scholarly journals Dynamics and Stability of Hopf Bifurcation for One Non-linear System

TEM Journal ◽  
2021 ◽  
pp. 820-824
Author(s):  
Vahidin Hadžiabdić ◽  
Midhat Mehuljić ◽  
Jasmin Bektešević ◽  
Adnan Mašić
Keyword(s):  
Hopf Bifurcation ◽  
Linear System ◽  
Differential Equations ◽  
Detailed Analysis ◽  
Limit Cycle ◽  
Local Stability ◽  
System Of Differential Equations ◽  
The One ◽  
Non Linear System ◽  
The Given

In this paper we will look at the one system of ODE and analyze it. We aim to determine the points of equilibrium; examine their character and establish the existence of a bifurcation for the corresponding parameter value. A detailed analysis of local stability was performed for all values of the given parameter. For a certain value of the parameter, the existence of supercritical Hopf bifurcation of the observed system of differential equations has been proved. Also, the existence of a limit cycle that is always stable has been proved.

scholarly journals Bilateral approximations and periodic solutions of systems of differential equations with impulses

1985 ◽  
Vol 31 (2) ◽  
pp. 293-307
Author(s):  
S.G. Hristova ◽  
D.D. Bainov
Keyword(s):  
Periodic Solution ◽  
Linear System ◽  
Differential Equations ◽  
Periodic Solutions ◽  
System Of Differential Equations ◽  
Systems Of Differential Equations ◽  
Non Linear ◽  
Impulsive Perturbations ◽  
Non Linear System

The paper justifies a method of bilateral approximations for finding the periodic solution of a non-linear system of differential equations with impulsive perturbations at fixed moments of time.

scholarly journals Analytical solution of system of differential equations by variational iteration method

BIBECHANA ◽  
2015 ◽  
Vol 13 ◽  
pp. 77-86
Author(s):  
Jamshad Ahmed ◽  
Faizan Hussain
Keyword(s):  
Linear System ◽  
Analytical Solution ◽  
Differential Equations ◽  
Iteration Method ◽  
Graphical Representation ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Numerical Results ◽  
System Of Differential Equations ◽  
Non Linear System

In this paper, Varitational Iteration Method using He’s Polynomials is used to construct the exact as well as approximate solutions of differential equations. From the obtained numerical results, it has been observed that this proposed technique is very efficient and reliable for the solution of the linear and non-linear system of differential equations. Numerical results and graphical representation reflect the accuracy and effectiveness of the proposed modification.BIBECHANA 13 (2016) 77-86

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