The concept of repulsivity in dynamical systems as motivated by persistence problems in population biology
- 31 July 1979
- journal article
- research article
- Published by Taylor & Francis in International Journal of Systems Science
- Vol. 10 (8) , 863-871
- https://doi.org/10.1080/00207727908941627
Abstract
An alternative to stability analysis in population biology is proposed for cases in which persistence problems such as coexistence of species and protectedness of genetic polymorphisms are of primary interest. In order to arrive at a general mathematical description, the concept of repulsivity of certain sets with respect to dynamical systems (continuous-time as well as discrete-time) defined on metric spaces is introduced. A first basic result linking this concept to the existence of Lyapunov functions is derived in analogy to the respective results from stability theory.This publication has 11 references indexed in Scilit:
- Biological populations obeying difference equations: Stable points, stable cycles, and chaosPublished by Elsevier ,2004
- Iterations of continuous mappings on metric spaces Asymptotic stability and Lyapunov functionsInternational Journal of Systems Science, 1979
- On the persistence of ecological systemsJournal of Theoretical Biology, 1977
- Stability Theory by Liapunov’s Direct MethodPublished by Springer Nature ,1977
- Population Persistence and Density DependenceEcological Monographs, 1976
- Period Three Implies ChaosThe American Mathematical Monthly, 1975
- A Characterization of Local Convergence for Fixed Point Iterations in $R^1 $SIAM Journal on Numerical Analysis, 1975
- Class of discrete Liapunov functionsJournal of Mathematical Analysis and Applications, 1975
- Stability Theory of Dynamical SystemsPublished by Springer Nature ,1970
- Über die Anwendung der Methode von Ljapunov auf DifferenzengleichungenMathematische Annalen, 1958