May (1972, 1973) and Hastings (1982a, b, 1983a, b) announced criteria for the probable stability or instability, as n ↑ ∞, of systems of n linear ordinary differential equations or difference equations with random coefficients fixed in time. However, simple, explicit counter-examples show that, without some additional conditions, the claims of May and Hastings can be false.
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- Biochemistry, Genetics and Molecular Biology(all)
- Immunology and Microbiology(all)
- Agricultural and Biological Sciences(all)
- Applied Mathematics