A class of n-dimensional ODEs with up to n feedbacks from the n’th variable is analysed. The feedbacks are represented by non-specific, bounded, non-negative C<sup>1</sup> functions. The main result is th...A class of n-dimensional ODEs with up to n feedbacks from the n’th variable is analysed. The feedbacks are represented by non-specific, bounded, non-negative C<sup>1</sup> functions. The main result is the formulation and proof of an easily applicable criterion for existence of a globally stable fixed point of the system. The proof relies on the contraction mapping theorem. Applications of this type of systems are numerous in biology, e.g., models of the hypothalamic-pituitary-adrenal axis and testosterone secretion. Some results important for modelling are: 1) Existence of an attractive trapping region. This is a bounded set with non-negative elements where solutions cannot escape. All solutions are shown to converge to a “minimal” trapping region. 2) At least one fixed point exists. 3) Sufficient criteria for a unique fixed point are formulated. One case where this is fulfilled is when the feedbacks are negative.展开更多
The present paper investigates how neighborhood effects are connected to chronic poverty. We examine a large sample of groups of households and find that neighborhood effects are significant in a majority of groups, e...The present paper investigates how neighborhood effects are connected to chronic poverty. We examine a large sample of groups of households and find that neighborhood effects are significant in a majority of groups, especially in the poorest groups. People living in poor communities tend to suffer from poverty over time. It is of theoretical and empirical importance to explore how neighborhood effects are interrelated with chronic poverty and the channels through which this occurs. Unlike other econometric analyses, we establish a multilevel econometric model to show that： （i） it is difficult for an individual living in a neighborhood with a high proportion of agricultural labor, low education levels, and poor transport and telecommunication infrastructure to escape from poverty traps; （ii） neighborhood effects dominate in poor communities; and （iii） although poverty is affected by group-level factors, individual factors still play a dominant role in regards to escaping poverty when income surpasses a threshold level Therefore, policy priority should be given to providing social protection and public services, especially in poor rural areas.展开更多
文摘A class of n-dimensional ODEs with up to n feedbacks from the n’th variable is analysed. The feedbacks are represented by non-specific, bounded, non-negative C<sup>1</sup> functions. The main result is the formulation and proof of an easily applicable criterion for existence of a globally stable fixed point of the system. The proof relies on the contraction mapping theorem. Applications of this type of systems are numerous in biology, e.g., models of the hypothalamic-pituitary-adrenal axis and testosterone secretion. Some results important for modelling are: 1) Existence of an attractive trapping region. This is a bounded set with non-negative elements where solutions cannot escape. All solutions are shown to converge to a “minimal” trapping region. 2) At least one fixed point exists. 3) Sufficient criteria for a unique fixed point are formulated. One case where this is fulfilled is when the feedbacks are negative.
基金financial support of the Key Grant Programs of the National Social Science Foundation of China (Grant Nos.10AZD013 and 11&ZD006)
文摘The present paper investigates how neighborhood effects are connected to chronic poverty. We examine a large sample of groups of households and find that neighborhood effects are significant in a majority of groups, especially in the poorest groups. People living in poor communities tend to suffer from poverty over time. It is of theoretical and empirical importance to explore how neighborhood effects are interrelated with chronic poverty and the channels through which this occurs. Unlike other econometric analyses, we establish a multilevel econometric model to show that： （i） it is difficult for an individual living in a neighborhood with a high proportion of agricultural labor, low education levels, and poor transport and telecommunication infrastructure to escape from poverty traps; （ii） neighborhood effects dominate in poor communities; and （iii） although poverty is affected by group-level factors, individual factors still play a dominant role in regards to escaping poverty when income surpasses a threshold level Therefore, policy priority should be given to providing social protection and public services, especially in poor rural areas.
