Abstract
The terrestrial carbon cycle is the most important constitution and plays a prominent role in the global carbon cycle. This paper investigates the dynamical behaviours and mathematical properties of a time fractional-order atmosphere-soil-land plant carbon cycle system. We give a sufficient condition for existence and uniqueness of the solution, and obtain the conditions for local asymptotically stable of the equilibrium points by using fractional Routh-Hurwitz stability conditions. Furthermore, we introduce a discretization process to discretize this fractional-order system, and study the necessary and sufficient conditions of stability of the discretization system. It shows that the stability of the discretization system is impacted by the system's fractional parameter. Numerical simulations show the richer dynamical behaviours of the fractional-order system and verify the theoretical results.
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