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Volume 13
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10.3390/sym13081547
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Article

Analysis of the Dynamical Behaviour of a Two-Dimensional Coupled Ecosystem with Stochastic Parameters

by
Xuefen Li
1,* and
Fangfang Shen
2
1
College of History and Ethnic Culture, Guizhou University, Guiyang 550025, China
2
School of Mathematics and Statistics, Guangxi Normal University, Guiling 541004, China
*
Author to whom correspondence should be addressed.
Symmetry 2021, 13(8), 1547; https://doi.org/10.3390/sym13081547
Submission received: 3 July 2021 / Revised: 8 August 2021 / Accepted: 20 August 2021 / Published: 23 August 2021
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Abstract

Because the two-dimensional coupled ecosystem has perfect symmetry, the dynamical behavior of symmetric dynamical system is discussed. The analysis of the dynamical behavior of a two-dimensional coupled ecosystem with stochastic parameters is explored in this paper. Firstly, a two-dimensional coupled ecosystem with stochastic parameters is established, it is transformed into a deterministic equivalent system by orthogonal polynomial approximation. Then, analysis of the dynamical behaviour of equivalently deterministic coupled ecosystems is performed using stability theory. At last, we analyzed the dynamical behaviour of non-trivial points by means of the mathematics analysis method and found the influence of random parameters on asymptotic stability in coupled ecosystem is prominent. The dynamical behaviour analysis results were verified by numerical simulation.
Keywords: coupled ecosystem; stochastic parameters; dynamical behaviour; numerical simulation coupled ecosystem; stochastic parameters; dynamical behaviour; numerical simulation

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MDPI and ACS Style

Li, X.; Shen, F. Analysis of the Dynamical Behaviour of a Two-Dimensional Coupled Ecosystem with Stochastic Parameters. Symmetry 2021, 13, 1547. https://doi.org/10.3390/sym13081547

AMA Style

Li X, Shen F. Analysis of the Dynamical Behaviour of a Two-Dimensional Coupled Ecosystem with Stochastic Parameters. Symmetry. 2021; 13(8):1547. https://doi.org/10.3390/sym13081547

Chicago/Turabian Style

Li, Xuefen, and Fangfang Shen. 2021. "Analysis of the Dynamical Behaviour of a Two-Dimensional Coupled Ecosystem with Stochastic Parameters" Symmetry 13, no. 8: 1547. https://doi.org/10.3390/sym13081547

APA Style

Li, X., & Shen, F. (2021). Analysis of the Dynamical Behaviour of a Two-Dimensional Coupled Ecosystem with Stochastic Parameters. Symmetry, 13(8), 1547. https://doi.org/10.3390/sym13081547

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