SDEs and SDDEs in population dynamics

Friday, June 8, 2018 - 10:30am - 11:00am
Lind 305
Chenggui Yuan (Swansea University)
In this talk, I will present several stochastic population dynamical models, for examples: the population models are characterised by stochastic differential equations, stochastic differential delay equations, stochastic differential equations driven by Brownian motion and Levy processes and the regime-switching diffusions, respectively. Many properties will be discussed. Firstly, we will prove that the solutions of each model will be nonnegative or positive; Secondly, we will show some long-term behaviour, under some conditions, the mean of the solutions or the mean square of the solutions are bounded. Moreover, we will give the conditions such that the size of the population will tend to zero with exponential rate; Thirdly, the property of persistence will be discussed, that is the population will never become extinct; Finally, the conditions for the population tend to equilibrium state will be present.