Nonautonomous systems: Mathematical properties and ecological applications

Background/Question/Methods

In mathematics, a non-autonomous system is a system of ordinary differential equations with the right hand side depending on the independent variable (typically time t) explicitly. In this talk, I will show some important Mathematical properties of non-autonomous systems, and the role these properties play in ecological applications. In particular, a terrestrial carbon cycle model recently proposed by Luo et al is a non-autonomous system. I will extend the Mathematical analysis to this model.

Results/Conclusions

I will derive the instantaneous steady state solution and the global attractor, and the conditions under which, these two converge to each other. Some numerical results will be given to demonstrate the prediction of the terrestrial carbon cycle, based on the global attractor.