interactions
increase, then the interactions inevitably drive the system unstable. In particular, we have
Theorem 1: If tr CfC > vitr.42vitr , then the system is unstable.
Theorem 1 is a higher ... where p,v < 0, has a positive eigenvalue if P12 > µv. The proof of theorem 1 is presented
in the supplementary material.
Theorem 1 implies that the interacting systems ... Applied to random matrices representing the
interactions between two parts of a complex system, theorem 1 reproduces the results of
May [4] for connection-driven instability. However, no assumptions concerning