STABILITY OF THE REST POINTS FRACTIONAL OSCILLATOR FITZHUGH-NAGUMO
In this paper, using the qualitative analysis, we studied the stability of the point of rest of the fractional oscillator FitzHugh-Nagumo in commensurate and incommensurable cases. For the corresponding point of rest, using the numerical method of the theory of finite difference schemes, phase traje...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
KamGU by Vitus Bering
2019-05-01
|
| Series: | Vestnik KRAUNC: Fiziko-Matematičeskie Nauki |
| Subjects: | |
| Online Access: | http://krasec.ru/lipko2019261/ |
| _version_ | 1817986355586662400 |
|---|---|
| author | O. D. Lipko |
| author_facet | O. D. Lipko |
| author_sort | O. D. Lipko |
| collection | DOAJ |
| description | In this paper, using the qualitative analysis, we studied the stability of the point of rest of the fractional oscillator FitzHugh-Nagumo in commensurate and incommensurable cases. For the corresponding point of rest, using the numerical method of the theory of finite difference schemes, phase trajectories were constructed. It is shown that quiescent points can be both asymptotically stable, which correspond to stable focus, and are asymptotically unstable (unstable focus), and for them the phase trajectories usually go to the limit cycle. |
| first_indexed | 2024-04-14T00:09:08Z |
| format | Article |
| id | doaj.art-ec1732aa6e9d4394999f7011afbccea2 |
| institution | Directory Open Access Journal |
| issn | 2079-6641 2079-665X |
| language | English |
| last_indexed | 2024-04-14T00:09:08Z |
| publishDate | 2019-05-01 |
| publisher | KamGU by Vitus Bering |
| record_format | Article |
| series | Vestnik KRAUNC: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-ec1732aa6e9d4394999f7011afbccea22022-12-22T02:23:26ZengKamGU by Vitus BeringVestnik KRAUNC: Fiziko-Matematičeskie Nauki2079-66412079-665X2019-05-01261637010.26117/2079-6641-2019-26-1-63-70STABILITY OF THE REST POINTS FRACTIONAL OSCILLATOR FITZHUGH-NAGUMOO. D. Lipko0Vitus Bering Kamchatka State University, 683031, Petropavlovsk-Kamchatsky, Pogranichnaya st., 4, RussiaIn this paper, using the qualitative analysis, we studied the stability of the point of rest of the fractional oscillator FitzHugh-Nagumo in commensurate and incommensurable cases. For the corresponding point of rest, using the numerical method of the theory of finite difference schemes, phase trajectories were constructed. It is shown that quiescent points can be both asymptotically stable, which correspond to stable focus, and are asymptotically unstable (unstable focus), and for them the phase trajectories usually go to the limit cycle.http://krasec.ru/lipko2019261/rest pointsstabilitylimit cycleFitzHugh-Nagumo fractional oscillator |
| spellingShingle | O. D. Lipko STABILITY OF THE REST POINTS FRACTIONAL OSCILLATOR FITZHUGH-NAGUMO Vestnik KRAUNC: Fiziko-Matematičeskie Nauki rest points stability limit cycle FitzHugh-Nagumo fractional oscillator |
| title | STABILITY OF THE REST POINTS FRACTIONAL OSCILLATOR FITZHUGH-NAGUMO |
| title_full | STABILITY OF THE REST POINTS FRACTIONAL OSCILLATOR FITZHUGH-NAGUMO |
| title_fullStr | STABILITY OF THE REST POINTS FRACTIONAL OSCILLATOR FITZHUGH-NAGUMO |
| title_full_unstemmed | STABILITY OF THE REST POINTS FRACTIONAL OSCILLATOR FITZHUGH-NAGUMO |
| title_short | STABILITY OF THE REST POINTS FRACTIONAL OSCILLATOR FITZHUGH-NAGUMO |
| title_sort | stability of the rest points fractional oscillator fitzhugh nagumo |
| topic | rest points stability limit cycle FitzHugh-Nagumo fractional oscillator |
| url | http://krasec.ru/lipko2019261/ |
| work_keys_str_mv | AT odlipko stabilityoftherestpointsfractionaloscillatorfitzhughnagumo |