stability in systems

Stable systems {stability, system} have attractors with short state-cycle length and large attraction basins, so changing from one state to nearby states, or changing transition rule slightly, leaves system in same attraction basin. In unstable systems, if state or transition rule slightly changes, system changes to long state-cycle length {chaos} or changes attraction basins {catastrophe}. If network is sparsely connected, network tends to stay in same attraction basin. If network is densely connected, network tends to be chaotic or catastrophic.

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