On the stability of equilibria in replicator dynamics modelling: an application in industrial dynamics considering resource constraints
Replicator dynamic modelling (rdm) is used to discuss industrial evolution problems with heterogeneous agents. However, some of the models tend to be very complex and, therefore, analytical solutions cannot be obtained. Hence, the paper proposes to start with a relatively simple model and check its stability of the equilibria before expanding the model. This strategy is more effective than relying on simulation based studies where instability cannot be ruled out ex ante. Thus, the aim of this paper is to introduce a stability check for rdm, especially, if one ore more real Eigenvalues with value zero occur. Besides the (Strogatz, 1994) and (Hilborn, 1994) local stability theorem, this method provides an alternative and more flexible procedure for stability analysis for rdm. To apply this approach, an industrial replicator dynamic model containing three differential equations is set up.
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