Dynamical systems under constant organiza-tion III: Cooperative and competitive behaviour of hypercy

  title={Dynamical systems under constant organiza-tion III: Cooperative and competitive behaviour of hypercy},
  author={Peter Schuster and Karl Sigmund and Ryu Jeong Wol},

Selfregulation of behaviour in animal societies

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

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

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

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

Asymptotic behavior of spatially distributed replicator systems

It is proved that there are situations when biologically unstable non-distributed replicator system becomes biologically stable in the distributed case.

Competition and cooperation in catalytic selfreplication

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

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

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.