Relative nonlinearity and permanence

Relative nonlinearity and permanence.

We modify the commonly used invasibility concept for coexistence of species to the stronger concept of uniform invasibility. For two-species discrete-time competition and predator-prey models, we use this concept to find broad easily checked sufficient conditions for the rigorous concept of permanent coexistence. With these results, permanent coexistence becomes a tractable concept for many dis...

permanence. Table of Contents

In this chapter we describe Theorema, a system for supporting mathematical proving by computer. The emphasis of the chapter is on showing how, in many situations, proving can be reduced to solving in algebraic domains. We first illustrate this by known techniques, in particular the Gröbner bases technique. Then we go into the details of describing the PCS technique, a new technique that is part...

Object Permanence 1

Nonlinearity In Exchange Rates and Forecasting

The probability of permanence.

Numerical experiments suggest that cooperation is a very rare phenomenon in autocatalytic networks with more than about five interacting species. There is strong evidence that the probability for cooperative behavior in random networks decreases at least exponentially and at most as an2 with the number n of interacting species. The evolution of larger persistent networks by subsequent incorpora...