Abstract

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.

Keywords: Projective Synchronization, Nonlinearities, Scaling factors, Runge­Kutta, and Quadratic and quartic nonlinearities