The Amplification Principle states that there are non-linearities which occur at large scale which do not occur at small to medium scale.

COROLLARY: In many large networks, even small things can and do cause huge events. In system-theoretic terms, in large systems such as these, even small perturbations on the input to a process can destabilize the system's output.

An important example of the Amplification Principle is non-linear resonant amplification, which is a powerful process that can transform dynamic systems, such as large networks, in surprising ways with seemingly small fluctuations. These small fluctuations may slowly accumulate, and if they are synchronized with other cycles, may produce major changes. Resonant phenomena are examples of non-linear behavior where small fluctuations may be amplified and have influences far exceeding their initial sizes. The natural world is filled with examples of resonant behavior that can produce system- wide changes ...

In the Internet domain, it has been shown that increased inter-connectivity results in more complex and often slower BGP routing convergence.