The presence of the debris in the Earth’s orbit poses a significant risk to human activity in outer space.This debris population continues to grow due to ground launches,the loss of external parts from space ships,an...The presence of the debris in the Earth’s orbit poses a significant risk to human activity in outer space.This debris population continues to grow due to ground launches,the loss of external parts from space ships,and uncontrollable collisions between objects.A computationally feasible continuum model for the growth of the debris population and its spatial distribution is therefore critical.Here we propose a diffusion-collision model for the evolution of the debris density in the low-Earth orbit and its dependence on the ground-launch policy.We parametrize this model and test it against data from publicly available object catalogs to examine timescales for the uncontrolled growth.Finally,we consider sensible launch policies and cleanup strategies and how they reduce the future risk of collisions with active satellites or space ships.展开更多
In the present work we study the global solvability of the Kolmogorov-Fisher type biological population task with double nonlinear diffusion and qualitative properties of the solution of the task based on the self-sim...In the present work we study the global solvability of the Kolmogorov-Fisher type biological population task with double nonlinear diffusion and qualitative properties of the solution of the task based on the self-similar analysis. In additional, in this paper we consider the model of two competing population with dual nonlinear cross-diffusion.展开更多
In this paper,we consider the long-term sustainability of the northeast Korean pine.We propose a class of natural Korean pine population system with time delay and diffusion term.First,by analyzing the roots distribut...In this paper,we consider the long-term sustainability of the northeast Korean pine.We propose a class of natural Korean pine population system with time delay and diffusion term.First,by analyzing the roots distribution of the characteristic equation,we study the stability of the model system with diffusion terms and prove the occurrence of Hopf bifurcation.Second,we introduce lactation time delay into a population model with a diffusion term,based on stability theory of ordinary differential equation,norm form methods and center manifold theorem,the stability of bifurcating periodic solutions and the relevant formula for the direction of Hopf bifurcation are given.Finally,some numerical simulations are given.展开更多
Sound pressure amplitude will be attenuated with propagation distance in a certain rule when sound wave is propagated in shallow sea.When processing the attenuated signal,time-variant gain circuit is usually used to c...Sound pressure amplitude will be attenuated with propagation distance in a certain rule when sound wave is propagated in shallow sea.When processing the attenuated signal,time-variant gain circuit is usually used to compensate its diffusion loss.In this paper,spherical diffusion loss is compensated by digital potentiometer and operational circuit and further investigation is also made on compensation of cylindrical diffusion loss and transition from spherical diffusion loss to cylindrical diffusion loss.Finally,a new compensation model is proposed for unknown propagation loss for the purpose of adjusting the dynamic range of signal to meet the requirement of A/D conversion.展开更多
It is a well known fact that studies on growth primarily take into account human populations, although currently many scientific fields （biology, economics, etc.） also use growth models to reflect behaviours in dive...It is a well known fact that studies on growth primarily take into account human populations, although currently many scientific fields （biology, economics, etc.） also use growth models to reflect behaviours in diverse phenomena. These deterministic models are difficult to apply in real populations since, as we know, the volume of a human population depends intrinsically on a large number of other socio-economic variables, including changes in fertility patterns, improvements in living conditions, individual health factors which produce an increase or decrease in the number of years lived, the state of economic well-being, or changes in migratory fluxes. In this study, we have examined the stochastic Gompertz non-homogenous diffusion process, analysing its transition probability density function and conducting inferences on the parameters of the process through discrete sampling All of the results are applied to the population of Andalusia with data disaggregated by sex during the period of 1981 to 2002, taking purely demographic variables as exogenous factors： life expectancy at birth, foreign immigration to Andalusia and total fertility rate展开更多
In this paper, we discussed population model of two competing populations with non-linear double diffusion and variable density which described by nonlinear system of competing individuals. We identify new properties,...In this paper, we discussed population model of two competing populations with non-linear double diffusion and variable density which described by nonlinear system of competing individuals. We identify new properties, such as finite speed of propagation, and localization of the outbreaks in a specific area.展开更多
In recent years, population growth models with spatial diffusion have beenextensively studied by many authors (for example, see [1-5]). In this paper, a populationgrowth model is considered with a discrete age-depende...In recent years, population growth models with spatial diffusion have beenextensively studied by many authors (for example, see [1-5]). In this paper, a populationgrowth model is considered with a discrete age-dependence and spatial diffusion, and isinvestigated in a semigroup framework. The spectral properties of the population oper-ator are given. On the basis of such spectral consideration, the asymptotic behaviourof the semigroup generated by the population operator is obtained. Finally, a nonlinearpopulation growth model is considered and its stability is analyzed.展开更多
The diffusion model in population genetics based on the stochastic theory has a great effect on the elucidation of both the genetic structure of Mendelian population and the molecular evolutionary mechanism. A series ...The diffusion model in population genetics based on the stochastic theory has a great effect on the elucidation of both the genetic structure of Mendelian population and the molecular evolutionary mechanism. A series of formulas used to verify the hypothesis of evolution are mostly derived from the diffusion theory established by Kimura and his coworkers. It is worthwhile to go further into the fundamentals of the stochastic model.展开更多
This paper discusses the most general time-varying population system, proves the necessary and sufficient conditions for systems to be stable in the sense of Lyapunov, and obtains the critical fertility rates β_(cr)(...This paper discusses the most general time-varying population system, proves the necessary and sufficient conditions for systems to be stable in the sense of Lyapunov, and obtains the critical fertility rates β_(cr)(t) and β_(cr) of females for the system related to the stability for the system. And the explicit analytic expressions for the state ot the system are deduced. These results can provide a strict theoretical datum for the decision ot population policies.展开更多
We consider a model for a population in a heterogeneous environment, with logistic-type local population dynamics, under the assumption that individuals can switch between two different nonzero rates of diffusion. Suc...We consider a model for a population in a heterogeneous environment, with logistic-type local population dynamics, under the assumption that individuals can switch between two different nonzero rates of diffusion. Such switching behavior has been observed in some natural systems. We study how environmental heterogeneity and the rates of switching and diffusion affect the persistence of the population. The reactiondiffusion systems in the models can be cooperative at some population densities and competitive at others. The results extend our previous work on similar models in homogeneous environments. We also consider competition between two populations that are ecologically identical, but where one population diffuses at a fixed rate and the other switches between two different diffusion rates. The motivation for that is to gain insight into when switching might be advantageous versus diffusing at a fixed rate. This is a variation on the classical results for ecologically identical competitors with differing fixed diffusion rates, where it is well known that "the slower diffuser wins".展开更多
基金supported by a graduate fellowship from the Department of Mathematical Sciences at the University of Wisconsin-Milwaukee.
文摘The presence of the debris in the Earth’s orbit poses a significant risk to human activity in outer space.This debris population continues to grow due to ground launches,the loss of external parts from space ships,and uncontrollable collisions between objects.A computationally feasible continuum model for the growth of the debris population and its spatial distribution is therefore critical.Here we propose a diffusion-collision model for the evolution of the debris density in the low-Earth orbit and its dependence on the ground-launch policy.We parametrize this model and test it against data from publicly available object catalogs to examine timescales for the uncontrolled growth.Finally,we consider sensible launch policies and cleanup strategies and how they reduce the future risk of collisions with active satellites or space ships.
文摘In the present work we study the global solvability of the Kolmogorov-Fisher type biological population task with double nonlinear diffusion and qualitative properties of the solution of the task based on the self-similar analysis. In additional, in this paper we consider the model of two competing population with dual nonlinear cross-diffusion.
基金supported by the National Natural Science Foundation of China(No.11201095)the Fundamental Research Funds for the Central Universities(No.3072022TS2402)+1 种基金the Postdoctoral research startup foundation of Heilongjiang(No.LBH-Q14044)the Science Research Funds for Overseas Returned Chinese Scholars of Heilongjiang Province(No.LC201502).
文摘In this paper,we consider the long-term sustainability of the northeast Korean pine.We propose a class of natural Korean pine population system with time delay and diffusion term.First,by analyzing the roots distribution of the characteristic equation,we study the stability of the model system with diffusion terms and prove the occurrence of Hopf bifurcation.Second,we introduce lactation time delay into a population model with a diffusion term,based on stability theory of ordinary differential equation,norm form methods and center manifold theorem,the stability of bifurcating periodic solutions and the relevant formula for the direction of Hopf bifurcation are given.Finally,some numerical simulations are given.
文摘Sound pressure amplitude will be attenuated with propagation distance in a certain rule when sound wave is propagated in shallow sea.When processing the attenuated signal,time-variant gain circuit is usually used to compensate its diffusion loss.In this paper,spherical diffusion loss is compensated by digital potentiometer and operational circuit and further investigation is also made on compensation of cylindrical diffusion loss and transition from spherical diffusion loss to cylindrical diffusion loss.Finally,a new compensation model is proposed for unknown propagation loss for the purpose of adjusting the dynamic range of signal to meet the requirement of A/D conversion.
文摘It is a well known fact that studies on growth primarily take into account human populations, although currently many scientific fields （biology, economics, etc.） also use growth models to reflect behaviours in diverse phenomena. These deterministic models are difficult to apply in real populations since, as we know, the volume of a human population depends intrinsically on a large number of other socio-economic variables, including changes in fertility patterns, improvements in living conditions, individual health factors which produce an increase or decrease in the number of years lived, the state of economic well-being, or changes in migratory fluxes. In this study, we have examined the stochastic Gompertz non-homogenous diffusion process, analysing its transition probability density function and conducting inferences on the parameters of the process through discrete sampling All of the results are applied to the population of Andalusia with data disaggregated by sex during the period of 1981 to 2002, taking purely demographic variables as exogenous factors： life expectancy at birth, foreign immigration to Andalusia and total fertility rate
文摘In this paper, we discussed population model of two competing populations with non-linear double diffusion and variable density which described by nonlinear system of competing individuals. We identify new properties, such as finite speed of propagation, and localization of the outbreaks in a specific area.
基金This research is supported by the National Natural Science Foundation of China.
文摘In recent years, population growth models with spatial diffusion have beenextensively studied by many authors (for example, see [1-5]). In this paper, a populationgrowth model is considered with a discrete age-dependence and spatial diffusion, and isinvestigated in a semigroup framework. The spectral properties of the population oper-ator are given. On the basis of such spectral consideration, the asymptotic behaviourof the semigroup generated by the population operator is obtained. Finally, a nonlinearpopulation growth model is considered and its stability is analyzed.
文摘The diffusion model in population genetics based on the stochastic theory has a great effect on the elucidation of both the genetic structure of Mendelian population and the molecular evolutionary mechanism. A series of formulas used to verify the hypothesis of evolution are mostly derived from the diffusion theory established by Kimura and his coworkers. It is worthwhile to go further into the fundamentals of the stochastic model.
基金Project supported by the National Natural Science Foundation of China
文摘This paper discusses the most general time-varying population system, proves the necessary and sufficient conditions for systems to be stable in the sense of Lyapunov, and obtains the critical fertility rates β_(cr)(t) and β_(cr) of females for the system related to the stability for the system. And the explicit analytic expressions for the state ot the system are deduced. These results can provide a strict theoretical datum for the decision ot population policies.
基金supported by National Science Foundation of USA (Grant No. DMS1514752)
文摘We consider a model for a population in a heterogeneous environment, with logistic-type local population dynamics, under the assumption that individuals can switch between two different nonzero rates of diffusion. Such switching behavior has been observed in some natural systems. We study how environmental heterogeneity and the rates of switching and diffusion affect the persistence of the population. The reactiondiffusion systems in the models can be cooperative at some population densities and competitive at others. The results extend our previous work on similar models in homogeneous environments. We also consider competition between two populations that are ecologically identical, but where one population diffuses at a fixed rate and the other switches between two different diffusion rates. The motivation for that is to gain insight into when switching might be advantageous versus diffusing at a fixed rate. This is a variation on the classical results for ecologically identical competitors with differing fixed diffusion rates, where it is well known that "the slower diffuser wins".
