Abstract: We proposed a grid multi-scroll hyper-chaotic system. The number of scrolls can be generated by extending saddle focal equilibrium points in x and y directions. Through dynamic analysis of Lyapunov exponential spectrum, equilibrium point, bifurcation diagram, complexity, the system exhibits hyper-chaotic state in a large parameter interval. With the increase of the number of scrolls, the complexity and largest Lyapunov exponent of the system increase obviously, and the dynamic behaviors of the system become more complicated. Based on the Lyapunov stability theory, we studied adaptive synchronization of the grid multi-scroll hyper-chaotic system with unknown parameters. The results of numerical experiments show that the syschronization time is short, and the synchronization effect is better.

Key words: grid multi-scroll attractor, hyper-chaotic system; , adaptive synchronization with unknown parameter, complexity