Investigating the dynamics, synchronization of a novel chaotic system reduced from a modified KdV–Burgers–Kuramoto equation

Chaos may arise in many nonlinear evolution equations which make the dynamics much more complex. In this study, we report the finding of a novel chaotic attractor in a modified KdV–Burgers–Kuramoto (mKBK) equation. For potential applications, we further study analytically its chaos synchronization including complete synchronization with known and unknown parameters, generalized functional projective synchronization (GFPS) with known and unknown parameters, and combined synchronization with known and unknown parameters via the designed nonlinear feedback controllers. Numerical illustrations are presented which agree well with the theoretical results.