论文标题
在污染环境中具有年龄结构和心理效应的单物种人群模型
Single-species population models with age structure and psychological effect in a polluted environment
论文作者
论文摘要
本文认为在污染环境中具有年龄结构和心理影响的单人群模型。我们将单个人口分为幼虫和成人结构的两个阶段。该模型使用逻辑输入，幼虫通过恒定比例转化为成人体。我们只考虑成年。心理影响的作用使成人和环境毒素之间的接触形式是功能形式，而幼虫和环境毒素之间的接触是线性的。 对于作为非线性时间变化系统体现的确定性模型，我们通过Lyapunov的一次性近似理论讨论了系统的渐近稳定性，并为建立稳定性提供了足够的条件。 考虑到本质上生物学和环境毒素之间的接触率并不总是恒定的，我们使接触率干扰白噪声，然后将接触率修改为随机过程，从而建立了相应的随机单人群模型。根据ITô公式和Lyapunov在功能方法中，我们首先证明在任意初始条件下为随机模型存在全球独特的正溶液，然后为预期意义上的单个人群提供了足够的条件。
This paper considers a single-population model with age structure and psychological effects in a polluted environment. We divide the single population into two stages of larval and adult structure. The model uses Logistic input, and the larvae are converted into adult bodies by constant ratio. We only consider adulthood. The role of psychological effects makes the contact between adult and environmental toxins a functional form, while the contact between larvae and environmental toxins is linear. For the deterministic model embodied as a nonlinear time-varying system, we discuss the asymptotic stability of the system by Lyapunov one-time approximation theory, and give a sufficient condition for stability to be established. Considering that the contact rate between biological and environmental toxins in nature is not always constant, we make the contact rate interfere with white noise, and then modify the contact rate into a stochastic process, thus establishing a corresponding random single-population model. According to Itô formula and Lyapunov in the function method, we first prove the existence of globally unique positive solutions for stochastic models under arbitrary initial conditions, and then give sufficient conditions for weak average long-term survival and random long-term survival for single populations in the expected sense.
