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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2504.01322 |
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| _version_ | 1866908296081833984 |
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| author | Calleja, Renato Padilla-Longoria, Pablo Rodríguez-Mendieta, Edgar |
| author_facet | Calleja, Renato Padilla-Longoria, Pablo Rodríguez-Mendieta, Edgar |
| contents | This paper focuses on the Hopf bifurcation in an activator-inhibitor system without diffusion which can be modeled as a delay differential equation. The main result of this paper is the existence of the Poincaré-Lindstedt series to all orders for the bifurcating periodic solutions. The model has a non-linearity which is non-polynomial, and yet this allows us to exploit the use of Fourier-Taylor series to develop order-by-order calculations that lead to linear recurrence equations for the coefficients of the Poincaré-Lindstedt series. As applications, we implement the computation of the coefficients of these series for any finite order, and use a pseudo-arclength continuation to compute branches of periodic solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01322 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Biological network dynamics: Poincaré-Lindstedt series and the effect of delays Calleja, Renato Padilla-Longoria, Pablo Rodríguez-Mendieta, Edgar Dynamical Systems This paper focuses on the Hopf bifurcation in an activator-inhibitor system without diffusion which can be modeled as a delay differential equation. The main result of this paper is the existence of the Poincaré-Lindstedt series to all orders for the bifurcating periodic solutions. The model has a non-linearity which is non-polynomial, and yet this allows us to exploit the use of Fourier-Taylor series to develop order-by-order calculations that lead to linear recurrence equations for the coefficients of the Poincaré-Lindstedt series. As applications, we implement the computation of the coefficients of these series for any finite order, and use a pseudo-arclength continuation to compute branches of periodic solutions. |
| title | Biological network dynamics: Poincaré-Lindstedt series and the effect of delays |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2504.01322 |