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Journal of Differential Equations, ISSN 0022-0396, 02/2019, Volume 266, Issue 4, pp. 1865 - 1898
We consider the real-valued differential equationx′(t)=f(x(t),x(t−d(xt))) with state-dependent delay, where f is strictly monotonic in its second argument. We... 
Poincaré–Bendixson theorem | State-dependent delay | MATHEMATICS | Poincare-Bendixson theorem | PERIODIC-SOLUTION
Journal Article
Transactions of the American Mathematical Society, ISSN 0002-9947, 05/2017, Volume 369, Issue 5, pp. 3387 - 3419
Here A is a linear operator on D(A)\subseteq X satisfying the Hille-Yosida conditions, x(t)\in \overline {D(A)}\subseteq X, a(t)\in {\mathbf {R}}^n, and X is a... 
STATE-DEPENDENT DELAY | functional differential equation | interpolation space | EQUATIONS | Banach manifold | nonlinear transport equation | structured population dynamics | SPACE | MATHEMATICS | MODELS | state dependent delay | POPULATION-DYNAMICS | Linearization | MANIFOLD
Journal Article
Journal of Computational and Applied Mathematics, ISSN 0377-0427, 03/2019, Volume 348, pp. 314 - 327
In this paper, we investigate the local superconvergence of the discontinuous Galerkin (DG) solutions on quasi-graded meshes for nonlinear delay differential... 
Vanishing delay | State dependent delay | Nonlinear delay differential equations | Superconvergence | Discontinuous Galerkin methods | ORDER | MATHEMATICS, APPLIED | RUNGE-KUTTA METHODS | STABILITY | GEOMETRIC MESHES | COLLOCATION METHODS
Journal Article
IEEE Transactions on Automatic Control, ISSN 0018-9286, 01/2018, Volume 63, Issue 1, pp. 306 - 311
Journal Article
Physics Reports, ISSN 0370-1573, 09/2019, Volume 824, pp. 1 - 40
The time needed to exchange information in the physical world induces a delay term when the respective system is modeled by differential equations. Time delays... 
Chaos | Testing for chaos | Attractor dimension | Time delay | Lyapunov exponents | STATE-DEPENDENT DELAY | FUNCTIONAL-DIFFERENTIAL-EQUATIONS | PHYSICS, MULTIDISCIPLINARY | STABILITY-CRITERIA | PERIOD-DOUBLING CASCADES | SEMICONDUCTOR-LASERS | DYNAMICAL-SYSTEMS | QUASI-PERIODICITY | EMBEDDING DIMENSION | BIFURCATION-ANALYSIS | Physics - Chaotic Dynamics
Journal Article
International Journal of Non-Linear Mechanics, ISSN 0020-7462, 03/2018, Volume 99, pp. 13 - 30
We present a detailed bifurcation analysis of the state-dependent delay model of rotary drilling considering only the axial and torsional modes. This analysis... 
Double Hopf point | Method of multiple scales | State-dependent delay | Rotary drilling | Bifurcation analysis | DIFFERENTIAL EQUATIONS | INSTABILITY | STABILITY | MULTIPLE SCALES | CHATTER | MECHANICS | TURNING PROCESSES | DYNAMICS | SYSTEMS | FRICTION-INDUCED VIBRATIONS
Journal Article
Computers and Mathematics with Applications, ISSN 0898-1221, 2011, Volume 62, Issue 3, pp. 1143 - 1149
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 11/2015, Volume 271, pp. 142 - 153
We propose and analyze a stage-structured predator–prey model in which the time from birth to maturity is directly related to the number of individuals... 
Predator–prey | Global stability | Stage structure | Harvesting | State-dependent | Predator-prey | SYSTEM | MATHEMATICS, APPLIED | STABILITY | POPULATION-GROWTH | TIME-DELAY | DISTRIBUTED MATURATION DELAY | DYNAMICS | BIFURCATION | Analysis | Models | Numerical analysis
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2012, Volume 385, Issue 1, pp. 506 - 516
Parabolic differential equations with discrete state-dependent delay are studied. The approach, based on an additional condition on the delay function... 
Partial functional differential equation | State-dependent delay | Well-posedness | Global attractor | MATHEMATICS | MATHEMATICS, APPLIED | BOUNDARY-LAYER PHENOMENA | DYNAMICS | INERTIAL MANIFOLDS | MODEL | UNIQUENESS
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 12/2016, Volume 261, Issue 12, pp. 6856 - 6882
We study the existence and uniqueness of C1+α-strict solutions for a general class of abstract differential equations with state dependent delay. We also study... 
State dependent delay equations | Analytic semigroup | Strict solutions | Partial differential equations | Bounded delay | NICHOLSONS BLOWFLIES EQUATION | MODEL | PARAMETERS | MATHEMATICS | RESPECT | DISCRETE | SYSTEMS | POPULATION-DYNAMICS
Journal Article
SIAM JOURNAL ON APPLIED MATHEMATICS, ISSN 0036-1399, 2019, Volume 79, Issue 4, pp. 1218 - 1243
We analyze the stability of a system of differential equations with a threshold-defined delay arising from a model for platelet production. We consider a... 
MATHEMATICS, APPLIED | megakaryopoiesis | DIFFERENTIAL-EQUATIONS | RECEPTOR | THROMBOPOIESIS REGULATION | PLATELET PRODUCTION | MATHEMATICAL-MODEL | MEGAKARYOCYTOPOIESIS | state-dependent delay | platelet | THROMBOCYTOPENIA | transcendental equation | oscillations | EXPRESSION | stability | Dynamical Systems | Mathematics
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 09/2014, Volume 243, pp. 161 - 175
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 09/2015, Volume 266, pp. 54 - 69
In this paper, we have a tendency to implement different fixed point theorem [ Banach contraction principle, Krasnoselskii’s [18] and Schaefer’s [, 18] coupled... 
Fixed point theorems | Semigroup theory | Fractional order differential equations | State-dependent delay | Impulsive conditions | MATHEMATICS, APPLIED | BOUNDARY-VALUE PROBLEM | DIFFERENTIAL-EQUATIONS | Analysis | Differential equations
Journal Article
Automatica, ISSN 0005-1098, 02/2020, Volume 112, p. 108674
This paper addresses the stability problem for systems with state-dependent state delay (delay which involves the state of the system). Different from the... 
Lyapunov stability | State-dependent state delay | Submarine positioning systems | Memoryless control | Lyapunov exponent | STABILIZATION | FUNCTIONAL-DIFFERENTIAL EQUATIONS | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC
Journal Article
Neurocomputing, ISSN 0925-2312, 01/2016, Volume 171, pp. 1375 - 1386
In this paper, a more general class of state-dependent impulsive Cohen–Grossberg neural networks having variable coefficients with time-varying delays is... 
Global exponential stability | State-dependent impulsive systems | Periodicity | Cohen–Grossberg neural networks | Cohen-Grossberg neural networks | EXISTENCE | PERIODIC-SOLUTIONS | DISCRETE | DIFFERENTIAL-EQUATIONS | DYNAMICAL ANALYSIS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Neural networks | Numerical analysis
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 09/2018, Volume 291, Issue 13, pp. 2045 - 2056
We study the existence and uniqueness of solutions, and the wellposedness of a general class of second order differential equations with state‐dependent delay.... 
34K30 | abstract Cauchy problem | state‐dependent delay | cosine function | 34G | 34K | 47D09 | state-dependent delay | EXISTENCE | 2ND-ORDER | PARAMETERS | MODEL | MATHEMATICS | RESPECT | DISCRETE | DYNAMICS | SYSTEMS | APPROXIMATE CONTROLLABILITY | Differential equations
Journal Article