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Relaxation oscillations are limit cycles with two clearly d ifferent time scales. In this article the spatio-temporal dynamics of a standard prey-pr edator system in the parameter region of relaxation oscillation is investigated. Both prey and pr edator population are distributed irreg- ularly at a relatively high average level between a maximal and a minimal value. However, the slowly developing complex pattern exhibits a feature of "inverse excitability": Both populations show collapses which occur erratically both in space and in time. The nature of these collapses is analysed statistically and it is shown that the model behavi our can be interpreted as a resolution of the paradox of enrichment.

Local Collapses in the Truscott-Brindley Model