Research in Applied Mathematics

Abstract

Hopf Bifurcation in a Delayed Solow-Verhulst Model

Author(s): A.Kaddar, S.Sahbani ,and H.Talibi Alaoui

In this paper, we propose a mathematical study of the relationship between populationdynamicsandeconomicgrowth.Todothis,thetotalpopulationisdividedintothree disjointclasses:employed,unemployedandeconomicallyinactivepopulation.Ontheonehand, theevolutionofthenumberofindividualsineachcompartmentisdescribedbyVerhulstmodel andontheotherhandtheeconomicgrowthisgovernedbytheSolowequation.Theresulting modelisasystemofdifferentialequationswithtimedelay.Thedynamics,ofthissystem,are studied in terms of local stability and of local Hopf bifurcation. Some numerical simulations aregiventoillustrateourtheoreticalresults.Additionallyweconcludewithsomeremarks.

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