THE LESLIE MATRIX IN POPULATION MODEL WITH AGE STRUCTURED


Oleh: Dwi Lestari

Abstract: The study of population growth is increasingly important. Some models have been developed to predict the population number in the future time. This paper will explain about an application of Leslie matrix in population model with age-structured. The Leslie matrix is a square matrix that contains non-negative elements. Finding the eigenvalue and eigenvector is very important to explain about the population changes. The dominant eigenvalue (\lambda_0) is the largest absolute value of eigenvalues of Leslie matrix. It will show whether the population is increasing, decreasing or staying constant.

If , the populations of all age groups will grow. If , all populations will tend to extinction, and if \lambda_0 = 1 , the populations of all groups will be asymtotically stationary. Using Matlab can give many information easily, to get eigenvalue and see the behavior of the population changes.

(Makalah ini telah dipresentasikan pada IndoMS International Conference on Mathematics and Its Applications 2009 (IICMA2009) di Matematika FMIPA UGM pada tanggal 12-13 Oktober 2009)

THE LESLIE MATRIX IN POPULATION MODEL WITH AGE STRUCTURED

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