High-dimensional oscillations from deterministic dynamical
systems: Linear filtering
L.V. Krasichkov and A.A. Kipchatov
College of Applied Science, Saratov State University,
Saratov, Russia
Problems of appearance and controlling of properties of high-dimensional oscillations are of very interest from the point of view creation of test signals for different applications as well as are important in understanding of ways to turbulence. To solve the problems and answer the questions The lattices of nonlinear elements are widely investigated (see for review [1] and references therein) in solving the above mentioned problems. At the same time, there is another way to high-dimensional chaos, namely, the linear transformation of low-dimensional chaotic oscillations by linear inertial systems (filters). The facts of dimension increase of chaotic oscillation [2-6] and complication of attractor structure [3,7,8] during filtering are well known.
In this work the last way is discussed. It is investigated the lattice of the linear filters under deterministic chaotic external force. Such system is the simplest model of medium which obeys with inertial properties only. The case when the inertial properties of each element of the lattice are very weak is considered.
It is shown that the system demonstrates a significant complication of chaotic oscillations with increasing of lattice length. Moreover, the output oscillations of the lattice, whose length is about one thousand, become similar to noise in its statistical and dynamical characteristics.