Controlling ideal turbulence in time-delayed chua´s circuits and an application to communications

We try to synchronize physical models described by wave equations with nonlinear boundary conditions. These systems are distributed parameter systems in which ideal turbulence, introduced by Sharkovsky et al., occurs. The behavior of such systems can be quite intricate both in time and space. However, by using the d´Alembert´s solution, the analysis of the dynamic characteristics can be reduced to that of a finite-dimensional difference equation. In this report, based on this analytical method using the d´Alembert´s solution, we design a control law to stabilize an equilibrium point and to synchronize a pair of the distributed parameter systems. And then, we show that this synchronization phenomenon can be applied to multichannel spread-spectrum communications.