2021 Fiscal Year Research-status Report
Building a Theory of Regular Structures for Non-Autonomous and Quasi-Linear Rough Evolution Equations, and Applying the Theory to Forest Kinematic Ecosystems
| Project/Area Number |
19K14555
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| Research Institution | Kyushu University |
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Principal Investigator |
タ・ビィエ トン 九州大学, 農学研究院, 准教授 (30771109)
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| Project Period (FY) |
2019-04-01 – 2023-03-31
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| Keywords | forest transition / swarming behavior / evolution equations |
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| Outline of Annual Research Achievements |
1) We have studied a forest kinematic ecosystem which includes densities of your and old trees, and density of seeds: a) A model of SPDEs has been constructed; b) The existence of global solutions has been proved.
2) We have investigated a forest transition which includes forest land size, agricultural land size, and abandonment land size: a) constructed a mathematical model of SDEs; b) proved the existence of global solutions in the "main" cases of initial data. c) performed numerical simulations in some cases of parameters. The Python programming language has been used for simulations.
3) We have investigated swarming behaviors: a) observed animal swarms avoiding predator to have a rule; b) constructed a mathematical model of SDEs for predator-avoidance swarms by using the rule; c) performed simulations in some cases. The results are consistent with real observations of biologists. We use Python for simulations.
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| Current Status of Research Progress |
Current Status of Research Progress
3: Progress in research has been slightly delayed.
Reason
As stated in "Summary of Research Achievements", in 1) we studied the forest kinematic model. We spent much time on studying but did not succeed in showing
+) the long-time behavior of solutions.
+) correct approximations for "spatial noise" term.
(In 2) and 3), there is only "time noise". We succeeded in handling "time noise".)
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| Strategy for Future Research Activity |
We will continue to study problems stated in "Summary of Research Achievements":
1) For forest kinematic model, we will try to make simulations using other approximations for "spatial noise" term.
2) For forest transition model, we will prove the existence of global solutions in the "critical" cases of initial data and perform simulations. We are now writing a paper about this model.
3) For predator-avoidance swarming, we will continue to find out patterns by changing parameters. We are now writing a paper about this model too.
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| Causes of Carryover |
It was still impossible to have face-to-face collaborations with international researchers due to coronavirus outbreak in this fiscal year. I would like to carry the amount to the next fiscal year. I do hope that the travel situation will be improved.
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