Bifurcation,Several Equilibria and Multiple Growth Paths in the Solow Model with Endogenous Demographic Transition

In this paper,the endogenous demographic transition function is integrated into the classical Solow model. It is proven that the differential equation which describes the model at least has a nonzero equilibrium. The differential equation has several equilibria when the technological level or the saving rate is not high enough and undergoes bifurcation at some specified parame-ter values. Therefore,the economy described by the model pre-sents multiple growth paths and ＂Malthusian Poverty Trap＂ when the technological level or the saving rate is low.

THE OPTIMAL ALLOCATION ABOUT CAPITAL AND LABOR IN THE ECONOMIC GROWTH WITH AN ENDOGENOUS TECHNICAL PROGRESS MODEL

In this paper, the balanced economic growth path was considered in a new growth model with endogenous technical progress. It is not only obtained the optimal allocation about capital and labor between a goods-producing sector and a R&D Sector, but also the optimal value of saving rates. By discussing the effect of parameters, it are also got the following results: When the rate of time preference (discount factor) rising, the fractions of Capital and labor in the goods-producing sector will increase, the fractions in R&D sector and the saving rates will decrease; When the population grows rapidly, the result will be contrary.

AN URBAN ECONOMIC GROWTH MODEL WITH ENDOGENOUS INFRASTRUCTURE ALLOCATION

In this paper, an urban economic growth model with endogenous infrastructure allocation is given by introducing the two-variable utility function for city＇s inhabitant. A twodimensional dynamical system is obtained by solving the utility maximization problem and it is proved that this system has the unique non-zero equilibrium which is a saddle. The model has the unique optimal growth and an optimal rate of infrastructure allocation.

An Improved Cass-Koopmans Model with Endogenous Fertility under the CES Production Technology

Under the CES production technology, an improved Cass Coopmans model with solvable endogenous fertility is given. We prove that there are multiple growth paths and multiple steady states when CES 0<σ<1 and the technology level is high enough; the growth path and the steady state is unique when σ>1 and the ratio of capital is smaller than a constant. So, the dynamic system which describes the model undergoes a bifurcation when σ=1 . We discuss the economic sense of the main results we give.

THE DYNAMICS OF FERTILITY IN C-K MODEL WITH ENDOGENOUS FERTILITY

Based on the Cass-Koopmans Model with endogenous fertility given in the paper [1-4], the fertility dynamics is discussed in this paper. It is proved that the first quadrant of the k,c plane is separated into two parts by a increasingly differentiable curve. The fertility increases with time on the upper half and decreases with time on the lower half. The fertility decreases along one arm of the economic growth path on which the per capita capital and per consumption increase and increases along the other arm of the economic growth path on which the per capita capital and per person consumption decrease under the condition 0 <θ≤α. This confirms the empirical finds that negative relationship between the economic growth and population growth.

Limiting stand density and basal area projection models for even-aged Tecomella undulata plantations in a hot arid region of India

This paper presents equations for estimating limiting stand density for Z undulata plantations grown in hot desert areas of Raj asthan State in India. Five different stand level basal area projection models, belonging to the path invariant algebraic difference form of a non-linear growth function, were also tested and compared. These models can be used to predict future basal area as a function of stand variables like dominant height and stem number per hectare and are necessary for reviewing different silvicultural treatment options. Data from 22 sample plots were used for modelling. An all possible growth intervals data structure was used. Both, qualitative and quantitative criteria were used to compare alternative models. The Akaike＇s information criteria differ- ence statistic was used to analyze the predictive ability of the models. Results show that the model proposed by Hui and Gadow performed best and hence this model is recommended for use in predicting basal area development in 12 undulata plantations in the study area. The data used were not from thinned stands, and hence the models may be less accurate when used for predictions when natural mortality is very significant.

THE C-K MODEL WITH SOLVABLE ENDOGENOUS FERTILITY

In this paper,a C\|K model with solvable endogenous fertility under the strongly additive utility function is presented.The discrimination conditions of the existence of the nonzero steady states are given.Under a kind of utility function and production function,we prove that these conditions are satisfied and the economy at least has an optimal growth path.The positional relationship of the multiple steady states on the plane is discussed when multiple steady states and multiple growth paths exist.By numerical analysis,the fertility decreases with the per capita capital and per capita consumption increasing and increases with the per capita capital and per capita consumption decreasing on the economic growth path are obtained.

An Improved Peridynamic Model with Energy-Based Micromodulus Correction Method for Fracture in Particle Reinforced Composites

We introduce an improved bond-based peridynamic(BPD)model for simulating brittle fracture in particle reinforced composites based on a micromodulus correction approach.In the peridynamic(PD)constitutive model of particle reinforced composites,three kinds of interactive bond forces are considered,and precise definition of mechanical properties for PD bonds is essential for the fracture analysis in particle reinforced composites.A new micromodulus model of PD bonds for particle reinforced composites is proposed based on the equivalence between the elastic strain energy density of classical continuum mechanics and peridynamic model and the harmonic average approach.The damage of particle reinforced composites is defined locally at the level of pairwise bond,and the critical stretch criterion is described as a function of fracture energy based on the composite failure theory.The algorithm procedure for the improved BPD model based on the finite element/discontinuous Galerkin finite element method is brought forward in detail.Several numerical examples are performed to test the feasibility and effectiveness of the proposed model and algorithm in analysis of elastic deformation,crack nucleation and propagation in particle reinforced composites.Additionally,the impact of distribution,shape and size of particles on the fractures of composite materials are also investigated.Numerical results demonstrate that the improved BPD model can effectively be used to analyze the fracture in particle reinforced composites.