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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.01322 |
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Table of 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.