The phrase "sensitive dependence" means that a small change in one thing can have a big impact or influence on another thing. It suggests that even tiny differences can lead to significant differences in outcomes or results. Full definition
The winter / summer point is that the climate is clearly not wildly unstable, in the sense of sensitive dependence on initial conditions, the way weather is. (mustelid.blogspot.ru)
The multiple simulations are conducted to account for the two usual sources of uncertainty in forecast models: (1) the errors introduced by the use of imperfect initial conditions, amplified by the chaotic nature of the evolution equations of the atmosphere, this is often referred to as sensitive dependence on the initial conditions; and (2) errors introduced because of imperfections in the model formulation, such as the approximate mathematical methods to solve the equations. (en.wikipedia.org)
Optimizing how well an ESM simulates climate statistics targets success metrics that are directly relevant for climate projections, and it avoids difficulties caused by sensitive dependences on atmospheric initial conditions and small - scale roughness that otherwise complicate data assimilation at high resolution. (climate-dynamics.org)