Dynamics and synchronization of numerical solutions of the Burgers equation

For Chebyshev spectral solutions of the forced Burgers equation with low values of the viscosity coefficient, several bifurcations and stable attractors can be observed. Periodic orbits, quasiperiodic and strange ones may arise. Bistability can also be observed. Necessary conditions for these attractors to appear are discussed and justification for the non emerging of bistability for an example of a system symmetry break is presented. As an application for the dynamical behavior of spectral solutions of Burgers equation, the dynamics and synchronization of unidirectionally coupling of Chebyshev spectral solutions of Burgers equations by means of a linear coupling are described and discussed. Also, a nonlinear coupling is proposed and discussed.