We present a tree-grass competition model on the basis of the forest kinematic model due to Kuznetsov-Antonovsky-Biktashev-Aponina [6]. The main purpose of the paper is to construct global solutions and to construct a dynamical system generated by the model equations. By numerical computations, we also show that our model actually admits coexisting solutions of trees and grass.

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In the preceding paper [21], we have introduced a tree-grass competition model for describing the kinematics of forest-grassland system and have found that the model admits some solutions showing coexistence of forest and grassland. The purpose of the present paper is then to investigate the boundary curves which partition forest patches and grassland patches. Through the investigations, we want to clarify the properties of segregation patterns of tree-grass coexistence in terms of forest connectivity. As it is very difficult to handle the very model equations in [21], we will make a reduction of the full model by extremely restricting the range where the parameters of equations can vary.

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The purpose of this study is to introduce and study the concept of biisotonic spaces. In this study, we introduce the notion of the continuous map between bi-isotonic spaces and give the characterizations of bi-isotonic maps. Moreover, we explore the topological concepts of separation axioms in bi-isotonic spaces.

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