Unveiling stabilization mechanisms in a chaotic fractional Cryosphere model

Abstract

This article investigates the influence of chaos control and time delay on a chaotic surface energy balance-mass balance model of the Cryosphere. This research delves into the effectiveness of employing the active control method to stabilize chaotic systems with different fractional orders. Moreover, the investigation uncovers a noteworthy aspect of system dynamics, highlighting the role of time delay as a stabilizing element in chaotic systems. The generalized predictor-corrector method has been used to solve the fractional delayed and non-delayed systems. Numerical simulations show that the addition of time lag confers stability to the chaotic model for fractional orders $\alpha=1$ and $0.95$. Remarkably, for $\alpha=0.90, 0.85, 0.80$ and $0.75$, the delayed model transitions into an asymptotically stable state, revealing the significant stabilizing effect of time delay.