论文标题
通过收获的立方种群模型的确定性和随机研究
Deterministic and Stochastic Research of Cubic Population Model with Harvesting
论文作者
论文摘要
通过考虑在Allee效应下的种群，具有代表收获的二次功能，通过扩展标准的立方确定性模型来详细检查收获对人口的影响。确定性模型首先讨论了弱和强大的效果效应过渡，承载能力和根据收获的阈值变化。从langevin方程开始获得的fokker planck方程与均值相关的高斯白噪声，均值为零，并且从langevin方程中获得了近似的fokker planck方程，这些方程式均以相关的高斯有色噪声与零平均值相关。这允许计算种群的固定概率分布，因此可以讨论在Allee效应下对种群的线性和非线性（Holling Type-II）收获的影响，并分别受到白色和彩色噪声的影响。
A detailed examination of the effect of harvesting on a population has been carried out by extending the standard cubic deterministic model by considering a population under Allee effect with a quadratic function representing harvesting. Weak and strong Allee effect transitions, carrying capacity, and Allee threshold change according to harvesting is first discussed in the deterministic model. A Fokker Planck equation has been obtained starting from a Langevin equation subject to correlated Gaussian white noise with zero mean, and an Approximate Fokker Planck Equation has been obtained from a Langevin equation subject to correlated Gaussian colored noise with zero mean. This allowed to calculate the stationary probability distributions of populations, and thus to discuss the effects of linear and nonlinear (Holling type-II) harvesting for populations under Allee effect and subject to white and colored noises respectively.
