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We consider a model proposed by one of the authors for a type of plasticinstability found in creep experiments which reproduces a number ofexperimentally observed features. The model consists of three couplednon-linear differential equations describing the evolution of three types ofdislocations. The transition to the instability has been shown to be via Hopfbifurcation leading to limit cycle solutions with respect to physicallyrelevant drive parameters. Here we use reductive perturbative method to extractan amplitude equation of up to seventh order to obtain an approximate analyticexpression for the order parameter. The analysis also enables us to obtain thebifurcation (phase) diagram of the instability. We find that whilesupercritical bifurcation dominates the major part of the instability region,subcritical bifurcation gradually takes over at one end of the region. Theseresults are compared with the known experimental results. Approximate analyticexpressions for the limit cycles for different types of bifurcations are shownto agree with their corresponding numerical solutions of the equationsdescribing the model. The analysis also shows that high order nonlinearitiesare important in the problem. This approach further allows us to map thetheoretical parameters to the experimentally observed macroscopic quantities.Comment: LaTex file and eps figures; Communicated to Phys. Rev.

High-order amplitude equation for steps on the creep curve