Abstract: A mathematical model is proposed considering the forest biomass density B(t), density of wood based industries W(t) and density of synthetic industries S(t). It is assumed that the forest biomass grows logistically in the absence of wood based industries, but depletion of forestry biomass is due to presence of wood based industries. The growth of wood based industries depends on B(t), while S(t) grows at a constant rate, independent of B(t). Further there is a competition between W(t) and S(t) according to market demand. The proposed model has four ecologically feasible steady states, namely, E1: forest biomass free and wood industries free equilibrium; E2: wood industries free equilibrium and two coexisting equilibria E∗1 , E∗2 . Behavior of the system near all feasible equilibria is analyzed using the stability theory of differential equations. In the proposed model, the natural depletion rate h1 is a crucial parameter and system exhibits Hopf-bifurcation about the non-trivial equilibrium with respect to h1. The analytical results are verified using numerical simulation.
Abstract: This study focuses on an evaluation of Hokkaido which
is the northernmost and largest prefecture by surface area in Japan and
particularly on two points: the rivalry between all kinds of land use
such as urban land and agricultural and forestry land in various cities
and their surrounding areas and the possibilities for forestry biomass in
areas other than those mentioned above and grasps which areas require
examination of the nature of land use control and guidance through
conducting land use analysis at the district level using GIS
(Geographic Information Systems). The results of analysis in this
study demonstrated that it is essential to divide the whole of Hokkaido
into two areas: those within delineated city planning areas and those
outside of delineated city planning areas and to conduct an evaluation
of each land use control.
In delineated urban areas, particularly urban areas, it is essential to
re-examine land use from the point of view of compact cities or smart
cities along with conducting an evaluation of land use control that
focuses on issues of rivalry between all kinds of land use such as urban
land and agricultural and forestry land. In areas outside of delineated
urban areas, it is desirable to aim to build a specific community
recycling range based on forest biomass utilization by conducting an
evaluation of land use control concerning the possibilities for forest
biomass focusing particularly on forests within and outside of city
planning areas.