimensional Differential Delay Model
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A Survey on Max-Type Difference Equations
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Generalized Sensitivity Analysis for Delay Differential Equations
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Geometric Ideas in the Stability Analysis of Delay Models in Biosciences
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Delay Differential Equations
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Strukturen in Biologischen Modellen
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Effective computation of periodic orbits and bifurcation diagrams in delay equations
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F-controllability and observability of linear retarded systems
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Comparison results for oscillations of delay equations
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Discrete waves and phase-locked oscillations in the growth of a single-species population over a patchy environment
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The advancement of oscillation theory of functional differential equations
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The Leray-Schauder continuation method is a constructive element in the numerical study of nonlinear eigenvalue and bifurcation problems
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Positivity and stability for cauchy problems with delay
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Bifurcation Analysis of a Coupled System Between a Transport Equation and an Ordinary Differential Equation with Time Delay
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Approximation of Solutions to the Optimal Control Problems for Systems with Maximum
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Exponential stabilization of 1-D wave network with boundary delay
inferred← citeshttps://doi.org/10.1007/s12591-021-00560-0openalex-snapshot
Feedback Stabilization of Delayed Bilinear Systems
inferred← citeshttps://doi.org/10.1016/0303-2647(95)01560-4openalex-snapshot
Adaptation in a stochastic prisoner's dilemma with delayed information
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State-structure models—A base for efficient control of fermentation processes
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On a nonlinear delay population model
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Nonlinear Systems Evolving with State Suprema as Multi-Mode Multi-Dimensional (M3D) Systems: Analysis & Observation
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Robust Optimal Control of Linear-Type Dynamic Systems with Random Delays
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Rational energy decay rate for the wave equation with delay term on the dynamical control
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Nonlinear integral inequalities involving maxima of unknown scalar functions
inferred← citeshttps://doi.org/10.1016/j.sysconle.2020.104700openalex-snapshot
Same decay rate of second order evolution equations with or without delay
inferred← citeshttps://doi.org/10.1017/s0308210500031395openalex-snapshot
Periodic solutions of a planar delay equation
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Stabilization of second order evolution equations with unbounded feedback with delay
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The exponential stability region of Timoshenko beam with interior delays and boundary damping
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Rapid stabilisation of multi-dimensional Schrödinger equation with the internal delay control
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General decay for a wave equation with Wentzell boundary conditions and nonlinear delay terms
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Sensitivity via the complex-step method for delay differential equations with non-smooth initial data
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On oscillation of nonlinear delay differential equations
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Periodic patterns in simple biological differential delay models
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On the optimal control of systems evolving with state suprema
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Existência de Soluções Periódicas para uma Classe de Equações Diferenciais Funcionais Retardadas e Aplicações
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Existence of periodic solutions for differential equations with multiple delays under dichotomy condition
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Distribution of the Zeros of the Solutions of Hyperbolic Differential Equations with Maxima
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Permanence in a class of delay differential equations with mixed monotonicity
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Linear Integral Inequalities Involving Maxima of the Unknown Scalar Functions
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On the stability of a class of nonlinear time delay systems
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Rational stabilization of the multidimensional wave equation with dynamical control and time-varying delay
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Theoretical foundations for traditional and generalized sensitivity functions for nonlinear delay differential equations
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Global asymptotic stability in a class of nonlinear differential delay equations
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The convexity based approach to optimal control of some classes of non-standard dynamic systems
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Linear integral inequalities involving maxima of the unknown scalar functions
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