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arXiv · 0801.1560

On differences between fractional and integer order differential equations for dynamical games

E. Ahmed·A. S. Elgazzar·M. I. Shehata
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Abstract

We argue that fractional order (FO) differential equations are more suitable to model complex adaptive systems (CAS). Hence they are applied in replicator equations for non-cooperative game. Rock-Scissors-Paper game is discussed. It is known that its integer order model does not have a stable equilibrium. Its fractional order model is shown to have a locally asymptotically stable internal solution. A FO asymmetric game is shown to have a locally asymptotically stable internal solution. This is not the case for its integer order counterpart.

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E. Ahmed, A. S. Elgazzar, M. I. Shehata. 2008-01-10. On differences between fractional and integer order differential equations for dynamical games. https://doi.org/10.1515/zna-2008-3-406

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