This paper investigates the stochastic dynamics of trophic cascade chemostat model perturbed by regime switching, Gaussian white noise and impulsive toxicant input. For the system with only white noise interference, s...This paper investigates the stochastic dynamics of trophic cascade chemostat model perturbed by regime switching, Gaussian white noise and impulsive toxicant input. For the system with only white noise interference, sufficient conditions for stochastically ultimate boundedness and stochastically permanence are obtained, and we demonstrate that the stochastic system has at least one nontrivial positive periodic solution. For the system with Markov regime switching, sufficient conditions for extinction of the microorganisms are established. Then we prove the system is ergodic and has a stationary distribution. The results show that both impulsive toxins input and stochastic noise have great effects on the survival and extinction of the microorganisms. Finally, a series of numerical simulations are presented to illustrate the theoretical analysis.展开更多
In this work, we construct a stage-structured single population system with winter hiber- nation and impulsive effect in polluted environment. All solutions of the investigated system are proved to be uniformly ultima...In this work, we construct a stage-structured single population system with winter hiber- nation and impulsive effect in polluted environment. All solutions of the investigated system are proved to be uniformly ultimately bounded. The conditions of the population- extinction solution of the investigated system are obtained. The permanent condition of the investigated system is also obtained. Finally, numerical analysis is inserted to illustrate the results. Our results indicate that the environmental pollution will reduce biological diversity of the natural world. Our results also provide reliable tactic basis for the practical biological resource management.展开更多
In this paper,we assume that the pest population is divided into susceptible pests and infected pests,and only susceptible pests do harm to crops.Considering the two methods of spraying pesticides and releasing infect...In this paper,we assume that the pest population is divided into susceptible pests and infected pests,and only susceptible pests do harm to crops.Considering the two methods of spraying pesticides and releasing infected pests and natural enemies to control susceptible pests(the former is applied more frequently),and assuming that only susceptible pests develop resistance to pesticides,a pest control model with resistance development is established.By using the basic theory of impulsive differential systems and analytical methods,the sufficient condition for the global attractiveness of the susceptible pest eradication periodic solution is given.Combined with numerical simulations,the effects of spraying frequency of pesticides on critical threshold conditions for eradicating susceptible pests are discussed.The results confirm that it is not that the more frequently the pesticides are sprayed,the better the result of the pest control is.Two control strategies for eradicating susceptible pests are proposed:switching pesticides and releasing natural enemies elastically.Finally,the parameters in the critical threshold are analyzed from the following two aspects:(1)The key factors affecting pest control are determined by parameter sensitivity analyses.The results indicate that the correlation of the critical threshold concerning the killing efficiency rate and the decay rate of pesticides to susceptible pests varies due to the resistance development of susceptible pests.(2)Three-dimensional graphs and contours of susceptible pest eradication critical threshold with two parameters are simulated,and the effects of the main parameters on the critical threshold are analyzed.展开更多
In this paper,we develop a single species evolutionary model with a continuous phenotypic trait in a pulsed pollution discharge environment and discuss the effects of pollution on the individual size of the species.Th...In this paper,we develop a single species evolutionary model with a continuous phenotypic trait in a pulsed pollution discharge environment and discuss the effects of pollution on the individual size of the species.The invasion fitness function of a moiiomorphic species is given,which involves the long-term average exponential growth rate of the species. Then the critical function analysis method is used to obtain the evolutionary dynamics of the system,which is related to interspecific competition intensity between mutant species and resident species and the curvature of the trade-off between individual size and the intrinsic growth rate.We conclude that,the pollution affects the evolutionary traits and evolutionary dynamics.The worsening of the pollution can lead to rapid stable evolution toward a smaller individual size,while the opposite is more likely to generate evolutionary branching and promote species diversity.The adaptive dynamics of coevolution of dimorphic species is further analyzed when evolutionary branching occurs.展开更多
Aphids are a major global wheat,pest that can cause considerable loss of yield.Modeling of aphid population dynamics is an integral part of management strategies to manage or control aphid populations.In this paper,fi...Aphids are a major global wheat,pest that can cause considerable loss of yield.Modeling of aphid population dynamics is an integral part of management strategies to manage or control aphid populations.In this paper,first,a wheat aphid population dynamics model was developed based on a logistic model and theⅠlollingⅢfunctional response,which includes three factors:temperature,natural enemies and insecticide.Second,this model fitted with a cusp catastrophe model to describe how abrupt changes in the wheat aphid population were influenced by these factors,Finally,the system was validated with field data from 2016 to 2018.The bifurcation set of the cusp catastrophe model was deemod to be the quantified dynamic control threshold,so an outbreak of aphid's population can be explained according to the variation of control variables.In short,this aphid population model was successfully validated on survey data,which can be used to guide the prevention and control of aphids.展开更多
The existence conditions of Hopf bifurcation for a predator prey model based on nutri- tion kinetics are given. The two results may appear as follows: one is that the model has a stable periodic trajectory from Hopf ...The existence conditions of Hopf bifurcation for a predator prey model based on nutri- tion kinetics are given. The two results may appear as follows: one is that the model has a stable periodic trajectory from Hopf bifurcation, which shows the system is in an eco- logical balance; the other is that periodic trajectory from Hopf bifurcation is unstable, which indicates the system is in a sharp or catastrophic loss of stability. For the latter, a bifurcation controller is designed to make the periodic trajectory stable. Finally, some simulations are carried out to prove the results.展开更多
基金the National Natural Science Foundation of China (No.12271308)the Research Fund for the Taishan Scholar Project of Shandong Province of ChinaShandong Provincial Natural Science Foundation of China (ZR2019MA003)。
文摘This paper investigates the stochastic dynamics of trophic cascade chemostat model perturbed by regime switching, Gaussian white noise and impulsive toxicant input. For the system with only white noise interference, sufficient conditions for stochastically ultimate boundedness and stochastically permanence are obtained, and we demonstrate that the stochastic system has at least one nontrivial positive periodic solution. For the system with Markov regime switching, sufficient conditions for extinction of the microorganisms are established. Then we prove the system is ergodic and has a stationary distribution. The results show that both impulsive toxins input and stochastic noise have great effects on the survival and extinction of the microorganisms. Finally, a series of numerical simulations are presented to illustrate the theoretical analysis.
基金Acknowledgments The work of the first author was supported by National Natural Science Foundation of China (No. 11361014) and the project of high level creative talents in Guizhou Province (No. 20164035). This research was supported by National Natural Science Foundation of China (Nos. 11361014, 10961008), the Science Technology Foundation of Guizhou Education Department (No. 2008038), and the Science Technology Foundation of Guizhou (No. 2010J2130).
文摘In this work, we construct a stage-structured single population system with winter hiber- nation and impulsive effect in polluted environment. All solutions of the investigated system are proved to be uniformly ultimately bounded. The conditions of the population- extinction solution of the investigated system are obtained. The permanent condition of the investigated system is also obtained. Finally, numerical analysis is inserted to illustrate the results. Our results indicate that the environmental pollution will reduce biological diversity of the natural world. Our results also provide reliable tactic basis for the practical biological resource management.
基金supported by the National Natural Science Foundation of China(No.11371030)the Natural Science Foundation of Liaoning Province(No.20170540001)Liaoning Bai Qian Wan Talents Program。
文摘In this paper,we assume that the pest population is divided into susceptible pests and infected pests,and only susceptible pests do harm to crops.Considering the two methods of spraying pesticides and releasing infected pests and natural enemies to control susceptible pests(the former is applied more frequently),and assuming that only susceptible pests develop resistance to pesticides,a pest control model with resistance development is established.By using the basic theory of impulsive differential systems and analytical methods,the sufficient condition for the global attractiveness of the susceptible pest eradication periodic solution is given.Combined with numerical simulations,the effects of spraying frequency of pesticides on critical threshold conditions for eradicating susceptible pests are discussed.The results confirm that it is not that the more frequently the pesticides are sprayed,the better the result of the pest control is.Two control strategies for eradicating susceptible pests are proposed:switching pesticides and releasing natural enemies elastically.Finally,the parameters in the critical threshold are analyzed from the following two aspects:(1)The key factors affecting pest control are determined by parameter sensitivity analyses.The results indicate that the correlation of the critical threshold concerning the killing efficiency rate and the decay rate of pesticides to susceptible pests varies due to the resistance development of susceptible pests.(2)Three-dimensional graphs and contours of susceptible pest eradication critical threshold with two parameters are simulated,and the effects of the main parameters on the critical threshold are analyzed.
基金This work is supported by the National Natural Science Foundation of China(11371030)the Natural Science Foundation of Liaoning Province(20170540001)Liaoning Bai Qian Wan Talents Program.
文摘In this paper,we develop a single species evolutionary model with a continuous phenotypic trait in a pulsed pollution discharge environment and discuss the effects of pollution on the individual size of the species.The invasion fitness function of a moiiomorphic species is given,which involves the long-term average exponential growth rate of the species. Then the critical function analysis method is used to obtain the evolutionary dynamics of the system,which is related to interspecific competition intensity between mutant species and resident species and the curvature of the trade-off between individual size and the intrinsic growth rate.We conclude that,the pollution affects the evolutionary traits and evolutionary dynamics.The worsening of the pollution can lead to rapid stable evolution toward a smaller individual size,while the opposite is more likely to generate evolutionary branching and promote species diversity.The adaptive dynamics of coevolution of dimorphic species is further analyzed when evolutionary branching occurs.
基金This research was funded by the National Key Research and Development Program of China(2018YFD0200402)Ph.D.Programs of the Foundation of Ministry of Education of China(20130204110004).
文摘Aphids are a major global wheat,pest that can cause considerable loss of yield.Modeling of aphid population dynamics is an integral part of management strategies to manage or control aphid populations.In this paper,first,a wheat aphid population dynamics model was developed based on a logistic model and theⅠlollingⅢfunctional response,which includes three factors:temperature,natural enemies and insecticide.Second,this model fitted with a cusp catastrophe model to describe how abrupt changes in the wheat aphid population were influenced by these factors,Finally,the system was validated with field data from 2016 to 2018.The bifurcation set of the cusp catastrophe model was deemod to be the quantified dynamic control threshold,so an outbreak of aphid's population can be explained according to the variation of control variables.In short,this aphid population model was successfully validated on survey data,which can be used to guide the prevention and control of aphids.
基金Acknowledgments This work was supported by the Science Foundation of Liaoning Province (20092179) and by the National Natural Science Foundation (60974004/F030101).
文摘The existence conditions of Hopf bifurcation for a predator prey model based on nutri- tion kinetics are given. The two results may appear as follows: one is that the model has a stable periodic trajectory from Hopf bifurcation, which shows the system is in an eco- logical balance; the other is that periodic trajectory from Hopf bifurcation is unstable, which indicates the system is in a sharp or catastrophic loss of stability. For the latter, a bifurcation controller is designed to make the periodic trajectory stable. Finally, some simulations are carried out to prove the results.