Studies of quantum and classical information processing systems must take into account interaction with environment, which is most effectively modeled by non-Markovian stochastic differential equations. We will study geometric properties of these systems, like stability of attractors and their bifurcations, which occur in modeling of the learning processes in networks consisting of finite state classical or quantum objects. We want to understand the types of bifurcations introduced by coupled influence of noise and interaction and/or control time delay in systems of excitable dynamical units like neurons or qubits. The stability of attractors will be investigated using the generalized Lyapunov method for the stochastic delay-differential equations. Analytical results will be compared with extensive numerical computations in various typical models of information processing systems in different environments.