Projective Synchronization of a 3D Chaotic System with Quadratic and Quartic Nonlinearities
Babatunde A. Idowu1, Kehinde S. Oyeleke2, Cornelius O. Ogabi3, and Olasunkanmi I. Olusola4
1Lagos State University, Nigeria, 2Lagos State University, Nigeria, 3Lagos State University, Nigeria, and 4Lagos State University, Nigeria
Introduction: Chaos is a state of dynamical systems whose apparently random states of disorder and irregularities are often governed by deterministic laws that are highly sensitive to initial conditions. In this work, the projective synchronization of two identical threedimensional chaotic system with quadratic and quartic nonlinearities was considered as well as the equilibrium and stability analysis of the system. The projective synchronization with same and different scaling factors was carried out in order to establish its synchronization.
Aim: To achieve projective synchronization of two identical threedimensional chaotic system with quadratic and quartic nonlinearities synchronizing to a scaling
factor and also present the equilibrium and stability analysis of the system.
Methods: We employed the adaptive synchronization technique to achieve projective synchronization of the system (master and slave) with different scaling factors, beta and the fourthorder RungeKutta algorithm was used for numerical solutions.
Results: In this work, the projective synchronization of two identical threedimensional systems with quadratic and quartic nonlinearities was achieved with the
same and different scaling factors, beta. The equilibrium and stability analysis of the system was also presented.
Conclusion: The investigated projective synchronization behaviour of two identical threedimensional system with two nonlinearities (quadratic and quartic) was
achieved for cases where the scaling factor is the same and when different. This shows that projective synchronization can be achieved for systems with varying
nonlinearities even when the scaling factor is different and this suggests its use in communication using chaotic wave forms as carriers, perhaps with a view to securing communication.
Projective Synchronization, Nonlinearities, Scaling factors, RungeKutta, and Quadratic and quartic nonlinearities