A sustainability condition for stochastic forest model
Ton Viet Ta, Linh Thi Hoai Nguyen, Atsushi Yagi
TL;DR
This paper analyzes a stochastic forest model, establishing conditions for sustainability and decline, proving mathematical properties of solutions, and providing numerical examples to illustrate the dynamics.
Contribution
It introduces a new stochastic forest model with proven existence, uniqueness, and boundedness of solutions, and provides criteria for forest sustainability and decline.
Findings
Existence and uniqueness of solutions proved
A sufficient condition for forest sustainability established
Numerical examples illustrating model dynamics provided
Abstract
A stochastic forest model of young and old age class trees is studied. First, we prove existence, uniqueness and boundedness of global nonnegative solutions. Second, we investigate asymptotic behavior of solutions by giving a sufficient condition for sustainability of the forest. Under this condition, we show existence of a Borel invariant measure. Third, we present several sufficient conditions for decline of the forest. Finally, we give some numerical examples.
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Taxonomy
TopicsMathematical and Theoretical Epidemiology and Ecology Models · Stability and Controllability of Differential Equations · Nonlinear Differential Equations Analysis