V.M. Moskovkin, Bilal N.E. Suleiman

Article is devoted mathematical modeling of processes in "a triangle of knowledge": researches - education - innovation by means of the equations population dynamics. It is supposed that close interaction of all components of "a triangle of knowledge - should lead to a powerful synergy and serve as the engine of the social and economic development based on scientific and technical achievements. Lisbon-s strategy of EU is based on this principle with its purpose to create by 2010 the most dynamical and competitive economy based on knowledge, and also one of its tools - EU Framework Programs on researches and developments (FP6 and FP7). The interaction model in "a triangle of knowledge" builds in limits of a wide class of models of competitive-cooperation interactions in social and economic systems, and it is obvious that the dynamic system describing such interactions in "triangle of knowledge" should be the third order. By analogy to models of competitive-cooperation interactions in social and economic systems, at such dynamic system of the third order there should be standard logistical members, and also the members who are responsible for cooperation interactions who generally can be nonlinearities, both the second, and the third order. In work triple cooperation interactions are considered only. Co-ordinates of the seven first singular points which were received in explicit form and appeared instabilities. The algebraic equation of the fifth degree for a finding of one of co-ordinates of not trivial eighth singular point is received. Numerical experiments with model in which are found out bifurcation of type: saddle-knot is done. In one special case asymptotic of the analytical decision of initial dynamic system is received.