Controlling ideal turbulence: Stabilization and synchronization of time-delayed Chua's circuits

We try to stabilize steady solutions of a physical model described by wave equations with nonlinear boundary conditions. This system is a distributed parameter system in which ideal turbulence, introduced by Sharkovsky et al., occurs. Although the behavior of the system is quite intricate both in time and space, 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 control laws to stabilize steady solutions and synchronize a pair of the distributed parameter systems. And then, we show that the stabilization and the synchronization can be accomplished only by boundary inputs.