Comparative analysis of two novel chaotic systems, and validation of hybrid function projective and complete synchronization using active-adaptive control

Abstract This study investigates the nonlinear characteristics of two novel 3D-chaotic models using phase portraits, bifurcation diagrams, Lyapunov exponents, time series analysis, and Poincaré maps. Here, we have examined hybrid-function projective and complete synchronization schemes via adaptive and active control methods. Moreover, the performance of hybrid-function projective synchronization, utilizing sine, cosine, and exponential terms, is compared to complete synchronization through two control strategies. Our designed controllers ensure asymptotic global chaotic synchronization based on Lyapunov stability principles. We have also compared our results with other competitive schemes and validated the theoretical findings through simulations on the MATLAB platform.