发表机构
Shenzhen MSU-BIT University; Southern University of Science and Technology; Peking University; North Minzu University（深圳莫斯科国立鲍曼技术大学; 南方科技大学; 北京大学; 北方民族大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对由布朗分支噪声和谱正稳定跳跃驱动的两类连续状态非线性捕食-被捕食分支模型，构建互补结构推导灭绝准则，发现有限时间灭绝与非灭绝共存 regime，明确非灭绝时种群联合收敛至零的性质。
AI 中文摘要
我们研究由布朗分支噪声和谱正稳定跳跃驱动的两类连续状态非线性分支模型中的灭绝与熄灭问题。种群受非线性自调节和混合符号的捕食-被捕食相互作用约束：第二类种群促进第一类，而第一类抑制第二类。我们构建了两种互补结构：精确的幂-对数抵消泛函可消除相互作用漂移，得到随机李雅普诺夫估计、非爆炸性质和边界准则；在乘性 regime 中，积分因子恒等式和几何 Lévy 因式分解通过加权暴露时钟表达灭绝，并将长期分析简化为有效衰减率。这些方法得到了几乎必然的灭绝准则，确定了有限时间灭绝与非灭绝共存的 regime；在非灭绝情况下，两类种群在所有有限时间均保持为正，且联合收敛至零，呈现联合熄灭而非正持续存在的性质。
英文摘要
We study extinction and extinguishment in a two-type continuous-state nonlinear branching model driven by Brownian branching noise and spectrally positive stable jumps. The populations are subject to nonlinear self-regulation and a mixed-sign predator--prey interaction: the second promotes the first, whereas the first suppresses the second. Two complementary structures are developed. An exact power--logarithmic cancellation functional removes the interaction drifts and yields stochastic Lyapunov estimates, nonexplosion, and boundary criteria. In the multiplicative regimes, integrating-factor identities and geometric Lévy factorizations express extinction through weighted exposure clocks and reduce the long-time analysis to effective decay rates. These methods yield almost-sure extinction criteria and identify a regime in which finite-time extinction and nonextinction coexist. On nonextinction, both populations remain positive at all finite times and converge jointly to zero, exhibiting joint extinguishment rather than positive persistence.
