Search results for "ordinary differential equation"

Multiplicity of solutions of Dirichlet problems associated with second-order equations in ℝ2

2009

AbstractWe study the existence of multiple solutions for a two-point boundary-value problem associated with a planar system of second-order ordinary differential equations by using a shooting technique. We consider asymptotically linear nonlinearities satisfying suitable sign conditions. Multiplicity is ensured by assumptions involving the Morse indices of the linearizations at zero and at infinity.

On a Retarded Nonlocal Ordinary Differential System with Discrete Diffusion Modeling Life Tables

2021

In this paper, we consider a system of ordinary differential equations with non-local discrete diffusion and finite delay and with either a finite or an infinite number of equations. We prove several properties of solutions such as comparison, stability and symmetry. We create a numerical simulation showing that this model can be appropriate to model dynamical life tables in actuarial or demographic sciences. In this way, some indicators of goodness and smoothness are improved when comparing with classical techniques.

NUMERICAL ALGORITHMS

2013

For many systems of differential equations modeling problems in science and engineering, there are natural splittings of the right hand side into two parts, one non-stiff or mildly stiff, and the other one stiff. For such systems implicit-explicit (IMEX) integration combines an explicit scheme for the non-stiff part with an implicit scheme for the stiff part. In a recent series of papers two of the authors (Sandu and Zhang) have developed IMEX GLMs, a family of implicit-explicit schemes based on general linear methods. It has been shown that, due to their high stage order, IMEX GLMs require no additional coupling order conditions, and are not marred by order reduction. This work develops a …

A Nullclines Approach to the Study of 2D Artificial Network

2019


 
 The system of two the first order ordinary differential equations arising in the gene regulatory networks theory is studied. The structure of attractors for this system is described for three important behavioral cases: activation, inhibition, mixed activation-inhibition. The geometrical approach combined with the vector field analysis allows treating the problem in full generality. A number of propositions are stated and the proof is geometrical, avoiding complex analytic. Although not all the possible cases are considered, the instructions are given what to do in any particular situation.

Small and hollow magnetic monopoles

2018

We deal with the presence of magnetic monopoles in a non Abelian model that generalizes the standard 't~Hooft-Polyakov model in three spatial dimensions. We investigate the energy density of the static and spherically symmetric solutions to find first order differential equations that solve the equations of motion. The system is further studied and two distinct classes of solutions are obtained, one that can also be described by analytical solutions which is called small monopole, since it is significantly smaller than the standard 't~Hooft-Polyakov monopole. The other type of structure is the hollow monopole, since the energy density is endowed with a hole at its core. The hollow monopole …

How to Get a Model in Pedestrian Dynamics to Produce Stop and Go Waves

2016

Stop and go waves in granular flow can often be described mathematically by a dynamical system with a Hopf bifurcation. We show that a certain class of microscopic, ordinary differential equation-based models in crowd dynamics fulfil certain conditions of Hopf bifurcations. The class is based on the Gradient Navigation Model. An interesting phenomenon arises: the number of pedestrians in the system must be greater than nine for a bifurcation—and hence for stop and go waves to be possible at all, independent of the density. Below this number, no parameter setting will cause the system to exhibit stable stop and go behaviour. The result is also interesting for car traffic, where similar model…

Modelling of a hydro-pneumatic system for heave compensation

2018

This paper presents a mathematical model of the dynamic behaviour of a passive heave compensation system. The main purpose is to develop a model that enables cost-efficient prototyping and testing of the control system in an active heave compensator. The physics are described by first principles, and result in 21 ordinary differential equations. Temperature calculations are included as an option during simulation in order to investigate its effect on the results. Similarly is a non-ideal gas law (Redlich-Kwong equation) implemented and compared to the ideal gas law. Verification against field data shows that the model is in good accordance with real-life drilling operations. It is further s…

2014

This paper is devoted to investigating stability in mean of partial variables for coupled stochastic reaction-diffusion systems on networks (CSRDSNs). By transforming the integral of the trajectory with respect to spatial variables as the solution of the stochastic ordinary differential equations (SODE) and using Itô formula, we establish some novel stability principles for uniform stability in mean, asymptotic stability in mean, uniformly asymptotic stability in mean, and exponential stability in mean of partial variables for CSRDSNs. These stability principles have a close relation with the topology property of the network. We also provide a systematic method for constructing global Lyapu…

DEGENERATE MATRIX METHOD FOR SOLVING NONLINEAR SYSTEMS OF DIFFERENTIAL EQUATIONS

1998

Degenerate matrix method for numerical solving nonlinear systems of ordinary differential equations is considered. The method is based on an application of special degenerate matrix and usual iteration procedure. The method, which is connected with an implicit Runge‐Kutta method, can be simply realized on computers. An estimation for the error of the method is given. First Published Online: 14 Oct 2010

A Friendly-Biological Reactor SIMulator (BioReSIM) for studying biological processes in wastewater treatment processes

2014

Biological processes for wastewater treatments are inherently dynamic systems because of the large variations in the influent wastewater flow rate, concentration composition and the adaptive behavior of the involved microorganisms. Moreover, the sludge retention time (SRT) is a critical factor to understand the bioreactor performances when changes in the influent or in the operation conditions take place. Since SRT are usually in the range of 10-30 days, the performance of biological reactors needs a long time to be monitored in a regular laboratory demonstration, limiting the knowledge that can be obtained in the experimental lab practice. In order to overcome this lack, mathematical model…