The term complex system formally refers to a system of many parts which are coupled in a nonlinear fashion.
When there are many non-linearities in a system (many components), behaviour can be highly unpredictable. Complex systems research studies such behaviour. Complex systems research overlaps substantially with nonlinear dynamics research, but complex systems specifically consist of a large number of mutually interacting dynamical parts.
Complex Earthquakes - Complex Rivers - Complexity in Carbonates
In general, complex behaviour cannot be predicted by considering one elementary component of the system. The behaviour is emergent. For example, sine wave pulses of car velocities in traffic jams or the Gutenberg-Richter Law.
Processes controlling carbonate deposition and erosion are complex, yet are important if we wish to be able to predict properties and geometries of fossilized carbonate strata observed in nature. This ability is particularly important in situations where pores in carbonate rocks hold extensive reservoirs of fluids. For example, more than 60% of the remaining recoverable world-wide reserves of hydrocarbons are held within carbonate reservoirs; the ability to predict the lateral variability in rock properties in these reservoirs greatly affects the efficiency with which the hydrocarbons can be extracted from the ground.