Integrated physiologic systems under neural control show persistent complex dynamical patterns and long-term correlations in their output signals. What is the origin of this complexity? To investigate whether physiologic complexity is confounded by coupling and nonlinear feed-backs between different individual systems, we developed a dynamical networks approach and hypothesize that physiologic transitions and changes in sympatho-vagal balance lead to reconfiguration of the physiologic network which in turn affects the level of complexity. When we fall asleep, sympatho-vagal balance changes paralleled by transitions in long-term correlations and complexity from high levels (during wake) to low levels (during DS). Here we show that during wake, LS and REM, persistent patterns in different physiologic systems as the brain, the cardiac and the respiratory systems, occur simultaneously indicating a connection between these systems. During DS those connections are diminished and the physiologic systems tend to operate autonomously. Thus, the low level of complexity during DS may be related to the breakdown of physiologic network connectivity.