scholarly journals Dynamics of the Oxygen, Carbon Dioxide, and Water Interaction across the Insect Spiracle

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
S. M. Simelane ◽  
S. Abelman ◽  
F. D. Duncan
Keyword(s):  
Carbon Dioxide ◽  
Water Vapor ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Ordinary Differential Equations ◽  
Continuous Time ◽  
Water Interaction ◽  
Stability And Instability ◽  
Respiratory Gases

This paper explores the dynamics of respiratory gases interactions which are accompanied by the loss of water through an insect’s spiracle. Here we investigate and analyze this interaction by deriving a system of ordinary differential equations for oxygen, carbon dioxide, and water vapor. The analysis is carried out in continuous time. The purpose of the research is to determine bounds for the gas volumes and to discuss the complexity and stability of the equilibria. Numerical simulations also demonstrate the dynamics of our model utilizing the new conditions for stability and instability.

scholarly journals Approximate ordinary differential equations for the optimal exercise boundaries of American put and call options

2013 ◽  
Vol 25 (1) ◽  
pp. 27-43 ◽  
Author(s):  
MARIANITO R. RODRIGO
Keyword(s):  
Differential Equations ◽  
Fluid Mechanics ◽  
Numerical Simulations ◽  
Ordinary Differential Equations ◽  
Boundary Layers ◽  
Mellin Transform ◽  
Call Option ◽  
Option Prices ◽  
Analytical Formulas ◽  
American Put

We revisit the American put and call option valuation problems. We derive analytical formulas for the option prices and approximate ordinary differential equations for the optimal exercise boundaries. Numerical simulations yield accurate option prices and comparable computational speeds when benchmarked against the binomial method for calculating option prices. Our approach is based on the Mellin transform and an adaptation of the Kármán–Pohlausen technique for boundary layers in fluid mechanics.

scholarly journals Numerical Simulations of a Modified SIR Model Fitting Statistical Datafor COVID19

2020 ◽  
Vol 8 ◽  
pp. 115-125
Author(s):  
Flavius Guiaş
Keyword(s):  
Differential Equations ◽  
Numerical Simulations ◽  
Ordinary Differential Equations ◽  
Model Fitting ◽  
Sir Model ◽  
Second Stage ◽  
Convalescence Time ◽  
Official Data ◽  
Infectious State

We consider a system of ordinary differential equations obtained by modifying the classical SIR modelin epidemiology in order to account for the particular features of COVID­19 and the structure of the availablestatistical data. Its main feature is that the infectious state is being split in two different stages. In the first one,which lasts a few days after being infected, the individuals are considered to be contagious and able to spreadfurther the disease. After this, the individuals are considered to be isolated and this second stage lasts until eitherrecovery or death is reported. The parameters of the model are fitted for several countries (Germany, Italy, Spain,Russia, USA, Romania) such that the solution matches the known number of new cases, active cases, recoveriesand deaths. The values of these parameters give insight regarding the evolution of the pandemy and can revealdifferent policies and approaches in reporting the official data. For example one of them can indicate that in certaincountries a substantial amount of cases were reported only post­mortem. The variation across several countries ofanother parameter, which models the average convalescence time (the duration of the second stage of the infectiousstate), points to the fact that the recoveries are reported at different rates, in some cases with significant delays.Since it can be assumed that this is only a matter of reporting, we also perform additional simulations for thesecountries by taking the average convalescence time the value of Germany, which is the smallest within the wholerange. The conclusion is that under this assumption, the evolution of the active cases for example in Italy andSpain, is not significantly different to that in Germany, the comparison being based on the fact that these countriesshowed a similar number of cases within the considered period.

scholarly journals Modeling Trajectories with Neural Ordinary Differential Equations

2021 ◽  
Author(s):  
Yuxuan Liang ◽  
Kun Ouyang ◽  
Hanshu Yan ◽  
Yiwei Wang ◽  
Zekun Tong ◽  
...  
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Real World ◽  
Continuous Time ◽  
Trajectory Data ◽  
Time Dynamics ◽  
Trajectory Classification ◽  
Novel Method ◽  
Spatial Trajectory ◽  
Hidden States

Recent advances in location-acquisition techniques have generated massive spatial trajectory data. Recurrent Neural Networks (RNNs) are modern tools for modeling such trajectory data. After revisiting RNN-based methods for trajectory modeling, we expose two common critical drawbacks in the existing uses. First, RNNs are discrete-time models that only update the hidden states upon the arrival of new observations, which makes them an awkward fit for learning real-world trajectories with continuous-time dynamics. Second, real-world trajectories are never perfectly accurate due to unexpected sensor noise. Most RNN-based approaches are deterministic and thereby vulnerable to such noise. To tackle these challenges, we devise a novel method entitled TrajODE for more natural modeling of trajectories. It combines the continuous-time characteristic of Neural Ordinary Differential Equations (ODE) with the robustness of stochastic latent spaces. Extensive experiments on the task of trajectory classification demonstrate the superiority of our framework against the RNN counterparts.

Perturbations of Multipliers of Systems of Periodic Ordinary Differential Equations

2011 ◽  
Vol 3 (5) ◽  
pp. 562-571
Author(s):  
Leonid Berezansky ◽  
Michael Gil’ ◽  
Liora Troib
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Periodic Systems ◽  
New Approach ◽  
Stability And Instability ◽  
Perturbed Systems ◽  
The Stability

AbstractThe paper deals with periodic systems of ordinary differential equations (ODEs). A new approach to the investigation of variations of multipliers under perturbations is suggested. It enables us to establish explicit conditions for the stability and instability of perturbed systems.

Mathematical modeling of adaptive immune response after transplantation

2020 ◽  
Vol 13 (08) ◽  
pp. 2050167
Author(s):  
Anka Markovska
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Immune Response ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Ordinary Differential Equations ◽  
Cellular Immunity ◽  
Adaptive Immune Response ◽  
Nonlinear Ordinary Differential Equations ◽  
Adaptive Immune

A mathematical model of adaptive immune response after transplantation is formulated by five nonlinear ordinary differential equations. Theorems of existence, uniqueness and nonnegativity of solution are proven. Numerical simulations of immune response after transplantation without suppression of acquired cellular immunity and after suppression were performed.

Nonlinear Dynamics of Two Discrete-Time Versions of the Continuous-Time Brusselator Model

2019 ◽  
Vol 29 (10) ◽  
pp. 1950142
Author(s):  
Paulo C. Rech
Keyword(s):  
Differential Equations ◽  
Mathematical Models ◽  
Ordinary Differential Equations ◽  
Discrete Time ◽  
Continuous Time ◽  
Periodic Structures ◽  
Parameter Spaces ◽  
First Order ◽  
Brusselator Model ◽  
Dynamical Behaviors

In this paper, we report results related with the dynamics of two discrete-time mathematical models, which are obtained from a same continuous-time Brusselator model consisting of two nonlinear first-order ordinary differential equations. Both discrete-time mathematical models are derived by integrating the set of ordinary differential equations, but using different methods. Such results are related, in each case, with parameter-spaces of the two-dimensional map which results from the respective discretization process. The parameter-spaces obtained using both maps are then compared, and we show that the occurrence of organized periodic structures embedded in a quasiperiodic region is verified in only one of the two cases. Bifurcation diagrams, Lyapunov exponents plots, and phase-space portraits are also used, to illustrate different dynamical behaviors in both discrete-time mathematical models.

Nonlinear Analysis of a Z-Shaped Planar Beam

2014 ◽  
Author(s):  
Wei Zhang ◽  
Wenhua Hu ◽  
Dongxing Cao ◽  
Xiaofeng Yang
Keyword(s):  
Differential Equations ◽  
Galerkin Method ◽  
Numerical Simulations ◽  
Ordinary Differential Equations ◽  
Nonlinear Analysis ◽  
Continuous System ◽  
Modal Interactions ◽  
Internal Resonances ◽  
Folding Angle ◽  
The Galerkin Method

In this paper, a z-shaped planar inextensible beam with harmonic foundation excitations is considered. The linear frequencies and modes of the beam with various folding angles are obtained through analytical formulations, and validated by numerical simulations. The continuous system is truncated into a system of ordinary differential equations with quadratic nonlinear terms by using the Galerkin method based on the modes obtained under a special folding angle, which may bring about modal interactions. The nonlinearities of the system are researched under the combined resonances, such as primary and internal resonances.

scholarly journals A mathematical model of p62-ubiquitin aggregates in autophagy

2021 ◽  
Vol 84 (1-2) ◽  
Author(s):  
Julia Delacour ◽  
Marie Doumic ◽  
Sascha Martens ◽  
Christian Schmeiser ◽  
Gabriele Zaffagnini
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Ordinary Differential Equations ◽  
Asymptotic Methods ◽  
Finite Size ◽  
Rigorous Results ◽  
The Third ◽  
Cellular Autophagy ◽  
Free Particles

AbstractAggregation of ubiquitinated cargo by oligomers of the protein p62 is an important preparatory step in cellular autophagy. In this work a mathematical model for the dynamics of these heterogeneous aggregates in the form of a system of ordinary differential equations is derived and analyzed. Three different parameter regimes are identified, where either aggregates are unstable, or their size saturates at a finite value, or their size grows indefinitely as long as free particles are abundant. The boundaries of these regimes as well as the finite size in the second case can be computed explicitly. The growth in the third case (quadratic in time) can also be made explicit by formal asymptotic methods. In the absence of rigorous results the dynamic stability of these structures has been investigated by numerical simulations. A comparison with recent experimental results permits a partial parametrization of the model.

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