Controlling the initial condition of coupled synchronization of chaotic fractional Newton-Leipnik system for its stability with minimal order

Abstract

The fractional-order Newton-Leipnik system (FoNLs) was studied in this paper from the point of view of two strange attractors. Within the same parameter condition of FoNLs, the different of initial conditions are numerically studied. The ranges are relatively wide for the different initial conditions used in this analysis and the synchronization of two identical FoNLs is investigated in this paper. An active control is the technique used for achieving the synchronization between chaotic FoNLs. Based on the theory of Laplace transformation (LTF), the conditions for achieving synchronisation of fractional order systems are studied. In order to verify the efficiency and viability of this process, numerical simulations are given, so the outcome of the process is simultaneously validated with theoretical models and computational methods. The above concept is also applied by this paper to secure communications using the chaotic masking system.

Subject Classification: (2010):

• 34D06
• 34D20

Keywords:

• Newton leipnik
• Fractional calculus
• Chaotic system
• Active control
• Synchronization
• Secure communication
• Cryptography