Synchronisation of integer-order and fractional-order discrete-time chaotic systems


Ouannas A., Khennaoui A.-A., Zehrour O., Bendoukha S., Grassi G., Pham V.-T.

Source title

Pramana - Journal of Physics

Publication year

This paper studies the synchronisation of integer- and fractional-order discrete-time chaotic systems with different dimensions. Control laws are proposed for the full-state hybrid projective synchronisation (FSHPS) of a master–slave pair, where the difference equations of the master have an integer order while those of the slave have a fractional order. Moreover, inverse FSHPS laws are proposed for a fractional-order master and an integer-order slave. The Lyapunov stability theory of integer-order maps and the stability theory of linear fractional-order maps are utilised to establish the asymptotic stability of the zero equilibrium corresponding to the synchronisation error system. Numerical results are presented to verify the findings of the study.