The limits of global growth lead to economic stagnation and social instability. This problem is considered on the model of a social system that includes a society consisting of reasonable, far-sighted (onward) elements and democratically elected politician. A neuropsychological model of the behavior of the onward element is proposed based on emotional expectation. It is assumed that the expectations of positive emotions by all onward elements ensure both social stability and politician reelection. One type of onward element is Progressive person who works in a supportive environment that generates incentives that facilitate the fulfillment of his desires. It is shown that for the stability of the social system with the society of such persons, it is sufficient to organize a favorable environment. Another type of onward element - Phobic works in a fears environment. It is shown that for the stability of the social system with the society of Phobics, there are enough regular stimuli that support their fears. But in the absence of new stimuli and the presence of positive incentives, the Phobic turn into Progressive person. Then the social system becomes unstable under growth limits. In this case, for the social system stability, it is enough to create a sequence of stimuli to support the fears of the Phobic.