Mathematical Demography pp 259-271 | Cite as

# Ergodic Properties of Population I: The One Sex Model

Chapter

## Abstract

The requirements Parlett introduces for stability of non-negative matrices, irreducibility and primitivity, have an intuitive base. Irreducibility translates as the restriction that the projection matrix be for a single population, as in the continuous form of the renewal equation. (Matrix techniques for extracting stable roots and vectors do not apply to non-interacting populations; nor in general would such populations have the same roots.)

## Keywords

Ergodic Theorem Projection Matrix Positive Element Intrinsic Growth Rate Nonnegative Matrice
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Preview

Unable to display preview. Download preview PDF.

## References

- Dulmage, A. L. and Mendelsohn, N. S. 1964. Gaps in the exponent set of primitive matrices,
*Illinois J. Math*.**8**, 642–656.zbMATHMathSciNetGoogle Scholar - Heap, B. R. AND Lynn, M. S. 1964. The index of primitivity of a non-negative matrix,
*Numer. Math*.**6**, 120–144.CrossRefzbMATHMathSciNetGoogle Scholar - Heap, B. R. AND Lynn, M. S. 1964. A Graph-theoretic algorithm for the solution of a linear diophantine problem of Frobenius,
*Numer. Math*.**6**, 346–354.CrossRefzbMATHMathSciNetGoogle Scholar - Heap, B. R. AND Lynn, M. S. 1965. On a linear diophantine problem of Frobenius: An improved algorithm,
*Numer. Math*.**7**, 226–231.CrossRefzbMATHMathSciNetGoogle Scholar - Keyfitz, N. 1968. “Introduction to the Mathematics of Population,” Addison-Wesley Publ. Co., Reading, Mass.Google Scholar
- Mcfarland, D. D. 1969. On the theory of stable populations. A new and elementary proof of the theorems under weaker assumptions,
*Demography***6**, 303–322.CrossRefGoogle Scholar - Rosenblatt, D. 1957. On the graphs and asymptotic forms of finite Boolean relation matrices and stochastic matrices,
*Naval Res. Logist. Quart*.**4**, 151–167.CrossRefMathSciNetGoogle Scholar - Marcus, M. AND Minc, H. 1964. “A Survey of Matrix Theory and Matrix Inequalities,” Allyn and Bacon, Inc., Boston, Mass.zbMATHGoogle Scholar
- Gartmacher, F. R. 1959. “Theory of Matrices,” Vol. 2, Chelsea, New York.Google Scholar
- Karlin, —. 1966. “A First Course in Stochastic Processes,” Academic Press, Inc., New York.Google Scholar
- Lopez, A. 1961. “Problems in Stable Population Theory,” Office of Population Research, Princeton, N. J.Google Scholar
- Berge, C. 1962. “The Theory of Graphs,” Methuen, London.zbMATHGoogle Scholar

## Copyright information

© Springer-Verlag Berlin · Heidelberg 1977