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Mathematical Model of Building Behavior of Apis mellifera

Following experimental observations on the building techniques of Apis melliftra, a model describing the construction of parallel combs in beehive is proposed. The model assumes as the essential elements in building activities the bee-wax and bee-bee interactions coupled by means of a feedback mechanism. The construction is represented by a set of dynamical non-linear partial difterential equations for the density of bees and the quantity of wax distributed in the hive. Using linear stability analysis the conditions for growth ofthe coherent spatially ordered inhomogeneous structure are derived. Numerical simulations depicting growth process in the nonlinear regime have been performed, illuminating the role of the competition between bees and the bee-wax interaction. The model reproduces the beginning ofthe growth of parallel and equidistant combs satisfactorily.