Asymptotics of solution of singularly perturbed problem with periodic turning points in complex plane
When studying any dynamical system the critical values of its parameters are of special interest. Properties of stationary or quasistationary regimes change fundamentally, i.e. the bifurcation is observed. One type of bifurcation, when asymptotic stability condition is disturbed and limiting process...
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| Format: | Article |
| Language: | Russian |
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Tomsk Polytechnic University
2019-05-01
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| Series: | Известия Томского политехнического университета: Инжиниринг георесурсов |
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| Online Access: | http://izvestiya.tpu.ru/archive/article/view/1304 |
| _version_ | 1797813130920722432 |
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| author | Dilmurat Tursunov |
| author_facet | Dilmurat Tursunov |
| author_sort | Dilmurat Tursunov |
| collection | DOAJ |
| description | When studying any dynamical system the critical values of its parameters are of special interest. Properties of stationary or quasistationary regimes change fundamentally, i.e. the bifurcation is observed. One type of bifurcation, when asymptotic stability condition is disturbed and limiting process is carried out, appears in the systems occurring in laser physics, chemical kinetics, plastic deformation, biophysics, in the modified Ziegler system, and when modeling the crown forest fire and safe combustion with maximum temperature. Using the stationary phase method the author has constructed the asymptotic for solving singularly perturbed ordinary differential equations with periodic turning points in the complex plane when the condition of asymptotic stability is disturbed. The obtained asymptotic estimation for solving the problem is not the improved one. |
| first_indexed | 2024-03-13T07:48:51Z |
| format | Article |
| id | doaj.art-446dfb8c5d714be7888dfa5b210aa4e8 |
| institution | Directory Open Access Journal |
| issn | 2500-1019 2413-1830 |
| language | Russian |
| last_indexed | 2024-03-13T07:48:51Z |
| publishDate | 2019-05-01 |
| publisher | Tomsk Polytechnic University |
| record_format | Article |
| series | Известия Томского политехнического университета: Инжиниринг георесурсов |
| spelling | doaj.art-446dfb8c5d714be7888dfa5b210aa4e82023-06-02T21:08:51ZrusTomsk Polytechnic UniversityИзвестия Томского политехнического университета: Инжиниринг георесурсов2500-10192413-18302019-05-013242Asymptotics of solution of singularly perturbed problem with periodic turning points in complex planeDilmurat TursunovWhen studying any dynamical system the critical values of its parameters are of special interest. Properties of stationary or quasistationary regimes change fundamentally, i.e. the bifurcation is observed. One type of bifurcation, when asymptotic stability condition is disturbed and limiting process is carried out, appears in the systems occurring in laser physics, chemical kinetics, plastic deformation, biophysics, in the modified Ziegler system, and when modeling the crown forest fire and safe combustion with maximum temperature. Using the stationary phase method the author has constructed the asymptotic for solving singularly perturbed ordinary differential equations with periodic turning points in the complex plane when the condition of asymptotic stability is disturbed. The obtained asymptotic estimation for solving the problem is not the improved one.http://izvestiya.tpu.ru/archive/article/view/1304solution asymptoticturning pointsingularly perturbationasymptotic stabilityStokes lineordinary differential equation |
| spellingShingle | Dilmurat Tursunov Asymptotics of solution of singularly perturbed problem with periodic turning points in complex plane Известия Томского политехнического университета: Инжиниринг георесурсов solution asymptotic turning point singularly perturbation asymptotic stability Stokes line ordinary differential equation |
| title | Asymptotics of solution of singularly perturbed problem with periodic turning points in complex plane |
| title_full | Asymptotics of solution of singularly perturbed problem with periodic turning points in complex plane |
| title_fullStr | Asymptotics of solution of singularly perturbed problem with periodic turning points in complex plane |
| title_full_unstemmed | Asymptotics of solution of singularly perturbed problem with periodic turning points in complex plane |
| title_short | Asymptotics of solution of singularly perturbed problem with periodic turning points in complex plane |
| title_sort | asymptotics of solution of singularly perturbed problem with periodic turning points in complex plane |
| topic | solution asymptotic turning point singularly perturbation asymptotic stability Stokes line ordinary differential equation |
| url | http://izvestiya.tpu.ru/archive/article/view/1304 |
| work_keys_str_mv | AT dilmurattursunov asymptoticsofsolutionofsingularlyperturbedproblemwithperiodicturningpointsincomplexplane |