Chaos and Turbulence
Chaos theory concerns the behavior of nonlinear dynamical systems and their sensitivity to initial and boundary conditions. The flow of a viscous fluid that governed by the complex nonlinear Navier-Stokes equations is one such system
ChaosLogisticTurbulence

The chaotic behavior associated with the logistic equation with increase of \(r\) \[ X_{\text{next}} = rX(1 - X) \]


1Gleick, J. (1988). Chaos: making a new science.