In this article, a class of Hindmarsh-Rose model is studied. First, all necessary conditions for the parameters of system are found in order to have one stable fixed point which presents the resting state for this famous model. After that, using the Hopf’s theorem proofs analytically the existence of a Hopf bifurcation, which is a critical point where a system’s stability switches and a periodic solution arises. More precisely, it is a local bifurcation in which a fixed point of a dynamical system loses stability, as a pair of complex conjugate eigenvalues cross the complex plane imaginary axis. Moreover, with the suitable assumptions for the dynamical system, a small-amplitude limit cycle branches from the fixed point.

The Southeast plays a very important role in Vietnam’s economic development. Despite a high concentration of social scientists in the Southeast region, there remains a paradox that the Southeast culture has not been sufficiently researched into. Applying the method of cultural zoning based on the changes of the three dimensions Subject – Space - Time developed by the author, the article concludes that the Southeast is a separate cultural zone besides the Southwest and lists some typical characteristics of the Southeast in terms of cultural elements (focusing on the organizational culture) and the system of cultural personality characteristics of Vietnamese people in the Southeast. An analysis of the Human Development Index (HDI) of the Southeast shows that this development is unbalanced and unsustainable. To achieve balance and sustainability, more investment must be made on the culture and the people; community-village type behaviors should be replaced by community-society type behaviors; and the urban way of living, the urban culture and good urban citizen character should be promoed while limiting the rural/agricultural lifestyle and characteristics.