Combination synchronisation of different kinds of spatiotemporal coupled systems with unknown parameters

In this study, spatiotemporal coupled systems with different kinds of local dynamic behaviours are introduced and combination synchronisation in such systems is studied. Especially, complex spatiotemporal coupled system consists of real number part and imaginary number part, so it can be synchronised with two real number systems at the same time and synchronisation is asymmetrical. Based on the backstepping method, the authors design controllers (fewer than the number of variables) with parameters identification. Sliding mode controllers are designed according to the Lyapunov stability theory and the fractional stability theory. Simulation results show the robustness and effectiveness of the authors methods.