Abstract
Introducing the effect of extinction into the so-called replicator equations in mathematical biology, we construct a general model where the diversity of species, i.e., the dimension of the equation, is a time-dependent variable. The system shows very different behavior from the original replicator equation, and leads to mass extinction when the system initially has high diversity. The present theory can serve as a mathematical foundation for the paleontologic theory for mass extinction. This extinction dynamics is a prototype of dynamical systems where the variable dimension is inevitable.
- Received 1 January 1998
DOI:https://doi.org/10.1103/PhysRevE.60.842
©1999 American Physical Society