The present study deals with the detection of bifurcation points in the problems that are not covered by the well-known conventional methods. The approach based on the non standard application of the topological degree of mapping notion is used to tackle the challenge. Universality of the involved mathematical tool to explore the wide scope of problems is demonstrated. Generalization of classical Hopf bifurcation Theorem on the case of functional differential equations is given.
Mathematics Subject Classification (2010). 34C23, 34C25, 39A28, 46N20, 47G20, 47H11.