Long time behavior of a degenerate stochastic system modeling the response of a population face to environmental impacts
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914783088869376 |
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| author | Collet, Pierre Ecotière, Claire Méléard, Sylvie |
| author_facet | Collet, Pierre Ecotière, Claire Méléard, Sylvie |
| contents | We study the asymptotics of a two-dimensional stochastic differential system with a degenerate diffusion matrix. This system describes the dynamics of a population where individuals contribute to the degradation of their environment through two different behaviors. We exploit the almost one-dimensional form of the dynamical system to compute explicitly the Freidlin-Wentzell action functional. That allows to give conditions under which the small noise regime of the invariant measureis concentrated around the equilibrium of the dynamical system having the smallest diffusion coefficient. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01898 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Long time behavior of a degenerate stochastic system modeling the response of a population face to environmental impacts Collet, Pierre Ecotière, Claire Méléard, Sylvie Dynamical Systems Probability We study the asymptotics of a two-dimensional stochastic differential system with a degenerate diffusion matrix. This system describes the dynamics of a population where individuals contribute to the degradation of their environment through two different behaviors. We exploit the almost one-dimensional form of the dynamical system to compute explicitly the Freidlin-Wentzell action functional. That allows to give conditions under which the small noise regime of the invariant measureis concentrated around the equilibrium of the dynamical system having the smallest diffusion coefficient. |
| title | Long time behavior of a degenerate stochastic system modeling the response of a population face to environmental impacts |
| topic | Dynamical Systems Probability |
| url | https://arxiv.org/abs/2405.01898 |