Method for Computer Simulation of Chaotic and Complex Periodic Oscillations

The possibility of constructing chaotic and complex periodic orbits of desired configurations is demonstrated on one-dimensional discontinuous maps. With appropriately located discontinuity, these maps can generate a rich selection of specific orbits with long laminar segments. A simple method is proposed to determine the features of the orbit obtained. This technique, applied to special maps with a horizontal linear branch, allows us to generate a great variety of stable periodic orbits with a specified future by only small variations of the map control parameter.