We consider the Leslie’s prey–predator model with discrete time.This model is given by a nonlinear evolution operator depending on five parameters.We show that this operator has two fixed points and define type of e...We consider the Leslie’s prey–predator model with discrete time.This model is given by a nonlinear evolution operator depending on five parameters.We show that this operator has two fixed points and define type of each fixed point depending on the parameters.Finding two invariant sets of the evolution operator,we study the dynamical systems generated by the operator on each invariant set.Depending on the parameters,we classify the dynamics between a predator and a prey of the Leslie’s model.展开更多
Quantitative dynamics and viability of a rare and wild Cycas fairylakea population were studied with a time-specific life table, a Leslie matrix model and a survival function in order to provide scientific guidance fo...Quantitative dynamics and viability of a rare and wild Cycas fairylakea population were studied with a time-specific life table, a Leslie matrix model and a survival function in order to provide scientific guidance for its protection. The results of the time- specific life table show that this C. fairylakea population suffered a high death rate in three age classes, i.e., age class 1 （0-15 years）, V （61-75 years） and VI （76-90 years）. The Leslie matrix model suggests that the number of plants would decline from the present 1613 to 59 per hectare in 150 years. Furthermore, the viability analysis indicates that seedlings have the highest mortality density rate and that middle-aged plants （i.e., 61-75 years, 76-90 years） have high mortality density rate and hazard rate. These conditions affect natural regeneration of the population and lead to a lack of seedlings which in turn causes the extinction of the population. An in situ conservation of the population should be established and protection measures taken as soon as possible.展开更多
基金Shoyimardonov thanks the El-Yurt Umidi Foundation under the Cabinet of Ministers of the Republic of Uzbekistan for financial support during his visit to the University of Montpellier(France)and Prof.R.Varro for the invitation。
文摘We consider the Leslie’s prey–predator model with discrete time.This model is given by a nonlinear evolution operator depending on five parameters.We show that this operator has two fixed points and define type of each fixed point depending on the parameters.Finding two invariant sets of the evolution operator,we study the dynamical systems generated by the operator on each invariant set.Depending on the parameters,we classify the dynamics between a predator and a prey of the Leslie’s model.
文摘Quantitative dynamics and viability of a rare and wild Cycas fairylakea population were studied with a time-specific life table, a Leslie matrix model and a survival function in order to provide scientific guidance for its protection. The results of the time- specific life table show that this C. fairylakea population suffered a high death rate in three age classes, i.e., age class 1 （0-15 years）, V （61-75 years） and VI （76-90 years）. The Leslie matrix model suggests that the number of plants would decline from the present 1613 to 59 per hectare in 150 years. Furthermore, the viability analysis indicates that seedlings have the highest mortality density rate and that middle-aged plants （i.e., 61-75 years, 76-90 years） have high mortality density rate and hazard rate. These conditions affect natural regeneration of the population and lead to a lack of seedlings which in turn causes the extinction of the population. An in situ conservation of the population should be established and protection measures taken as soon as possible.
