Dynamical behaviour of fractional-order atmosphere-soil-land plant carbon cycle system

Wenjun Liu; Zhijing Chen; Wenjun Liu; Zhijing Chen

doi:10.3934/math.2020105

AIMS Mathematics

2020, Volume 5, Issue 2: 1532-1549. doi: 10.3934/math.2020105

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Research article

Dynamical behaviour of fractional-order atmosphere-soil-land plant carbon cycle system

Wenjun Liu ^,,
Zhijing Chen

School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China

Received: 03 October 2019 Accepted: 13 January 2020 Published: 21 January 2020
MSC : 34A08, 37N25

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.
- dynamical behaviour,
- fractional-order system,
- carbon cycle
Citation: Wenjun Liu, Zhijing Chen. Dynamical behaviour of fractional-order atmosphere-soil-land plant carbon cycle system[J]. AIMS Mathematics, 2020, 5(2): 1532-1549. doi: 10.3934/math.2020105

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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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