The logistic equation with Lévy noise is considered.Under suitable conditions,the global existence and uniqueness is obtained;it is shown that the unique positive equilibrium is globally attractive if the initial...The logistic equation with Lévy noise is considered.Under suitable conditions,the global existence and uniqueness is obtained;it is shown that the unique positive equilibrium is globally attractive if the initial value is less than the carrying capacity.展开更多
In the present paper, we consider the existence of positive periodic solutions for a kind of delay Logistic equations. By using a fixed point theorem in cones, we give some new existence results of single and multiple...In the present paper, we consider the existence of positive periodic solutions for a kind of delay Logistic equations. By using a fixed point theorem in cones, we give some new existence results of single and multiple positive periodic solutions for a kind of delay Logistic equations. Some biomathematical models are presented to illustrate our results.展开更多
This paper discusses a randomized Logistic equation $\dot N(t) = (r + \alpha \dot B(t))N(t)[1 - \frac{{N(t)}}{K}]$ with an initial value N(0) = N 0, and N 0 is a random variable satisfying 0 < N 0 < K. The exist...This paper discusses a randomized Logistic equation $\dot N(t) = (r + \alpha \dot B(t))N(t)[1 - \frac{{N(t)}}{K}]$ with an initial value N(0) = N 0, and N 0 is a random variable satisfying 0 < N 0 < K. The existence, uniqueness and global attractivity of positive solutions and maximum likelihood estimate (MLE) of the parameters of the equation are studied.展开更多
Empirical likelihood(EL) combined with estimating equations(EE) provides a modern semi-parametric alternative to classical estimation techniques such as maximum likelihood estimation(MLE). This paper not only uses clo...Empirical likelihood(EL) combined with estimating equations(EE) provides a modern semi-parametric alternative to classical estimation techniques such as maximum likelihood estimation(MLE). This paper not only uses closed form of conditional expectation and conditional variance of Logistic equation with random perturbation to perform maximum empirical likelihood estimation(MELE) for the model parameters, but also proposes an empirical likelihood ratio statistic(ELRS) for hypotheses concerning the interesting parameter. Monte Carlo simulation results show that MELE and ELRS provide competitive performance to parametric alternatives.展开更多
In this paper, we obtain some necessary and sufficient conditions for the oscillation of all positive solutions of a delay Logistic equation with continuous and piecewise constant arguments about the positive equilibr...In this paper, we obtain some necessary and sufficient conditions for the oscillation of all positive solutions of a delay Logistic equation with continuous and piecewise constant arguments about the positive equilibrium.展开更多
Eucalyptus is the most valuable cultivated forest genus in the tropical and subtropical areas nowadays.It has been a challenge for foresters to model growth due to the genetic variations,management regimes,and multipl...Eucalyptus is the most valuable cultivated forest genus in the tropical and subtropical areas nowadays.It has been a challenge for foresters to model growth due to the genetic variations,management regimes,and multiple products generated from the plantations.In this paper,Logistic equation was used to study the stock growth process of E.urophylla×E.grandis plantation at age of 14 with 6 spacing treatments.And the biological interpretation of the parameters of Logistic equation was analyzed.The results show that it is flexible,precise and accurate to fit the growth process.展开更多
The purpose of this paper is to study the asymptotic behavior of the positive solutions of the problem tu- △u=au-b（x）up in Ω×R＋,u（0）=u0,u（t ）｜ Ω=0, as p→ ＋∞, where Ω is a bounded domain, and b（x...The purpose of this paper is to study the asymptotic behavior of the positive solutions of the problem tu- △u=au-b（x）up in Ω×R＋,u（0）=u0,u（t ）｜ Ω=0, as p→ ＋∞, where Ω is a bounded domain, and b（x） is a nonnegative function. The authors deduce that the limiting configuration solves a parabolic obstacle problem, and afterwards fully describe its long time behavior.展开更多
As the function of the decomposition of fungi has been clearly researched in the global carbon cycle,it is obviously of value to explore the decomposition rate of fungal populations.This study analyzed the relationshi...As the function of the decomposition of fungi has been clearly researched in the global carbon cycle,it is obviously of value to explore the decomposition rate of fungal populations.This study analyzed the relationship between environmental factors and biodiversity step by step.In order to explore the interaction between the fungi and the relationship between the decomposition rate of fungi with time,the model based on the Logistic model was built and the Lotka-Volterra model was employed in the condition of two kinds of fungi existing in an environment with limited resources.The changing trend of population number and decomposition rate of several fungi under different environmental conditions can be predicted through the model.To illustrate the applicability of the model,Laetiporus conifericola and Hyphoderma setigerum were applied as examples.The results showed that the higher the degree of population diversity,the greater the decomposition rate,and the higher the decomposition efficiency of the ecosystem.Its rich species diversity is conducive to accelerating the decomposition of litter,lignocellulose,and the circulation of the entire ecosystem.Based on the above model and using the data from measuring the mycelial elongation rate of each isolate at 10℃,16℃,and 22℃ under standardized laboratory conditions,the growth patterns of the five fungi combinations were simulated.The results revealed a general increase in growth rate with increasing temperature,which verifies the accuracy of the model.Moreover,it also revealed that the total decomposition rate after fungal incorporation was negatively correlated with the decomposition rate of a fungal single action.Based on the above model,predictions can be made for fungal growth in different environments,and suitable environments for fungal growth can be determined.In the future,the model can be further optimized,and lignin and cellulose decomposition factors can be added to fit the decomposition of logs.The application scenarios of the model can be further broadened,which can contribute to the restoration and management of the ecological environment,as well as produce good effects in the fields of fungi assisting the global carbon cycle and soil problem restoration.展开更多
Accurate prediction of tropical cyclone(TC)intensity remains a challenge due to the complex physical processes involved in TC intensity changes.A seven-day TC intensity prediction scheme based on the logistic growth e...Accurate prediction of tropical cyclone(TC)intensity remains a challenge due to the complex physical processes involved in TC intensity changes.A seven-day TC intensity prediction scheme based on the logistic growth equation(LGE)for the western North Pacific(WNP)has been developed using the observed and reanalysis data.In the LGE,TC intensity change is determined by a growth term and a decay term.These two terms are comprised of four free parameters which include a time-dependent growth rate,a maximum potential intensity(MPI),and two constants.Using 33 years of training samples,optimal predictors are selected first,and then the two constants are determined based on the least square method,forcing the regressed growth rate from the optimal predictors to be as close to the observed as possible.The estimation of the growth rate is further refined based on a step-wise regression(SWR)method and a machine learning(ML)method for the period 1982−2014.Using the LGE-based scheme,a total of 80 TCs during 2015−17 are used to make independent forecasts.Results show that the root mean square errors of the LGE-based scheme are much smaller than those of the official intensity forecasts from the China Meteorological Administration(CMA),especially for TCs in the coastal regions of East Asia.Moreover,the scheme based on ML demonstrates better forecast skill than that based on SWR.The new prediction scheme offers strong potential for both improving the forecasts for rapid intensification and weakening of TCs as well as for extending the 5-day forecasts currently issued by the CMA to 7-day forecasts.展开更多
In this paper, we study the Logistic type equation x= a（t）x -b（t）x^2＋ e（t）. Under the assumptions that e（t） is small enough and a（t）, b（t） are contained in some positive intervals, we prove that this equa...In this paper, we study the Logistic type equation x= a（t）x -b（t）x^2＋ e（t）. Under the assumptions that e（t） is small enough and a（t）, b（t） are contained in some positive intervals, we prove that this equation has a positive bounded solution which is stable. Moreover, this solution is a periodic solution if a（t）, b（t） and e（t） are periodic functions, and this solution is an almost periodic solution if a（t）, b（t） and e（t） are almost periodic functions.展开更多
Consider the nonautonomous delay logistic equation △yn=pnyn（1-yn-ln/k）,n≥0, where {Pn}n≥0 is a sequence of nonnegative real numbers, {In}n≥0 is a sequence of positive integers satisfying n→∞lim（n-ln）=∞, and...Consider the nonautonomous delay logistic equation △yn=pnyn（1-yn-ln/k）,n≥0, where {Pn}n≥0 is a sequence of nonnegative real numbers, {In}n≥0 is a sequence of positive integers satisfying n→∞lim（n-ln）=∞, and k is a positive constant. Only solutions which are positive for n ≥ 0 are considered. We obtain a new sufficient for all positive solutions of （1） to oscillate about k which contains the corresponding result in [2] when i = 1.展开更多
This paper studies the global attractivity of the positive equilibrium 1 of the delay logistic difference equation Δ y n=p ny n(1-y τ(n) ), n=0,1,2,...,(*)where {p n} is a sequence of positive real n...This paper studies the global attractivity of the positive equilibrium 1 of the delay logistic difference equation Δ y n=p ny n(1-y τ(n) ), n=0,1,2,...,(*)where {p n} is a sequence of positive real numbers, {τ(n)} is a nondecreasing sequence of integers, τ(n)<n and lim n→∞τ(n)=∞ .It is proved that ifnj=τ(n)p j≤54 for sufficiently large n and ∞j=0p j=∞,then all positive solutions of Eq.(*) tend to 1 as n→∞ .The results improve the existing results in literature.展开更多
The author studied the existence of positive solutions of the delay logistic difference equation Δ y n=p ny n(1-y τ(n) ), n =0,1,2,.... where { p n } is a sequence of positive real numbers, { τ(n) } is a nondecreas...The author studied the existence of positive solutions of the delay logistic difference equation Δ y n=p ny n(1-y τ(n) ), n =0,1,2,.... where { p n } is a sequence of positive real numbers, { τ(n) } is a nondecreasing sequence of integers, τ(n)<n and lim n →∞ τ(n) =∞. A sufficient condition for the existence of positive solutions of the equation was given.展开更多
Letτ∈C{0},let p and q be distinct positive integers,and let a,b,c be meromorphic functions such that at least one of b and c is not identically equal to zero.The main purpose of this paper is to study the logistic d...Letτ∈C{0},let p and q be distinct positive integers,and let a,b,c be meromorphic functions such that at least one of b and c is not identically equal to zero.The main purpose of this paper is to study the logistic delay differential equations of the Lotka-Volterra type w′(z)=w(z)[a(z)+b(z)w^(p)(z-τ)+c(z)w^(q)(z-τ)]We prove that any admissible meromorphic solution w of the equation satisfies that the counting function N(r,w)of poles and the characteristic function T(r,w)have the same growth category.Furthermore,we obtain that“most”of admissible meromorphic solutions of a more general delay differential equation w′(z)=w(z)[a(z)+k∑j=1b_(j)w^(j)(z-τ)],have a pole at least.展开更多
An analysis of logistic stochastic differential equations(SDEs)with general power-law and driven by a Wiener process is conducted.We prove existence of unique,strong Markovian,continuous solutions.The solutions live(a...An analysis of logistic stochastic differential equations(SDEs)with general power-law and driven by a Wiener process is conducted.We prove existence of unique,strong Markovian,continuous solutions.The solutions live(a.s.)on bounded domains D=[0,K]required by applications to biology,ecology and physics with nonrandom threshold parameter K>0(i.e.the maximum carrying constant).Moreover,we present and justify nonstandard numerical methods constructed by specified balanced implicit methods(BIMs).Their weak and L^(p)-convergence follows from the fact that these methods with local Lipschitz-continuous coefficients of logistic SDEs“produce”positive numerical approximations on bounded domain[0,K](a.s.).As commonly known,standard numerical methods such as Taylor-type ones for SDEs fail to do that.Finally,asymptotic stability of nontrivial equilibria x_(∗)=K is proven for both continuous time logistic SDEs and discrete time approximations by BIMs.We exploit the technique of positive,sufficiently smooth and Lyapunov functionals governed by well-known Dynkin’s formula for SDEs.展开更多
A new water soluble surfaCe film-forming material was developed and its effect on reducing ammonia volatilization from an alkaline solution was investigated in laborstory. Results showed that the new film formed by th...A new water soluble surfaCe film-forming material was developed and its effect on reducing ammonia volatilization from an alkaline solution was investigated in laborstory. Results showed that the new film formed by the material was not only more effective in reducing ammonia loss than any other films tested but also much cheaper. The optimum amount of addition of the new film-forming material was about 10times the theoretical amount to form a monomolecular film. Under the experimental conditions, the new film could effectively depress the ammonia volatilization for at least 6 days. The cumulative ammonia loss rates for different films were fitted to a simple logistic equation, and some important parameters such as the cumulative loss, and the maximum and average volatilization rates were calculated. The effect of different films could be, therefore, compared quantitatively, indicating the new film was most effective in depressing ammonia volatilization.展开更多
Sufficient conditions are obtained for the existence and global stability of a positive periodic solution in a periodic logistic integrodifferential equation with feedback control by using the technique of coincidence...Sufficient conditions are obtained for the existence and global stability of a positive periodic solution in a periodic logistic integrodifferential equation with feedback control by using the technique of coincidence degree and Lyapunov functional.展开更多
The field of environmental sciences is abundant with various interfaces and is the right place for the application of new fundamental approaches leading towards a better understanding of environmental phenomena. Follo...The field of environmental sciences is abundant with various interfaces and is the right place for the application of new fundamental approaches leading towards a better understanding of environmental phenomena. Following the definition of environmental interface by Mihailovic and Bala? [1], such interface can be, for example, placed between: human or animal bodies and surrounding air, aquatic species and water and air around them, and natural or artificially built surfaces (vegetation, ice, snow, barren soil, water, urban communities) and the atmosphere, cells and surrounding environment, etc. Complex environmental interface systems are (i) open and hierarchically organised (ii) interactions between their constituent parts are nonlinear, and (iii) their interaction with the surrounding environment is noisy. These systems are therefore very sensitive to initial conditions, deterministic external perturbations and random fluctuations always present in nature. The study of noisy non-equilibrium processes is fundamental for modelling the dynamics of environmental interface regarded as biophysical complex system and for understanding the mechanisms of spatio-temporal pattern formation in contemporary environmental sciences. In this paper we will investigate an aspect of dynamics of energy flow based on the energy balance equation. The energy exchange between interacting environmen- tal interfaces regarded as biophysical complex systems can be represented by coupled maps. Therefore, we will numerically investigate coupled maps representing that exchange. In ana- lysis of behaviour of these maps we applied Lyapunov exponent and cross sample entropy.展开更多
We apply the imperfect bifurcation theory in Banach spaces to study the exact multiplicity of solutions to a perturbed logistic type equations on a symmetric spatial domain. We obtain the precise bifurcation diagrams.
基金Supported by the Startup Fund of Dalian University of Technology(Grant No.DUT17RC(3)005)。
文摘The logistic equation with Lévy noise is considered.Under suitable conditions,the global existence and uniqueness is obtained;it is shown that the unique positive equilibrium is globally attractive if the initial value is less than the carrying capacity.
文摘In the present paper, we consider the existence of positive periodic solutions for a kind of delay Logistic equations. By using a fixed point theorem in cones, we give some new existence results of single and multiple positive periodic solutions for a kind of delay Logistic equations. Some biomathematical models are presented to illustrate our results.
基金This work was partially supported by the National Natural Science Foundation of China(Grant Nos.10431010 and 10571021)the Key Laboratory for Applied Statistics of Ministry of Education of China(KLAS)
文摘This paper discusses a randomized Logistic equation $\dot N(t) = (r + \alpha \dot B(t))N(t)[1 - \frac{{N(t)}}{K}]$ with an initial value N(0) = N 0, and N 0 is a random variable satisfying 0 < N 0 < K. The existence, uniqueness and global attractivity of positive solutions and maximum likelihood estimate (MLE) of the parameters of the equation are studied.
基金supported by the National Natural Science Foundation of China under Grant No.11101452the Natural Science Foundation Project of CQ CSTC under Grant No.2012jjA00035the National Basic Research Program of China under Grant No.2011CB808000
文摘Empirical likelihood(EL) combined with estimating equations(EE) provides a modern semi-parametric alternative to classical estimation techniques such as maximum likelihood estimation(MLE). This paper not only uses closed form of conditional expectation and conditional variance of Logistic equation with random perturbation to perform maximum empirical likelihood estimation(MELE) for the model parameters, but also proposes an empirical likelihood ratio statistic(ELRS) for hypotheses concerning the interesting parameter. Monte Carlo simulation results show that MELE and ELRS provide competitive performance to parametric alternatives.
基金This work was partially supported by the National Natural Science Foundation of China (10071045)Foundation of Zhejiang for Middle-young-aged Leader of Branch of Learning.
文摘In this paper, we obtain some necessary and sufficient conditions for the oscillation of all positive solutions of a delay Logistic equation with continuous and piecewise constant arguments about the positive equilibrium.
文摘Eucalyptus is the most valuable cultivated forest genus in the tropical and subtropical areas nowadays.It has been a challenge for foresters to model growth due to the genetic variations,management regimes,and multiple products generated from the plantations.In this paper,Logistic equation was used to study the stock growth process of E.urophylla×E.grandis plantation at age of 14 with 6 spacing treatments.And the biological interpretation of the parameters of Logistic equation was analyzed.The results show that it is flexible,precise and accurate to fit the growth process.
基金Project supported by Fundaco para a Ciência e a Tecnologia (FCT) (No. PEst OE/MAT/UI0209/2011)supported by an FCT grant (No. SFRH/BPD/69314/201)
文摘The purpose of this paper is to study the asymptotic behavior of the positive solutions of the problem tu- △u=au-b（x）up in Ω×R＋,u（0）=u0,u（t ）｜ Ω=0, as p→ ＋∞, where Ω is a bounded domain, and b（x） is a nonnegative function. The authors deduce that the limiting configuration solves a parabolic obstacle problem, and afterwards fully describe its long time behavior.
基金supported in part by the National Key Research and Development Program of China(Grant No.2022YFD2001405)in part by the Key Laboratory of Spatial-temporal Big Data Analysis and Application of Natural Resources in Megacities,MNR(Grant No.KFKT-2022-05)+8 种基金in part by the Open Fund of Key Laboratory of Urban Land Resources Monitoring and Simulation,Ministry of Natural Resources(Grant No.KF-2021-06-115)in part by the National Natural Science Foundation of China(Grant No.51979275)in part by the Open Project Program of Key Laboratory of Smart Agricultural Technology in Tropical South China,Ministry of Agriculture and Rural Affairs(Grant No.HNZHNY-KFKT-202202)in part by the Open Project Program of State Key Laboratory of Virtual Reality Technology and Systems,Beihang University(Grant No.VRLAB2022C10)in part by the Jiangsu Province and Education Ministry Co-sponsored Synergistic Innovation Center of Modern Agricultural Equipment(Grant No.XTCX2002)in part by the State Key Laboratory of Clean Energy Utilization(Open Fund Project No.ZJUCEU2022002)in part by Shenzhen Science and Technology Program(Grant No.ZDSYS20210623091808026)in part by the Earmarked Fund(CARS-20)and in part by the 2115 Talent Development Program of China Agricultural University.
文摘As the function of the decomposition of fungi has been clearly researched in the global carbon cycle,it is obviously of value to explore the decomposition rate of fungal populations.This study analyzed the relationship between environmental factors and biodiversity step by step.In order to explore the interaction between the fungi and the relationship between the decomposition rate of fungi with time,the model based on the Logistic model was built and the Lotka-Volterra model was employed in the condition of two kinds of fungi existing in an environment with limited resources.The changing trend of population number and decomposition rate of several fungi under different environmental conditions can be predicted through the model.To illustrate the applicability of the model,Laetiporus conifericola and Hyphoderma setigerum were applied as examples.The results showed that the higher the degree of population diversity,the greater the decomposition rate,and the higher the decomposition efficiency of the ecosystem.Its rich species diversity is conducive to accelerating the decomposition of litter,lignocellulose,and the circulation of the entire ecosystem.Based on the above model and using the data from measuring the mycelial elongation rate of each isolate at 10℃,16℃,and 22℃ under standardized laboratory conditions,the growth patterns of the five fungi combinations were simulated.The results revealed a general increase in growth rate with increasing temperature,which verifies the accuracy of the model.Moreover,it also revealed that the total decomposition rate after fungal incorporation was negatively correlated with the decomposition rate of a fungal single action.Based on the above model,predictions can be made for fungal growth in different environments,and suitable environments for fungal growth can be determined.In the future,the model can be further optimized,and lignin and cellulose decomposition factors can be added to fit the decomposition of logs.The application scenarios of the model can be further broadened,which can contribute to the restoration and management of the ecological environment,as well as produce good effects in the fields of fungi assisting the global carbon cycle and soil problem restoration.
基金This study is supported by the National Key R&D Program of China(Grant Nos.2017YFC1501604 and 2019YFC1509101)the National Natural Science Foundation of China(Grant Nos.41875114,41875057,and 91937302).
文摘Accurate prediction of tropical cyclone(TC)intensity remains a challenge due to the complex physical processes involved in TC intensity changes.A seven-day TC intensity prediction scheme based on the logistic growth equation(LGE)for the western North Pacific(WNP)has been developed using the observed and reanalysis data.In the LGE,TC intensity change is determined by a growth term and a decay term.These two terms are comprised of four free parameters which include a time-dependent growth rate,a maximum potential intensity(MPI),and two constants.Using 33 years of training samples,optimal predictors are selected first,and then the two constants are determined based on the least square method,forcing the regressed growth rate from the optimal predictors to be as close to the observed as possible.The estimation of the growth rate is further refined based on a step-wise regression(SWR)method and a machine learning(ML)method for the period 1982−2014.Using the LGE-based scheme,a total of 80 TCs during 2015−17 are used to make independent forecasts.Results show that the root mean square errors of the LGE-based scheme are much smaller than those of the official intensity forecasts from the China Meteorological Administration(CMA),especially for TCs in the coastal regions of East Asia.Moreover,the scheme based on ML demonstrates better forecast skill than that based on SWR.The new prediction scheme offers strong potential for both improving the forecasts for rapid intensification and weakening of TCs as well as for extending the 5-day forecasts currently issued by the CMA to 7-day forecasts.
文摘In this paper, we study the Logistic type equation x= a（t）x -b（t）x^2＋ e（t）. Under the assumptions that e（t） is small enough and a（t）, b（t） are contained in some positive intervals, we prove that this equation has a positive bounded solution which is stable. Moreover, this solution is a periodic solution if a（t）, b（t） and e（t） are periodic functions, and this solution is an almost periodic solution if a（t）, b（t） and e（t） are almost periodic functions.
文摘Consider the nonautonomous delay logistic equation △yn=pnyn（1-yn-ln/k）,n≥0, where {Pn}n≥0 is a sequence of nonnegative real numbers, {In}n≥0 is a sequence of positive integers satisfying n→∞lim（n-ln）=∞, and k is a positive constant. Only solutions which are positive for n ≥ 0 are considered. We obtain a new sufficient for all positive solutions of （1） to oscillate about k which contains the corresponding result in [2] when i = 1.
文摘This paper studies the global attractivity of the positive equilibrium 1 of the delay logistic difference equation Δ y n=p ny n(1-y τ(n) ), n=0,1,2,...,(*)where {p n} is a sequence of positive real numbers, {τ(n)} is a nondecreasing sequence of integers, τ(n)<n and lim n→∞τ(n)=∞ .It is proved that ifnj=τ(n)p j≤54 for sufficiently large n and ∞j=0p j=∞,then all positive solutions of Eq.(*) tend to 1 as n→∞ .The results improve the existing results in literature.
文摘The author studied the existence of positive solutions of the delay logistic difference equation Δ y n=p ny n(1-y τ(n) ), n =0,1,2,.... where { p n } is a sequence of positive real numbers, { τ(n) } is a nondecreasing sequence of integers, τ(n)<n and lim n →∞ τ(n) =∞. A sufficient condition for the existence of positive solutions of the equation was given.
基金supported by the National Natural Science Foundation of China(#12571082)the Jiangxi Natural Science Foundation(#20232ACB201005)+1 种基金the Shandong Natural Science Foundation(#ZR2024MA024)the Doctoral Science Foundation of Jiangxi Science and Technology Normal University(#2021BSQD30)。
文摘Letτ∈C{0},let p and q be distinct positive integers,and let a,b,c be meromorphic functions such that at least one of b and c is not identically equal to zero.The main purpose of this paper is to study the logistic delay differential equations of the Lotka-Volterra type w′(z)=w(z)[a(z)+b(z)w^(p)(z-τ)+c(z)w^(q)(z-τ)]We prove that any admissible meromorphic solution w of the equation satisfies that the counting function N(r,w)of poles and the characteristic function T(r,w)have the same growth category.Furthermore,we obtain that“most”of admissible meromorphic solutions of a more general delay differential equation w′(z)=w(z)[a(z)+k∑j=1b_(j)w^(j)(z-τ)],have a pole at least.
文摘An analysis of logistic stochastic differential equations(SDEs)with general power-law and driven by a Wiener process is conducted.We prove existence of unique,strong Markovian,continuous solutions.The solutions live(a.s.)on bounded domains D=[0,K]required by applications to biology,ecology and physics with nonrandom threshold parameter K>0(i.e.the maximum carrying constant).Moreover,we present and justify nonstandard numerical methods constructed by specified balanced implicit methods(BIMs).Their weak and L^(p)-convergence follows from the fact that these methods with local Lipschitz-continuous coefficients of logistic SDEs“produce”positive numerical approximations on bounded domain[0,K](a.s.).As commonly known,standard numerical methods such as Taylor-type ones for SDEs fail to do that.Finally,asymptotic stability of nontrivial equilibria x_(∗)=K is proven for both continuous time logistic SDEs and discrete time approximations by BIMs.We exploit the technique of positive,sufficiently smooth and Lyapunov functionals governed by well-known Dynkin’s formula for SDEs.
文摘A new water soluble surfaCe film-forming material was developed and its effect on reducing ammonia volatilization from an alkaline solution was investigated in laborstory. Results showed that the new film formed by the material was not only more effective in reducing ammonia loss than any other films tested but also much cheaper. The optimum amount of addition of the new film-forming material was about 10times the theoretical amount to form a monomolecular film. Under the experimental conditions, the new film could effectively depress the ammonia volatilization for at least 6 days. The cumulative ammonia loss rates for different films were fitted to a simple logistic equation, and some important parameters such as the cumulative loss, and the maximum and average volatilization rates were calculated. The effect of different films could be, therefore, compared quantitatively, indicating the new film was most effective in depressing ammonia volatilization.
文摘Sufficient conditions are obtained for the existence and global stability of a positive periodic solution in a periodic logistic integrodifferential equation with feedback control by using the technique of coincidence degree and Lyapunov functional.
基金funded by the Serbian Ministry of Science and Technology under the project No.III 43007“Research of climate changes and their impact on environment.Monitoring of the impact,adaptation and moderation”for 2011-2014.
文摘The field of environmental sciences is abundant with various interfaces and is the right place for the application of new fundamental approaches leading towards a better understanding of environmental phenomena. Following the definition of environmental interface by Mihailovic and Bala? [1], such interface can be, for example, placed between: human or animal bodies and surrounding air, aquatic species and water and air around them, and natural or artificially built surfaces (vegetation, ice, snow, barren soil, water, urban communities) and the atmosphere, cells and surrounding environment, etc. Complex environmental interface systems are (i) open and hierarchically organised (ii) interactions between their constituent parts are nonlinear, and (iii) their interaction with the surrounding environment is noisy. These systems are therefore very sensitive to initial conditions, deterministic external perturbations and random fluctuations always present in nature. The study of noisy non-equilibrium processes is fundamental for modelling the dynamics of environmental interface regarded as biophysical complex system and for understanding the mechanisms of spatio-temporal pattern formation in contemporary environmental sciences. In this paper we will investigate an aspect of dynamics of energy flow based on the energy balance equation. The energy exchange between interacting environmen- tal interfaces regarded as biophysical complex systems can be represented by coupled maps. Therefore, we will numerically investigate coupled maps representing that exchange. In ana- lysis of behaviour of these maps we applied Lyapunov exponent and cross sample entropy.
基金the National Natural Science Foundation of China (Grant No. 10671049), Longjiang Scholar GrantScience Research Fund of the Education Department of Heilongjiang Province (Grant No.11531246)Harbin Normal University Academic Backbone of Youth Project
文摘We apply the imperfect bifurcation theory in Banach spaces to study the exact multiplicity of solutions to a perturbed logistic type equations on a symmetric spatial domain. We obtain the precise bifurcation diagrams.
