Nonuniform relaxation oscillations near SNIPER bifurcations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917484639027200 |
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| author | Knobloch, Edgar Yochelis, Arik |
| author_facet | Knobloch, Edgar Yochelis, Arik |
| contents | Properties of spatially dependent relaxation oscillations near a SNIPER bifurcation are described. A SNIPER bifurcation creates a large-amplitude long-period periodic orbit via the annihilation of a pair of fixed points in a saddle-node bifurcation. We show that in spatially extended media, this orbit may undergo a long-wavelength instability, leading to spatially modulated oscillations that persist on both sides of the SNIPER. The oscillations take different forms depending on the system: a chimera state in a theta-reaction-diffusion model, and chaotic spiking in an activator-inhibitor-substrate model. The results are expected to have applications in a number of physical systems exhibiting SNIPER bifurcations, ranging from models of the nervous system through chemical reactions to nonlinear optics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11878 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nonuniform relaxation oscillations near SNIPER bifurcations Knobloch, Edgar Yochelis, Arik Pattern Formation and Solitons Properties of spatially dependent relaxation oscillations near a SNIPER bifurcation are described. A SNIPER bifurcation creates a large-amplitude long-period periodic orbit via the annihilation of a pair of fixed points in a saddle-node bifurcation. We show that in spatially extended media, this orbit may undergo a long-wavelength instability, leading to spatially modulated oscillations that persist on both sides of the SNIPER. The oscillations take different forms depending on the system: a chimera state in a theta-reaction-diffusion model, and chaotic spiking in an activator-inhibitor-substrate model. The results are expected to have applications in a number of physical systems exhibiting SNIPER bifurcations, ranging from models of the nervous system through chemical reactions to nonlinear optics. |
| title | Nonuniform relaxation oscillations near SNIPER bifurcations |
| topic | Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2605.11878 |