We explore the connection between a stochastic simulation model and an ordinary differential equations (ODEs) model of the dynamics of an excitable gene circuit that exhibits noise-induced oscillations. Near a bifurcation point in the ODE model, the stochastic simulation model yields behavior dramatically different from that predicted by the ODE model. We analyze how that behavior depends on th...

In this paper, the fault detection problem for nonlinear dynamic power systems based an observer is treated. The nonlinear dynamic model based on differential algebraic equations (DAE) is transformed in to ordinary differential equations (ODE). Three nonlinear observers are used and compared for generating the residual signals. Which are: the extended Kalman filter, the extended Kalman estimato...

Ordinary differential equations (ODEs) and delay differential equations (DDEs) are used to describe many phenomena of physical interest. While ODEs contain derivatives which depend on the solution at the present value of the independent variable (“time”), DDEs contain in addition derivatives which depend on the solution at previous times. DDEs arise in models throughout the sciences [1]. Despit...

We present two individual based models of disease systems using PEPA (Performance Evaluation Process Algebra). The models explore contrasting mechanisms of disease transmission: direct transmission (e.g. measles) and indirect transmission (e.g. malaria, via mosquitos). We extract ordinary differential equations (ODEs) as a continuous approximation to the PEPA models using the Hillston method an...

The parallel solution of initial value problems for ordinary differential equations (ODE-IVPs) has been a very active field of investigation in the past years. In general, the possibility of using parallel computing in this setting concerns different aspects of the numerical solution of ODEs, usually depending on the parallel platform to be used and/or on the complexity of the problem to be sol...

With the advancement of nanoscale semiconductor technology,semiconductor optical amplifiers are used to amplify and process all-optical signals. Inthis paper, with the aim of calculating the gain of quantum dot semiconductor opticalamplifier (QD-SOA), two groups of rate equations and the optical signal propagatingequation are used in the active layer of the device. For t...

We study the linear differential system associated with supersymmetric affine Toda field equations for Lie superalgebras, which has a purely odd simple root system. For an algebra, problem modified by conformal transformation leads to ordinary equation (ODE) that provides functional relations in integrable models. This is known as ODE/IM correspondence. superconformal are shown reduce couple of...

We study the WKB periods for third order ordinary differential equation (ODE) with polynomial potential, which is obtained by Nekrasov-Shatashvili limit of ($A_2,A_N$) Argyres-Douglas theory in Omega background. In minimal chamber moduli space, we derive Y-system and thermodynamic Bethe ansatz (TBA) equations using ODE/IM correspondence. The exact are identified Y-functions. Varying parameters ...

Viscous profiles of shock waves in systems of conservation laws can be viewed as heteroclinic orbits in associated systems of ordinary differential equations (ODE). In the case of overcompressive shock waves, these orbits occur in multi-parameter families. We propose a numerical method to compute families of heteroclinic orbits in general systems of ODE. The key point is a special parameterizat...

Differential equations are extensively used for modeling dynamics of physical processes in many scientific fields such as engineering, physics, and biomedical sciences. Parameter estimation of differential equation models is a challenging problem because of high computational cost and high-dimensional parameter space. In this article, we propose a novel class of methods for estimating parameter...