Difference equations versus differential equations, a possible equivalence for the Rössler system?
The authors discuss the possible equivalence between ordinary differential equations and difference equations which are obtained by discretization. First the paper deals with the Rössler system, several simulations about the discrete equation are obtained which explain the evolution of the dynamics. The authors establish that the solutions of the discrete equation are topologically equivalent to the solutions of the Rössler system as long as the the time step must be less than the threshold value associated with the Nyquist criterion. Then it is proved that the discretisation of two nonlinear ordinary differential can exhibit a chaotic regime. The dynamics of solutions depend on the discretization time step of each ordinary differential equation. To illustrate this result, several numerical simulations are given.
scientific article; zbMATH DE number 2115237
scientific article