Using Shannon Entropy and Contagion Index to Interpret Pattern Self-Organization in a Dynamic Vegetation-Sand Model
Vegetation pattern is one of the most important self-organized patterns in ecological systems. The formation mechanism of vegetation patterns has been attributed to dynamic bifurcations, while from the external perspective, the regularity of patterns could also be influenced by some statistical indi...
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| Format: | Article |
| Language: | English |
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IEEE
2020-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/8963966/ |
| _version_ | 1818732839017906176 |
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| author | Feifan Zhang Lei Yao Wenjiao Zhou Qinjing You Huayong Zhang |
| author_facet | Feifan Zhang Lei Yao Wenjiao Zhou Qinjing You Huayong Zhang |
| author_sort | Feifan Zhang |
| collection | DOAJ |
| description | Vegetation pattern is one of the most important self-organized patterns in ecological systems. The formation mechanism of vegetation patterns has been attributed to dynamic bifurcations, while from the external perspective, the regularity of patterns could also be influenced by some statistical indicators. Shannon entropy and contagion index are the most commonly used indicators of landscape diversity and connectivity in landscape ecology. These two indicators can explain the self-organization of vegetation patterns. In this research, vegetation patterns are neither randomly generated nor captured from vegetation map. Based on a discrete vegetation-sand model, formation process of vegetation patterns are simulated in different situations of bifurcations. Given different situations of bifurcations (Turing bifurcation, Neimark-Sacker bifurcation and Turing-Neimark-Sacker bifurcation), several formation processes are studied. Along the process, the corresponding Shannon entropy and contagion index of simulated vegetation patterns are calculated based on slightly modified calculation formulas. Comparing different variation curves of Shannon entropy and contagion index, we can see that variation trends of both Shannon entropy and contagion index are closely related to the formation stages of vegetation patterns. The different final values of Shannon entropy and contagion index in different patterns can be used to determine which bifurcation is in dominant when both bifurcations occur. |
| first_indexed | 2024-12-17T23:39:56Z |
| format | Article |
| id | doaj.art-006b0845162f4d8db65ee2bcd1464222 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-17T23:39:56Z |
| publishDate | 2020-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-006b0845162f4d8db65ee2bcd14642222022-12-21T21:28:27ZengIEEEIEEE Access2169-35362020-01-018172211723010.1109/ACCESS.2020.29682428963966Using Shannon Entropy and Contagion Index to Interpret Pattern Self-Organization in a Dynamic Vegetation-Sand ModelFeifan Zhang0https://orcid.org/0000-0002-1992-089XLei Yao1https://orcid.org/0000-0003-0799-1700Wenjiao Zhou2https://orcid.org/0000-0002-7722-725XQinjing You3https://orcid.org/0000-0001-5430-8738Huayong Zhang4https://orcid.org/0000-0001-8898-8567Research Center for Engineering Ecology and Nonlinear Science, North China Electric Power University, Beijing, ChinaResearch Center for Engineering Ecology and Nonlinear Science, North China Electric Power University, Beijing, ChinaResearch Center for Engineering Ecology and Nonlinear Science, North China Electric Power University, Beijing, ChinaResearch Center for Engineering Ecology and Nonlinear Science, North China Electric Power University, Beijing, ChinaResearch Center for Engineering Ecology and Nonlinear Science, North China Electric Power University, Beijing, ChinaVegetation pattern is one of the most important self-organized patterns in ecological systems. The formation mechanism of vegetation patterns has been attributed to dynamic bifurcations, while from the external perspective, the regularity of patterns could also be influenced by some statistical indicators. Shannon entropy and contagion index are the most commonly used indicators of landscape diversity and connectivity in landscape ecology. These two indicators can explain the self-organization of vegetation patterns. In this research, vegetation patterns are neither randomly generated nor captured from vegetation map. Based on a discrete vegetation-sand model, formation process of vegetation patterns are simulated in different situations of bifurcations. Given different situations of bifurcations (Turing bifurcation, Neimark-Sacker bifurcation and Turing-Neimark-Sacker bifurcation), several formation processes are studied. Along the process, the corresponding Shannon entropy and contagion index of simulated vegetation patterns are calculated based on slightly modified calculation formulas. Comparing different variation curves of Shannon entropy and contagion index, we can see that variation trends of both Shannon entropy and contagion index are closely related to the formation stages of vegetation patterns. The different final values of Shannon entropy and contagion index in different patterns can be used to determine which bifurcation is in dominant when both bifurcations occur.https://ieeexplore.ieee.org/document/8963966/Contagion indexNeimark-Sacker bifurcationShannon entropyTuring bifurcation |
| spellingShingle | Feifan Zhang Lei Yao Wenjiao Zhou Qinjing You Huayong Zhang Using Shannon Entropy and Contagion Index to Interpret Pattern Self-Organization in a Dynamic Vegetation-Sand Model IEEE Access Contagion index Neimark-Sacker bifurcation Shannon entropy Turing bifurcation |
| title | Using Shannon Entropy and Contagion Index to Interpret Pattern Self-Organization in a Dynamic Vegetation-Sand Model |
| title_full | Using Shannon Entropy and Contagion Index to Interpret Pattern Self-Organization in a Dynamic Vegetation-Sand Model |
| title_fullStr | Using Shannon Entropy and Contagion Index to Interpret Pattern Self-Organization in a Dynamic Vegetation-Sand Model |
| title_full_unstemmed | Using Shannon Entropy and Contagion Index to Interpret Pattern Self-Organization in a Dynamic Vegetation-Sand Model |
| title_short | Using Shannon Entropy and Contagion Index to Interpret Pattern Self-Organization in a Dynamic Vegetation-Sand Model |
| title_sort | using shannon entropy and contagion index to interpret pattern self organization in a dynamic vegetation sand model |
| topic | Contagion index Neimark-Sacker bifurcation Shannon entropy Turing bifurcation |
| url | https://ieeexplore.ieee.org/document/8963966/ |
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