The Australian Journal of Mathematical Analysis and Applications

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Paper's Title:

Reduced Generalized Combination Synchronization Between Two n-Dimensional Integer-Order Hyperchaotic Systems and One m-Dimensional Fractional-Order Chaotic System


Smail Kaouache, Mohammed Salah Abdelouahab and Rabah Bououden

Laboratory of Mathematics and their interactions,
Abdelhafid Boussouf University Center, Mila.


This paper is devoted to investigate the problem of reduced generalized combination synchronization (RGCS) between two n-dimensional integer-order hyperchaotic drive systems and one m-dimensional fractional-order chaotic response system. According to the stability theorem of fractional-order linear system, an active mode controller is proposed to accomplish this end. Moreover, the proposed synchronization scheme is applied to synchronize three different chaotic systems, which are the Danca hyperchaotic system, the modified hyperchaotic Rossler system, and the fractional-order Rabinovich-Fabrikant chaotic system. Finally, numerical results are presented to fit our theoretical analysis.

1: Paper Source PDF document

Paper's Title:

A General Fractional Control Scheme for Compound Combination Synchronization Between Different Fractional-Order Identical Chaotic Systems


Soumia Bensimessaoud and Smail Kaouache

Laboratory of Mathematics and their interactions, Abdelhafid Boussouf University Center, Mila, Algeria.


In this paper, we aim to investigate the problem of compound combination synchronization (CCS) between four different fractional-order identical chaotic systems. Based on Laplace transformation and stability theory of linear dynamical systems, a new control law is proposed to assure the achievement of this kind of synchronization. Secondly, this control scheme is applied to realised CCS between four identical unified chaotic systems. Recall, that the proposed control scheme can be applied to wide classes of chaotic and hyperchaotic systems. Numerical simulations are given to show the effectiveness of the proposed method.

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