Keywords : Stability


Stability Analysis of a fluid in Horizontal and Inclined Channels

Alaa Ahmed Hammodat; Taghred Hamdoon Shuker

AL-Rafidain Journal of Computer Sciences and Mathematics, 2014, Volume 11, Issue 2, Pages 89-97
DOI: 10.33899/csmj.2014.163758

This paper is devoted to analysis the stability of horizontal and inclination in a glazing cavities of equations that we expose to disturbance. This analysis is done by finding the eigenvalues of the system which enable us to investigate the grow of disturbance after setting glazing cavities equations in linearization form. We obtain from our results that the equations are stable when the real part of wave velocity is negative , and unstable when it is positive .
 

Linear Stability of Thin Liquid Films flows down on an Inclined Plane using Integral Approximation

Hajar Farhan Ismael

AL-Rafidain Journal of Computer Sciences and Mathematics, 2014, Volume 11, Issue 2, Pages 13-24
DOI: 10.33899/csmj.2014.163747

In this paper, the stability and dynamics of a thin liquid films flowing down on an inclined plane are investigated by using integral approximation. The strong non-linear evolution equations are derived by the integral approximation with a specified velocity profile. The evolution equations are used to study the linear stability for liquid films. As a result, output of this research, we showed that the effect of inclination of films is an unstable factor.
 

Studying the Stability of a Non-linear Autoregressive Model (Polynomial with Hyperbolic Cosine Function)

Abdulghafoor Gasim Salim; Anas Salim Youns Abdullah

AL-Rafidain Journal of Computer Sciences and Mathematics, 2014, Volume 11, Issue 1, Pages 81-91
DOI: 10.33899/csmj.2014.163733

            In this paper we study the statistical properties of one of a non-linear autoregressive model with hyperbolic triangle function(polynomial with hyperbolic cosinefunction)by using the local linearization  approximation method to find the stability of the model  (singular point and its stability conditions and the stability of  limit cycle).Where we started by the model of lower order (first and second and third order) and generalized the idea, and we tried to apply these theory results by using some of examples to explain one of important truth that says (if the model has unstable singular point, then it, maybe, has a stable limit cycle).    
 

Stability Study of the Orbits of Satellites around the Earth

Thair Y. Thanoon; Marwa Khaled fathy

AL-Rafidain Journal of Computer Sciences and Mathematics, 2013, Volume 10, Issue 3, Pages 143-156
DOI: 10.33899/csmj.2013.163541

In this research, we have studied of the motion of satellite orbits and rotation around the earth and that are subject to the laws of kepler and relationships associated with this motion, such as changing angular and circular time league and the gravitational constant, etc. In the case of circular orbits of Earth satellites. As compounds are calculated position vector  and vector velocity compounds  any time  satellite orbiting the earth geocentric spherical coordinates  . It was a study tracks and various forms taken by this motion in both cases using the language (Matlab). Were also study the stability of the motion of satellites using chetayev method assisted integrals were finding the conditions stabiliting motion.  
 

Stability Study of Double and Spherical Pendulum

Thair Y. Thanoon; Noor Husain Abdullah

AL-Rafidain Journal of Computer Sciences and Mathematics, 2012, Volume 9, Issue 2, Pages 13-26
DOI: 10.33899/csmj.2012.163716

This paper devoted to study the stability of periodic motion for physical application which is leads to differential equations of second order )Double and Spherical Pendulum( respectively by using the stability of equilibrium position given by Laypunov and Ghetagev's methods which depends on principle of energy conservation, also we will describe periodic motion and explain the phase plane )The trajectory of solutions( and state of the stability for double and spherical pendulum by using )Maple(.
 

Generating a New Hyperchaotic Pan System Via State Feedback Control

Saad Fawzi AL-Azzawi

AL-Rafidain Journal of Computer Sciences and Mathematics, 2012, Volume 9, Issue 2, Pages 229-241
DOI: 10.33899/csmj.2012.163714

This paper proposes a new four-dimensional continuous autonomous hyperchaotic system based on the 3D Pan system by introducing a nonlinear state feedback controller. Dynamical behaviors of the new system are analyzed, both theoretically and numerically, including equilibrium points, Lyapunov exponents spectrum  stability and bifurcation , finally, an illustrative example is given. 
 

New Study of Stability for New Lorenz-like System

Ahmmed Jumaa; Alaa Hammodat

AL-Rafidain Journal of Computer Sciences and Mathematics, 2012, Volume 9, Issue 1, Pages 155-161
DOI: 10.33899/csmj.2012.163679

In this paper, we  studied differential system like of three dimensional Lorenz system. Nonlinear characteristic and basic dynamic properties of three dimensional autonomous system are studied by means of nonlinear dynamics theory, including the stability and we found that the value  is effected by the form of the roots.
 

Using Δ - Discriminate Method to Determine the Stability and Bifurcation of Chen Chaotic System

Saad Fawzi AL-Azzawi; Karam A. Abed

AL-Rafidain Journal of Computer Sciences and Mathematics, 2011, Volume 8, Issue 2, Pages 111-122
DOI: 10.33899/csmj.2011.163646

The aim of this paper to found that the stability and bifurcation of Chen System by using a new method which called - discriminate method as will as we found the stability at the second critical point by another method, and we showed that the new method depended on the roots to determent  the stability and bifurcation of this system while the previous methods depended on the parameters , also we showed the method which used to find the stability at the second critical point depended on the critical value  and parameter . Finally, we get the same previous results but easily method.
 
 

Studying the Stability of One of Non-Linear Autoregressive Relational Models

Abdulghafoor Gasim Salim; Hamed Mohammed Kalaf

AL-Rafidain Journal of Computer Sciences and Mathematics, 2011, Volume 8, Issue 1, Pages 81-95
DOI: 10.33899/csmj.2011.163625

Time series are usually built on basic assumptions involving stability, Linearity and normality, these three features are so important in both  estimating and building the time series models.
The study of time series involves these assumption and how to manipulate the unstable time series on the basis of which the suitable mathematical models fit for  these series.
In this paper, we suggestion the stationarity of one of the non linear -Autoregressive time series models called rational model has been studied which is a fraction whose numerator is the cosine function and its denominator is an exponential Autoregressive models. The singular point and the limit cycle of the models and its stationarity study have been found by adopting the linear approximation technique.
 

Studying the Stability of one of Non-Linear Autoregressive Models with Application

Abdulghafoor Gasim Salim; Raadi Awad Alhamdan

AL-Rafidain Journal of Computer Sciences and Mathematics, 2011, Volume 8, Issue 1, Pages 149-159
DOI: 10.33899/csmj.2011.163630

In This paper we suggest one of the models for non-linear Autoregressive by using local linear approximation method, then we studied the conditions of stationarity of the model specifically the conditions of stationarity the non-zero singular point of the model. And the conditions for stationarity to limit cycle stationarity.
            Conditions are applied in the aforementioned theories on data represent the monthly average wind speed in model of Baghdad city. The samples are classified by using  one of non-linear Autoregressive model the findings are the value of non-zero fixed point and the conditions of suggested stationarity model .
 

Stability Conditions for Flow Rate of Liquid Between Two Vessels

Thair Y. Thanoon; Nagham N. Hana

AL-Rafidain Journal of Computer Sciences and Mathematics, 2009, Volume 6, Issue 3, Pages 141-150
DOI: 10.33899/csmj.2009.163828

In this paper we obtain the conditions under which the trivial solution is stable for the following  perturbed differential system :



 


 
 



 
 
 
 
 
 
 
where _ constants. 
which described the flow rate of liquid or gases between two vessels, we transform this differential system to auxiliary system which gives the stability conditions of solution by Perron principle, these conditions represent stability conditions for required differential system.
     

Stability Analysis of Unified Chaotic System

Saad Fawzi AL-Azzawi

AL-Rafidain Journal of Computer Sciences and Mathematics, 2009, Volume 6, Issue 3, Pages 161-171
DOI: 10.33899/csmj.2009.163830

The aim of this paper is to find the stability of unified chaotic system through studying different systems. The unified chaotic system is divided into three systems by depending on the values of   , when    , the unified chaotic system becomes Lorenz system; when; it becomes L system, when    ; the unified chaotic system becomes Chen system. Investigations the stability analysis of these systems leads to the stability of the unified chaotic system.
 

Studying the Stability of Some Non-Linear Time Series Models with Application

Abdulghafoor Gasim Salim; Nihad Sharif Khalaf

AL-Rafidain Journal of Computer Sciences and Mathematics, 2008, Volume 5, Issue 2, Pages 99-116
DOI: 10.33899/csmj.2008.163988

In this paper we study the stability of time series models in general, and for some non-linear time series models as a special case. Lagrange method to find the stability of non-linear models has been given.
            The Leishmaniasis time series was studied and modeled by different non-linear models such as, seasonal ARIMA model by using the logarithmic transformation, exponential model of order two and the polynomial model. The stability of all such models by the above method has been obtained. From the comparison we find that the SARIMA is the best among all such models which we used for forecasting one year ago.
 

Stability Conditions of Zero Solution for Third Order Differential Equation in Critical Case

Thair Y . Thanoon; Saad Fawzi AL-Azzawi

AL-Rafidain Journal of Computer Sciences and Mathematics, 2008, Volume 5, Issue 1, Pages 127-138
DOI: 10.33899/csmj.2008.163955

    In this paper, we study the conditions under which the zero solution is stable in the semi- liner case for certain third order differential equation of the form :
          
Where
   ,   s = 1,2,3  ,       ,         
               ,        

    The characteristic equation of the above differential equation has complex roots of the form :
 and the other root has the following                 ,       .        property
 

New Parallel Algorithms for BVPs in ODEs

Bashir M. Khalaf

AL-Rafidain Journal of Computer Sciences and Mathematics, 2004, Volume 1, Issue 2, Pages 47-66
DOI: 10.33899/csmj.2004.164111

The main objective of this paper is the development of a new parallel integration algorithm for Solving Boundary Value Problem (BVPs) in Ordinary Differential Equation, (ODEs). This algorithm is suitable for running on MIMD computing systems. We will analysis the stability and error control of the developed algorithm .We shall also consider the treatment of stiff boundary value problems by developed technique.