Nonlineardynamicalsystemsaresometimesundertheinfluenceofrandomfluctuations.Itisdesirabletoexaminepossiblebifurcationsforstochasticdynamicalsystemswhenaparametervaries.Acomputationalanalysisisconductedtoinvestigatebifurcationsofasimpledynamicalsystemundernon-Gaussianα-stableLévymotions,byexaminingthechangesinstationaryprobabilitydensityfunctionsforthesolutionorbitsofthisstochasticsystem.ThestationaryprobabilitydensityfunctionsareobtainedbysolvinganonlocalFokker-Planckequationnumerically.Thisallowsnumericallyinvestigatingphenomenologicalbifurcation,orP-bifurcation,forstochasticdifferentialequationswithnon-GaussianLévynoises.