报告题目：Stochastic Delay Population Systems
报告人：Professor Xuerong Mao，University of Strathclyde
The differential delay equations (DDEs) have been widely used to model the population growth of interacting species. There is an extensive literature concerned with the dynamics of the DDE models in population systems. On the other hand, population systems consist of many uncertainties and random factors including environmental noises. The question is: do the uncertainties and random factors affect population systems so significantly that they cannot be ignored? Recent research in stochastic modelling of population systems strongly indicates the answer is “yes”. In fact, Mao’s group revealed an important fact that the environmental noise could suppress a potential population explosion in a population system while they also found that the noise might make the population become extinctive.
In these serial talks, we will explain how stochastic differential delay equations (SDDEs) may be developed from the classical DDE models to take into account various different types of environmental noise. We will discuss if the SDDE models
· will preserve the positivity of the solutions,
· will explode to infinity in a finite time,
· will be ultimately bounded,
· and will become extinct or not.
We will reveal that different types of noises may affect the SDDE population systems significantly differently.
Xuerong Mao is a professor in the Department of Mathematics and Statistics at the University of Strathclyde, UK. He is a Fellow of the Royal Society of Edinburgh (Scottish Academy). He is also a Yangtze River Professor. Recently he receives the Royal Society Wolfson Research Merit Award. He is a world leading expert and has established high reputation in the areas of stochastic stability and control. He is a founder of modern stochastic stability. He is good at stochastic analysis and has made significant contributions to stability and control. The methods and techniques established by him have been very much welcome and used by many researchers. For example, his theory on the stabilization by noise has influenced many researchers; he initiated the numerical analysis of SDEs under the local Lipschitz condition; he made outstanding contributions to stochastic population systems; he established the LaSalle principle for SDEs and investigated the hybrid SDEs systematically. His books and papers have been studied, used and cited by many authors. For example, his book “Stochastic Differential Equations and Their Applications (the 2nd ed.), Elsevier, 2007” has more than 4000 Google Scholar citations.