Solving DDEs in Matlab

Shampine, L. F.; Thompson, Sharon

doi:10.1016/s0168-9274(00)00055-6

Cited by 475 publications

(235 citation statements)

References 12 publications

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“…To study the dynamical behavior of (M1)-(M13), we use the delay differential equation solver DDE23 of Shampine and Thompson (2001). Tables 1 and 2 without further adjustment to the parameters.…”

Section: Ovarian Modelmentioning

confidence: 99%

Multiple Stable Periodic Solutions in a Model for Hormonal Control of the Menstrual Cycle

Clark

Schlosser

Selgrade

2003

Bulletin of Mathematical Biology

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This study presents a nonlinear system of delay differential equations to model the concentrations of five hormones important for regulation and maintenance of the menstrual cycle. Linear model components for the ovaries and pituitary were previously analyzed and reported separately. Results for the integrated model are now presented here. This model predicts serum levels of ovarian and pituitary hormones which agree with data in the literature for normally cycling women. In addition, the model indicates the existence and stability of an abnormal cycle. Hence, the model may be used to simulate the effects of external hormone therapies on abnormally cycling women as well as the effects of exogenous compounds on normally cycling women. Such simulations may be helpful in understanding the role of xenobiotics in fertility problems, in predicting successful hormone therapies, and for testing hormonal methods of birth control.

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Section: Ovarian Modelmentioning

confidence: 99%

Multiple Stable Periodic Solutions in a Model for Hormonal Control of the Menstrual Cycle

Clark

Schlosser

Selgrade

2003

Bulletin of Mathematical Biology

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“…In this work, the MATLAB function ode113, an ODE (ordinary differential equation) solver based on a variable order Adams-Bashforth-Moulton PECE(predict-evaluatecorrect-evaluate) method (Shampine et al 2003) has been used to solve the system of ODEs, and the MATLAB function dde23, a DDE (Delay Differential Equation) solver based on the explicit Runge-Kutta (2,3) method (Shampine and Thompson 2001) has been used to solve the system of DDEs, and considered the plots, which represents the concentration of activated MAPKs' only for the sake of analysis. Availability of quantitative values for molar concentrations and reaction rate constants has been a bottleneck for the researchers who are interested to study the dynamic behaviors of the signaling pathways for which pathway diagram alone deposited in the databases.…”

Section: Resultsmentioning

confidence: 99%

Lose and gain: impacts of ERK5 and JNK cascades on each other

Pandurangan

Gakkhar

2010

Syst Synth Biol

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Kinase cascades in ERK5 (Extracellular signalregulated kinases) and JNK (c-Jun N-terminal kinases) signaling pathways mediate the sensing and processing of stimuli. Cross-talks between signaling cascades is a likely phenomenon that can cause apparently different biological responses from a single pathway, on its activation. Feedback loops have the potential to greatly alter the properties of a pathway and its response to stimuli. Based on enzyme kinetic reactions, mathematical models have been developed to predict and analyze the impacts of cross-talks and feedback loops in ERK5 and JNK cascades. It has been observed that, there is no significant impact on neither ERK5 activation nor JNKs' activation due to cross-talks between them. But it is due to cross-talks and feedback loops in ERK5 and JNK cascade, ERK5 gets activated in a transient manner in the absence of input signals. Planning to obtain the parameter values from the experimentalist and the result should be validated by experimental verification.

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“…With this value, damped oscillations can be observed in (2). We mention that all numerical simulations presented in this section have been done with dde23 [40].…”

Section: Periodic Oscillations: Numerical Illustrationsmentioning

confidence: 97%

Periodic oscillations in leukopoiesis models with two delays

Adimy

Crauste

Ruan

2006

Journal of Theoretical Biology

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The term leukopoiesis describes processes leading to the production and regulation of white blood cells. It is based on stem cells differentiation and may exhibit abnormalities resulting in severe diseases, such as cyclical neutropenia and leukemias. We consider a nonlinear system of two equations, describing the evolution of a stem cell population and the resulting white blood cell population. Two delays appear in this model to describe the cell cycle duration of the stem cell population and the time required to produce white blood cells. We establish sufficient conditions for the asymptotic stability of the unique nontrivial positive steady state of the model by analyzing roots of a second degree exponential polynomial characteristic equation with delay-dependent coefficients. We also prove the existence of a Hopf bifurcation which leads to periodic solutions. Numerical simulations of the model with parameter values reported in the literature demonstrate that periodic oscillations (with short and long periods) agree with observations of cyclical neutropenia in patients.

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Solving DDEs in Matlab

Cited by 475 publications

References 12 publications

Multiple Stable Periodic Solutions in a Model for Hormonal Control of the Menstrual Cycle

Multiple Stable Periodic Solutions in a Model for Hormonal Control of the Menstrual Cycle

Lose and gain: impacts of ERK5 and JNK cascades on each other

Periodic oscillations in leukopoiesis models with two delays

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