# 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