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Some time-inhomogeneous diffusion models for population growth in random environments
Communications in Nonlinear Science and Numerical Simulation ( IF 3.4 ) Pub Date : 2024-12-06 , DOI: 10.1016/j.cnsns.2024.108502 Virginia Giorno, Amelia G. Nobile
Communications in Nonlinear Science and Numerical Simulation ( IF 3.4 ) Pub Date : 2024-12-06 , DOI: 10.1016/j.cnsns.2024.108502 Virginia Giorno, Amelia G. Nobile
Deterministic growth laws, expressed by first order differential equations with time-depending intrinsic growth intensity function, are initially introduced. Such equations are then parameterized in a way to allow random fluctuations of the intrinsic growth intensity function. This procedure leads to time-inhomogeneous diffusion processes for which a detailed study of transition probability density functions and of the first-passage time densities through arbitrarily fixed threshold values is performed. Some statistically significant quantities, such as the mean and the variance of the time necessary for the process to attain an assigned state, are obtained in closed form. The behaviors of several diffusion processes, suitable to describe the growth of populations, are finally analyzed and compared. Various numerical computations are performed in the presence of periodic intrinsic intensity function.
中文翻译:
一些随机环境中种群增长的时间非均匀扩散模型
最初介绍了由具有时间变化的内禀增长强度函数的一阶微分方程表示的确定性增长定律。然后,以允许固有生长强度函数的随机波动的方式对此类方程进行参数化。此过程导致时间不均匀的扩散过程,为此,通过任意固定的阈值对跃迁概率密度函数和首次通过时间密度进行详细研究。一些具有统计意义的量(例如,过程达到指定状态所需的时间的平均值和方差)以封闭形式获得。最后分析和比较了适合描述种群增长的几个扩散过程的行为。在存在周期性本征强度函数的情况下执行各种数值计算。
更新日期:2024-12-06
中文翻译:
一些随机环境中种群增长的时间非均匀扩散模型
最初介绍了由具有时间变化的内禀增长强度函数的一阶微分方程表示的确定性增长定律。然后,以允许固有生长强度函数的随机波动的方式对此类方程进行参数化。此过程导致时间不均匀的扩散过程,为此,通过任意固定的阈值对跃迁概率密度函数和首次通过时间密度进行详细研究。一些具有统计意义的量(例如,过程达到指定状态所需的时间的平均值和方差)以封闭形式获得。最后分析和比较了适合描述种群增长的几个扩散过程的行为。在存在周期性本征强度函数的情况下执行各种数值计算。