# Complex Systems Seminar

*by Allan Motyer (Ph.D. student) and Alana Moore (Ph.D. student)*

*Institution:*MASCOS, University of Melbourne

*Date: Fri 4th August 2006*

*Time: 3:15 PM*

*Location: Theatre 1, Ground Floor ICT Building, 111 Barry St*

*Abstract*: Truncation schemes for Markov chains and QBDs. When modelling a random system with an infinite number of states as a Markov chain it may not be possible to find a closed form solution for the equilibrium distribution. In this situation we truncate the state space of the system to a sufficiently large but finite number of states in order to find a numerical solution. It is desirable that as the number of states in the truncated system is increased, the numerical solution converges to the (unknown) solution for the system with infinite states. This is not something that can be taken for granted. I will outline conditions under which such convergence occurs, give examples of when it doesn't, and apply the known results to a special type of Markov chain - the quasi-birth-and-death process.

Optimal Monitoring for Fox Management. Since its introduction in the 1900's, the European red fox has had a major negative impact on native Australian fauna and is held responsible for the extinction of several Australian marsupial species. Once established, complete eradication of invasive species such as foxes is usually infeasible and control strategies employed in an attempt to save native species are often expensive and require intensive management programs. It is intuitive that effective management requires information about the system in question, but how much? Given obtaining information is usually difficult and costly, and budgets for park management are limited, it is unclear how effort should be split between monitoring and control in order to most effectively manage fox populations. I present a simple model which may be used to calculate optimal monitoring and management regimes.

*For More Information:* Emma Lockwood emmal@ms.unimelb.edu.au Tel: +61 3 8344 1617