A model for roundoff and collapse in computation of chaotic dynamical systems Original Research Article

Computer simulations of dynamical systems contain discretizations, where finite machine arithmetic replaces continuum state space. For chaotic dynamical systems, the main features of this discretization are stochastically related to the parameters both, of the underlying continuous system and of the computer arithmetic. A model of this process is required to describe and analyze its statistical properties and this is carried out for the family of mappings fl(x) = 1 − |1 − 2x|l, x ∈ [0, 1], l > 2. Computer modeling results are presented.