Model of two scientific fields interaction with quadratic restriction of achievements growth (analogous of model suggested by V.V. Kachak, E.S. Mchedlova) taking into account inertia with which scientific fellowship perceives «own» and «strange» scientific achievements is investigated. It is offered to supplement a construction of phase portraits and temporal realizations by a construction of initial-final maps (term of the authors) for clearing up of joint effect of delay, initial conditions and types of two scientific fields interaction оп dynamics of its efficiency. 
The limit cycles (including resonance on torus) and also chaotic regime (an ergodic torus) are discovered. «The windows of periodicity» are exhibited due to growth of delay: ergodic torus alternates а resonance оп torus. It is showed that achievements perception inertia is capable to complicate process of scientific fields interaction.