Effect of slow manifold structure on relaxation oscillations and one-dimensional map in a model for plastic instability

Abstract

Relaxation oscillations or stick-slip dynamics exhibited by a model, originally proposed for a form of plastic instability namely, Portevin Le-Chatelier effect, has been analysed. The model exhibits atypical slow manifold which has a bent structure. It is this geometry that gives rise to a new mechanism of relaxation oscillations. A partial representation of the slow manifold in the form of the next maximal amplitude (NMA) maps has also been analysed. Minimal information of principal periodic orbit embedded in four dimensions and the slow manifold structure is shown to be sufficient to reproduce the qualitative features of the NMA maps.