Sensitive dependence on parameters

For a family of dynamical systems we define sensitive dependence on parameters in a way resembling Guckenheimer's definition of sensitive dependence on initial conditions. While sensitive dependence on initial conditions tells us that if we know the initial condition only approximately then we cannot make deterministic predictions, sensitive dependence on parameters tells us that if we know the parameter value only approximately then we cannot make statistical predictions. We show that the family of logistic maps has sensitive dependence on parameters. Moreover, the long-time response of the system to the change of the parameter is practically independent of the immediate response. (C) 2010 American Institute of Physics. [doi:10.1063/1.3499615]