Abstract: Based on the zero-dimensional climate model a formula of nonlinear mapping is derived, equilibria and a stability basin of the climate system represented by the formula are studied. A regulating feature of oceanic capacities C in the climate system is revealed by means of mapping iterations. Computation results show that there is a narrow sensitive C’s interval which controls a behaviour of the climate system: if C value is greater than that of the upper limit of the interval, the system will tend to a equilibrium state, i. e. present climate: if C value is less than that of the lower limit of the interval, the system will lose its stability. Within the sensitive interval, periodic and chaotic behaviours are emerged in the system. By doubling the period with increasing C, the way to chaos is depicted.