Analysis of two novel chaotic systems with a hyperbolic sinusoidal nonlinearity and their adaptive chaos synchronization

In this research work, we first describe two novel 3-D chaotic system with a hyperbolic sinusoidal (or cosinusoidal) nonlinearity and two quadratic nonlinearities. Next, we describe a qualitative analysis of the two novel chaotic systems, denoted as chaotic systems (A) and (B). We detail the important properties of the chaotic systems (A) and (B). Next, we obtain the Lyapunov exponents and Kaplan-Yorke dimension of the chaotic systems (A) and (B). It is observed that the maximal Lyapunov exponent (MLE) for the novel chaotic systems (A) and (B) have a large value, viz. L₁ =11.7943 for system (A) and L₁ = 15.1121 for system (B). Thus, both chaotic systems (A) and (B) depict strong chaotic behaviour. Next, this research work derives adaptive synchronizers for novel chaotic systems (A) and (B) with unknown system parameters. We have shown MATLAB simulations to show the adaptive synchronizers design of the novel chaotic systems (A) and (B) with unknown system parameters.