Parameter estimation and antisynchronization of multi-wing chaotic flows via adaptive control

In this paper, we study the antisynchronization by adaptive controllers, of a generalized multi-wing butterfly attractor design template using the four-wing (n=1) structure as a case study. It was assumed that the parameters of the response system are not available for measurement while the two systems are identical. The direct coupling of the sawtooth wave functions of the identical systems with appropriate tuning of the gain coefficients of the adaptive nonlinear controllers resulted to the antisychronized trajectories of the drive and response systems in two-dimension space. Simulation results show that the chaotic regimes achieved antisychrony while the error and parameter error systems asymptotically stabilized in finite time in the sense of Lyapunov.