THE INFLUENCE OF ZEROS AND POLES ON THE ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF SINGULARLY PERTURBED PROBLEMS IN THE CASE OF STABILITY CHANGE

2021 ◽  
Vol 3 (1) ◽  
pp. 49-54
Author(s):  
Saly Karimov ◽  
Akbermet Abdijalilovna Abdilazizova
Keyword(s):  
Asymptotic Behavior ◽  
Singularly Perturbed ◽  
Asymptotic Behavior Of Solutions ◽  
Singularly Perturbed Problems ◽  
Stability Change ◽  
Zeros And Poles

DELAYED BIFURCATION IN FIRST-ORDER SINGULARLY PERTURBED PROBLEMS WITH A NONGENERIC TURNING POINT

2012 ◽  
Vol 22 (12) ◽  
pp. 1250302 ◽  
Author(s):  
JIANHE SHEN ◽  
MAOAN HAN
Keyword(s):  
Asymptotic Behavior ◽  
Hopf Bifurcation ◽  
Turning Point ◽  
Upper And Lower Solutions ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problems ◽  
First Order ◽  
Delayed Bifurcation ◽  
Dynamical Properties ◽  
Theoretical Results

In this paper, based on the method of upper and lower solutions, delayed bifurcation in first-order singularly perturbed problems with a nongeneric turning point is studied. The asymptotic behavior of the solutions is understood by constructing the upper and lower solutions with the desired dynamical properties. As an application of the obtained results, delayed phenomenon of degenerate Hopf bifurcation in a planar polynomial differential system with a slowly varying parameter is discussed in detail and the maximal delay is calculated. Numerical simulations are carried out to verify the theoretical results.

scholarly journals Singularly Perturbed Linear Neumann Problem with the Characteristic Roots on the Imaginary Axis

2010 ◽  
Vol 18 (28) ◽  
pp. 163-168
Author(s):  
Ľudmila Vaculíková ◽  
Vladimír Liška
Keyword(s):  
Integral Equation ◽  
Asymptotic Behavior ◽  
Neumann Problem ◽  
Imaginary Axis ◽  
Singularly Perturbed ◽  
Asymptotic Behavior Of Solutions ◽  
Characteristic Roots

Singularly Perturbed Linear Neumann Problem with the Characteristic Roots on the Imaginary Axis We investigate the problem of existence and asymptotic behavior of solutions for the singularly perturbed linear Neumann problem <img src="/fulltext-image.asp?format=htmlnonpaginated&src=C6551P41673P4147_html\Journal10186_Volume18_Issue28_20_paper.gif" alt=""/> Our approach relies on the analysis of integral equation equivalent to the problem above.

Regularization of Integral Operators in Singularly Perturbed Problems Using Normal Forms

Vestnik MEI ◽  
2019 ◽  
Vol 6 ◽  
pp. 131-137
Author(s):  
Abdukhafiz A. Bobodzhanova ◽  
◽  
Valeriy F. Safonov ◽  
Keyword(s):  
Normal Forms ◽  
Integral Operators ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problems
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