Computation of Stability Criterion for Fractional Ocean Circulation Box Model Using Optimal Routh—Hurwitz Conditions

Abstract

Atlantic ocean thermohaline circulation is a deep ocean circulation occur in the Atlantic ocean which shows mixed of salt and freshwater transportation. The ocean circulation box model is defined to cover the large-scale behavior of the thermohaline circulation. On the other hand, fractional order dynamical systems are more flexible and realistic for real-life problems if compare with integer order dynamical systems. Hence, research on the stability for fractional dynamical systems is still infant and more difficult to analyze analytically. In this paper, we will extend the ocean circulation 3-box model into fractional order and investigate stability criterion for this fractional model by applying fractional Routh-Hurwitz conditions. Routh-Hurwitz conditions allow us to find the range of adjustable control parameter F1 which can detect the stability criterion for the fractional ocean circulation model.