A note on stability of stochastic logistic equation

作者：Liu Meng^*; Wang Ke

来源：Applied Mathematics Letters, 2013, 26(6): 601-606.

DOI：10.1016/j.aml.2012.12.015

• Logistic equation
• Random perturbations
• Global asymptotical stability

This report is concerned with a famous stochastic logistic equation
dx(t) = x(t)(1 - x(t)/K)[r(t)dt + sigma(t)dB(t)],
where B(t) is a standard Brownian motion. Under a simple assumption, sufficient conditions that are close to the necessary conditions for global asymptotical stability of the zero solution and the positive equilibrium are established. Numerical simulations are introduced to support the results. The results show that the noise is unfavorable for the stability of the positive equilibrium.

• 出版日期2013-6
• 单位淮阴师范学院; 哈尔滨工业大学