Dynamical systems under constant organiza-tion III: Cooperative and competitive behaviour of hypercy
@inproceedings{Schuster1979DynamicalSU, title={Dynamical systems under constant organiza-tion III: Cooperative and competitive behaviour of hypercy}, author={Peter Schuster and Karl Sigmund and Ryu Jeong Wol}, year={1979} }
128 Citations
Selfregulation of behaviour in animal societies
- MathematicsBiological Cybernetics
- 2004
The ordinary differential equation which transformes the game theoretical model of Maynard-Smith into a dynamical system is discussed and some important theorems and applications to symmetric…
A permanence theorem for dynamical systems
- Mathematics
- 2013
We provide a necessary and sucient condition for permanence related to a dynamical system on a suitable topological space. We then illustrate an application to a Lotka{Volterra predator{prey model…
A Mathematical Model of the Hypercycle
- Physics
- 1980
The emergence of life can be studied under two aspects, as a historical investigation or as an engineering problem.
A general cooperation theorem for hypercycles
- Mathematics
- 1981
We derive a condition for a closed invariant subset of a compact dynamical system to be an attractor (resp. repellor) combining the usual Ljapunov function methods with time averages. Applications…
Competition and cooperation in catalytic selfreplication
- Chemistry
- 1981
It is shown that in a flow reactor, hypercyclic coupling of self-reproducing macromolecular species leads to cooperation, i.e. none of the concentrations will vanish, and the number of surving species increases with the total concentration.
Permanence and Uninvadability for Deterministic Population Models
- Mathematics
- 1984
The notion of permanence is used to deal with population dynamical systems which are too complicated to allow a detailed analysis of their asymptotic behaviour. This paper offers an exposition of…
Coexistence for systems governed by difference equations of Lotka-Volterra type
- MathematicsJournal of mathematical biology
- 1987
It is shown that in spite of the complex dynamics associated with the simplest of Lotka-Volterra difference equations systems, it is possible to obtain readily applicable criteria for permanence in a wide range of cases.
References
SHOWING 1-2 OF 2 REFERENCES
Dynamical systems under constant organization I. Topological analysis of a family of non-linear differential equations--a model for catalytic hypercycles.
- MathematicsBulletin of mathematical biology
- 1978