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arXiv · 2609.25626

Behaviors near infinity for mutually enhancing continuous-state population dynamics

Jie Xiong·Xu Yang·Xiaowen Zhou
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Abstract

In this paper we consider a two-dimensional generalized continuous-state branching process with mutually enhancing two-way interactions characterized by two stochastic differential equations driven by Brownian motions and spectrally positive $α$-stable random measures. Such continuous-state population dynamics can also be identified as a stochastic Lotka-Volterra type population model. Infinite behavior such as explosion/nonexplosion for this population and staying infinite/coming down from infinity are derived under various conditions on the coefficients involved in the model and the conclusions are rather sharp

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Jie Xiong, Xu Yang, Xiaowen Zhou. 2026-09-22. Behaviors near infinity for mutually enhancing continuous-state population dynamics. https://arxiv.org/abs/2609.25626

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