The dynamics of a predator-prey system, where prey population has two stages, an immature stage and a mature stage with harvesting, the growth of predator population is of Lotka-Volterra nature, are modelled by a sys... The dynamics of a predator-prey system, where prey population has two stages, an immature stage and a mature stage with harvesting, the growth of predator population is of Lotka-Volterra nature, are modelled by a system of retarded functional differential equations. We obtain conditions for global asymptotic stability of three nonnegative equilibria and a threshold of harvesting for the mature prey population. The effect of delay on the population at positive equilibrium and the optimal harvesting of the mature prey population are also considered.展开更多
Abstract. In this paper, we consider a stage structure population model with two lifestages, immature and mature, with harvesting mature population and stocking immaturepopulation. It is shown that under suitable hypo...Abstract. In this paper, we consider a stage structure population model with two lifestages, immature and mature, with harvesting mature population and stocking immaturepopulation. It is shown that under suitable hypotheses there exists a globally asymptoti-cally stable positive equilibrium. The effect of the delay on the populations at equilibriumand the optimal harvesting policy for mature population are also considered.展开更多
The herbaceous peony is one of the cut flowers that has become increasingly popular in the international market in recent years. In the study, 11 cultivars of herbaceous peonies suitable for cutting flowers were selec...The herbaceous peony is one of the cut flowers that has become increasingly popular in the international market in recent years. In the study, 11 cultivars of herbaceous peonies suitable for cutting flowers were selected; different harvesting stages （three or four stages） were identified according to bud development observation （bud firmness, bud diameter, sepal angle, petal angle, and color showing）. Moreover, flower development and vase life were also recorded in the experiment of vase. Bud development observation shows that there are great differences in optimum harvesting stage between the culti- vars, especially between the hybrid peony group and lactiflora group. This implies that bud diameter could not be the only indicator for optimum harvesting stage. Bud description, including sepal opening angle, sepal color, petal color showing, and degree of firmness, is necessary for the determination of the harvesting stage. Among the 11 cultivars,‘Pink Hawaiian Coral＇, ‘Red Charm＇, ‘Edulis Superba＇, ‘Red Magic＇, and ‘Sarah Bernhardt＇ should be harvested at stage 1. ‘Duchesse de Nemours＇, ‘Taff＇, ‘Sorbet＇ and ‘Monsieur Jules Elie＇ should be harvested at stage 2. ‘Kansas＇ should be at stage 3 and ‘Karl Rosenfield＇ at stage 4. The determination of optimum harvesting stage for each cultivar is an important element in cut flower production.展开更多
We investigate a stage-structured delayed predator-prey model with impulsive stocking on prey and continuous harvesting on predator. According to the fact of biological resource management, we improve the assumption o...We investigate a stage-structured delayed predator-prey model with impulsive stocking on prey and continuous harvesting on predator. According to the fact of biological resource management, we improve the assumption of a predator-prey model with stage structure for predator population that each individual predator has the same ability to capture prey. It is assumed that the immature and mature individuals of the predator population are divided by a fixed age, and immature predator population does not have the ability to attach prey. Sufficient conditions are obtained, which guarantee the global attractivity of predator-extinction periodic solution and the permanence of the system. Our results show that the behavior of impulsive stocking on prey plays an important role for the permanence of the system, and provide tactical basis for the biological resource management. Numerical analysis is presented to illuminate the dynamics of the system.展开更多
基金the National Natural Science Foundation of China (No.10171106)the Natural Science Foundation of Henan Province (No.0211010400).
文摘 The dynamics of a predator-prey system, where prey population has two stages, an immature stage and a mature stage with harvesting, the growth of predator population is of Lotka-Volterra nature, are modelled by a system of retarded functional differential equations. We obtain conditions for global asymptotic stability of three nonnegative equilibria and a threshold of harvesting for the mature prey population. The effect of delay on the population at positive equilibrium and the optimal harvesting of the mature prey population are also considered.
基金the National Natural Science Foundation of China and Natural Science Foundation of Henan Province.
文摘Abstract. In this paper, we consider a stage structure population model with two lifestages, immature and mature, with harvesting mature population and stocking immaturepopulation. It is shown that under suitable hypotheses there exists a globally asymptoti-cally stable positive equilibrium. The effect of the delay on the populations at equilibriumand the optimal harvesting policy for mature population are also considered.
基金supported by the Fundamental Research Funds for the Central Universities (BLYX200931)National Science and Technology Program in the 12th Five-year Plan of China
文摘The herbaceous peony is one of the cut flowers that has become increasingly popular in the international market in recent years. In the study, 11 cultivars of herbaceous peonies suitable for cutting flowers were selected; different harvesting stages （three or four stages） were identified according to bud development observation （bud firmness, bud diameter, sepal angle, petal angle, and color showing）. Moreover, flower development and vase life were also recorded in the experiment of vase. Bud development observation shows that there are great differences in optimum harvesting stage between the culti- vars, especially between the hybrid peony group and lactiflora group. This implies that bud diameter could not be the only indicator for optimum harvesting stage. Bud description, including sepal opening angle, sepal color, petal color showing, and degree of firmness, is necessary for the determination of the harvesting stage. Among the 11 cultivars,‘Pink Hawaiian Coral＇, ‘Red Charm＇, ‘Edulis Superba＇, ‘Red Magic＇, and ‘Sarah Bernhardt＇ should be harvested at stage 1. ‘Duchesse de Nemours＇, ‘Taff＇, ‘Sorbet＇ and ‘Monsieur Jules Elie＇ should be harvested at stage 2. ‘Kansas＇ should be at stage 3 and ‘Karl Rosenfield＇ at stage 4. The determination of optimum harvesting stage for each cultivar is an important element in cut flower production.
基金the National Natural Science Foundation of China(No.10771179)the Emphasis Subject of Guizhou Province of China
文摘We investigate a stage-structured delayed predator-prey model with impulsive stocking on prey and continuous harvesting on predator. According to the fact of biological resource management, we improve the assumption of a predator-prey model with stage structure for predator population that each individual predator has the same ability to capture prey. It is assumed that the immature and mature individuals of the predator population are divided by a fixed age, and immature predator population does not have the ability to attach prey. Sufficient conditions are obtained, which guarantee the global attractivity of predator-extinction periodic solution and the permanence of the system. Our results show that the behavior of impulsive stocking on prey plays an important role for the permanence of the system, and provide tactical basis for the biological resource management. Numerical analysis is presented to illuminate the dynamics of the system.
