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PreprintCC0arXiv

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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Cite

BibTeXRIS
BibTeX
@misc{xiong2026behaviors,
  title = {{Behaviors near infinity for mutually enhancing continuous-state population dynamics}},
  author = {Jie Xiong and Xu Yang and Xiaowen Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.25626},
  eprint = {2609.25626},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.25626},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Behaviors near infinity for mutually enhancing continuous-state population dynamics
AU  - Jie Xiong
AU  - Xu Yang
AU  - Xiaowen Zhou
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.25626
UR  - https://arxiv.org/abs/2609.25626
AB  - 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
ER  -