Modelling Forest Growth Indices on Vegetation Pattern Formation

Peter Kwesi Nyarko; Christiana Cynthia Nyarko

doi:doi:10.11648/j.ajam.20210904.13

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Modelling Forest Growth Indices on Vegetation Pattern Formation

Peter Kwesi Nyarko, Christiana Cynthia Nyarko

Published in American Journal of Applied Mathematics (Volume 9, Issue 4)

Received: 16 July 2021 Accepted: 24 July 2021 Published: 2 August 2021

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Abstract

Forest dynamics is mostly concerned with the changes in forest structure and composition over time, including its behavior in response to anthropogenic and natural destructions which is one of the primary evidence of forest change. This study presents the dynamics of vegetation pattern formation taken into account all the interaction measure indices such as light, water, temperature and nutrients fertility. Michaelis-Menten Kinetics and a Continuous-Time Markov (CTM) method were employed to determine plant metabolism responses to all the inputs. The Continuous-Time Markov (CTM) technique was then used to obtain a simple plant growth component by synthesizing the four - measure indices or resources (light, water and nutrients and temperature). Stability analysis of the formulated model was carried out to determine the possible phase regions associated with the various stability states for a sufficiently precise representation of the essential features of the model. Results of the β values for the spatial patterns obtained indicate association or interaction among the various soil fertility levels under different water conditions. For instance, a β value of 0.05605 represents control fertility under arid conditions, indicates a vegetation pattern with numerous and wider patches of bare or almost bare land compared to patterns exhibited by the other fertility levels.

Published in	American Journal of Applied Mathematics (Volume 9, Issue 4)
DOI	10.11648/j.ajam.20210904.13
Page(s)	108-122
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

Vegetation, Pattern, Control Fertility, Low Fertility, Average Water, Aridity

References

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APA Style

Peter Kwesi Nyarko, Christiana Cynthia Nyarko. (2021). Modelling Forest Growth Indices on Vegetation Pattern Formation. American Journal of Applied Mathematics, 9(4), 108-122. https://doi.org/10.11648/j.ajam.20210904.13

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ACS Style

Peter Kwesi Nyarko; Christiana Cynthia Nyarko. Modelling Forest Growth Indices on Vegetation Pattern Formation. Am. J. Appl. Math. 2021, 9(4), 108-122. doi: 10.11648/j.ajam.20210904.13

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AMA Style

Peter Kwesi Nyarko, Christiana Cynthia Nyarko. Modelling Forest Growth Indices on Vegetation Pattern Formation. Am J Appl Math. 2021;9(4):108-122. doi: 10.11648/j.ajam.20210904.13

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@article{10.11648/j.ajam.20210904.13,
  author = {Peter Kwesi Nyarko and Christiana Cynthia Nyarko},
  title = {Modelling Forest Growth Indices on Vegetation Pattern Formation},
  journal = {American Journal of Applied Mathematics},
  volume = {9},
  number = {4},
  pages = {108-122},
  doi = {10.11648/j.ajam.20210904.13},
  url = {https://doi.org/10.11648/j.ajam.20210904.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20210904.13},
  abstract = {Forest dynamics is mostly concerned with the changes in forest structure and composition over time, including its behavior in response to anthropogenic and natural destructions which is one of the primary evidence of forest change. This study presents the dynamics of vegetation pattern formation taken into account all the interaction measure indices such as light, water, temperature and nutrients fertility. Michaelis-Menten Kinetics and a Continuous-Time Markov (CTM) method were employed to determine plant metabolism responses to all the inputs. The Continuous-Time Markov (CTM) technique was then used to obtain a simple plant growth component by synthesizing the four - measure indices or resources (light, water and nutrients and temperature). Stability analysis of the formulated model was carried out to determine the possible phase regions associated with the various stability states for a sufficiently precise representation of the essential features of the model. Results of the β values for the spatial patterns obtained indicate association or interaction among the various soil fertility levels under different water conditions. For instance, a β value of 0.05605 represents control fertility under arid conditions, indicates a vegetation pattern with numerous and wider patches of bare or almost bare land compared to patterns exhibited by the other fertility levels.},
 year = {2021}
}

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TY  - JOUR
T1  - Modelling Forest Growth Indices on Vegetation Pattern Formation
AU  - Peter Kwesi Nyarko
AU  - Christiana Cynthia Nyarko
Y1  - 2021/08/02
PY  - 2021
N1  - https://doi.org/10.11648/j.ajam.20210904.13
DO  - 10.11648/j.ajam.20210904.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 108
EP  - 122
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20210904.13
AB  - Forest dynamics is mostly concerned with the changes in forest structure and composition over time, including its behavior in response to anthropogenic and natural destructions which is one of the primary evidence of forest change. This study presents the dynamics of vegetation pattern formation taken into account all the interaction measure indices such as light, water, temperature and nutrients fertility. Michaelis-Menten Kinetics and a Continuous-Time Markov (CTM) method were employed to determine plant metabolism responses to all the inputs. The Continuous-Time Markov (CTM) technique was then used to obtain a simple plant growth component by synthesizing the four - measure indices or resources (light, water and nutrients and temperature). Stability analysis of the formulated model was carried out to determine the possible phase regions associated with the various stability states for a sufficiently precise representation of the essential features of the model. Results of the β values for the spatial patterns obtained indicate association or interaction among the various soil fertility levels under different water conditions. For instance, a β value of 0.05605 represents control fertility under arid conditions, indicates a vegetation pattern with numerous and wider patches of bare or almost bare land compared to patterns exhibited by the other fertility levels.
VL  - 9
IS  - 4
ER  -

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Author Information

Peter Kwesi Nyarko

Department of Mathematical Sciences, Faculty of Engineering, University of Mines and Technology, Tarkwa, Ghana
Christiana Cynthia Nyarko

Department of Mathematical Sciences, Faculty of Engineering, University of Mines and Technology, Tarkwa, Ghana

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Peter Kwesi Nyarko, Christiana Cynthia Nyarko. (2021). Modelling Forest Growth Indices on Vegetation Pattern Formation. American Journal of Applied Mathematics, 9(4), 108-122. https://doi.org/10.11648/j.ajam.20210904.13

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ACS Style

Peter Kwesi Nyarko; Christiana Cynthia Nyarko. Modelling Forest Growth Indices on Vegetation Pattern Formation. Am. J. Appl. Math. 2021, 9(4), 108-122. doi: 10.11648/j.ajam.20210904.13

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AMA Style

Peter Kwesi Nyarko, Christiana Cynthia Nyarko. Modelling Forest Growth Indices on Vegetation Pattern Formation. Am J Appl Math. 2021;9(4):108-122. doi: 10.11648/j.ajam.20210904.13

Copy | Download

@article{10.11648/j.ajam.20210904.13,
  author = {Peter Kwesi Nyarko and Christiana Cynthia Nyarko},
  title = {Modelling Forest Growth Indices on Vegetation Pattern Formation},
  journal = {American Journal of Applied Mathematics},
  volume = {9},
  number = {4},
  pages = {108-122},
  doi = {10.11648/j.ajam.20210904.13},
  url = {https://doi.org/10.11648/j.ajam.20210904.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20210904.13},
  abstract = {Forest dynamics is mostly concerned with the changes in forest structure and composition over time, including its behavior in response to anthropogenic and natural destructions which is one of the primary evidence of forest change. This study presents the dynamics of vegetation pattern formation taken into account all the interaction measure indices such as light, water, temperature and nutrients fertility. Michaelis-Menten Kinetics and a Continuous-Time Markov (CTM) method were employed to determine plant metabolism responses to all the inputs. The Continuous-Time Markov (CTM) technique was then used to obtain a simple plant growth component by synthesizing the four - measure indices or resources (light, water and nutrients and temperature). Stability analysis of the formulated model was carried out to determine the possible phase regions associated with the various stability states for a sufficiently precise representation of the essential features of the model. Results of the β values for the spatial patterns obtained indicate association or interaction among the various soil fertility levels under different water conditions. For instance, a β value of 0.05605 represents control fertility under arid conditions, indicates a vegetation pattern with numerous and wider patches of bare or almost bare land compared to patterns exhibited by the other fertility levels.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Modelling Forest Growth Indices on Vegetation Pattern Formation
AU  - Peter Kwesi Nyarko
AU  - Christiana Cynthia Nyarko
Y1  - 2021/08/02
PY  - 2021
N1  - https://doi.org/10.11648/j.ajam.20210904.13
DO  - 10.11648/j.ajam.20210904.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 108
EP  - 122
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20210904.13
AB  - Forest dynamics is mostly concerned with the changes in forest structure and composition over time, including its behavior in response to anthropogenic and natural destructions which is one of the primary evidence of forest change. This study presents the dynamics of vegetation pattern formation taken into account all the interaction measure indices such as light, water, temperature and nutrients fertility. Michaelis-Menten Kinetics and a Continuous-Time Markov (CTM) method were employed to determine plant metabolism responses to all the inputs. The Continuous-Time Markov (CTM) technique was then used to obtain a simple plant growth component by synthesizing the four - measure indices or resources (light, water and nutrients and temperature). Stability analysis of the formulated model was carried out to determine the possible phase regions associated with the various stability states for a sufficiently precise representation of the essential features of the model. Results of the β values for the spatial patterns obtained indicate association or interaction among the various soil fertility levels under different water conditions. For instance, a β value of 0.05605 represents control fertility under arid conditions, indicates a vegetation pattern with numerous and wider patches of bare or almost bare land compared to patterns exhibited by the other fertility levels.
VL  - 9
IS  - 4
ER  -

Copy | Download