It is the purpose of the present paper to study 'global structure' of the state space of an N-body interacting fermion system, which exhibits regular, transient and stochastic phases depending on strength of the interaction. An optimum representation called a dynamical representation plays an essential role in this investigation. The concept of the dynamical representation has been introduced in the quantum theory of dynamical subspace in our previous paper, in order to determine self-consistently an optimum collective subspace as well as an optimum collective Hamiltonian. In the theory, furthermore, dynamical conditions called separability and stability conditions have been provided in order to identify the optimum collective subspace as an approximate invariant subspace of the Hamiltonian. Physical meaning of these conditions are clarified from a viewpoint to relate breaking of them with bifurcation of the collectivity and an onset of quantum chaos from the regular collective motion, by illustrating the general idea with numerical results obtained for a simple soluble model. It turns out that the onset of the stochastic phase is associated with dissolution of the quantum numbers to specify the collective subspace and this dissolution is induced by the breaking of the separability condition in the dynamical representation. (author).