Chaos Multiscale-Synchronization Between Two Different Fractional-Order Hyperchaotic Systems Based on Feedback Control

In this paper, the chaos multiscale-synchronization between two different Fractional-order
Hyperchaotic System (FOHCS)s have been investigated. The L¨u-like and its FOHCS are also
studied. The L¨u-like FOHCS is controlled to be multiscale-synchronization with Liu FOHCS and
new Lorenz FOHCS, respectively. The analytical conditions for the multiscale-synchronization
of these pairs of different FOHCSs are derived by utilizing Laplace transform. Furthermore,
multiscale-synchronization between two different FOHCSs is achieved by utilizing the different
linear and nonlinear feedback control method in a short period and both remain in chaotic
states. Numerical simulations are used to verify the theoretical analysis using different values of
the fractional-order parameter and the different linear and nonlinear control functions.