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arXiv · 2509.22513

Age-structured stochastic populations under dynamic harvesters' behavior: well-posedness, asymptotic stability and numerically-amenable approximations

M. Isidora Ávila-Thieme·Kerlyns Martínez·Héctor Olivero·Mauricio Tejo·Leonardo Videla
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Abstract

In this paper we study a model of age-structured ecological populations in continuous interaction with a community of harvesters. We propose an individual-based model for this feedback interactions and prove its convergence to a system of coupled stochastic differential equations. This limit process is complemented with socio-ecological and environmental factors. For the resulting system we establish well-posedness, positivity, and the non-attainability of extinction boundaries, together with its long-term behavior and numerical approximation, relying on ad-hoc arguments to handle the super-linear growth and non-Lipschitz coefficients. Finally, we illustrate some of our findings with numerical experiments.

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M. Isidora Ávila-Thieme, Kerlyns Martínez, Héctor Olivero, Mauricio Tejo, Leonardo Videla. 2025-09-26. Age-structured stochastic populations under dynamic harvesters' behavior: well-posedness, asymptotic stability and numerically-amenable approximations. https://arxiv.org/abs/2509.22513

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