Fluctuations of blowup time in a simple model of a super-Malthusian catastrophe
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908288061276160 |
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| author | Meerson, Baruch |
| author_facet | Meerson, Baruch |
| contents | Motivated by the paradigm of a super-Maltusian population catastrophe, we study a simple stochastic population model which exhibits a finite-time blowup of the population size and is strongly affected by intrinsic noise. We focus on the fluctuations of the blowup time $T$ in the asexual binary reproduction model $2A \to 3A$, where two identical individuals give birth to a third one. We determine exactly the average blowup time as well as the probability distribution $\mathcal{P}(T)$ of the blowup time and its moments. In particular, we show that the long-time tail $\mathcal{P}(T\to \infty)$ is purely exponential. The short-time tail $\mathcal{P}(T\to 0)$ exhibits an essential singularity at $T=0$, and it is dominated by a single (the most likely) population trajectory which we determine analytically. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_07083 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fluctuations of blowup time in a simple model of a super-Malthusian catastrophe Meerson, Baruch Statistical Mechanics Probability Populations and Evolution Motivated by the paradigm of a super-Maltusian population catastrophe, we study a simple stochastic population model which exhibits a finite-time blowup of the population size and is strongly affected by intrinsic noise. We focus on the fluctuations of the blowup time $T$ in the asexual binary reproduction model $2A \to 3A$, where two identical individuals give birth to a third one. We determine exactly the average blowup time as well as the probability distribution $\mathcal{P}(T)$ of the blowup time and its moments. In particular, we show that the long-time tail $\mathcal{P}(T\to \infty)$ is purely exponential. The short-time tail $\mathcal{P}(T\to 0)$ exhibits an essential singularity at $T=0$, and it is dominated by a single (the most likely) population trajectory which we determine analytically. |
| title | Fluctuations of blowup time in a simple model of a super-Malthusian catastrophe |
| topic | Statistical Mechanics Probability Populations and Evolution |
| url | https://arxiv.org/abs/2503.07083 |