New theorems of asymptotical stability and uniformly asymptotical stability for nonautonomous difference equations are given in this paper. The classical Liapunov asymptotical stability theorem of nonautonomous differ...New theorems of asymptotical stability and uniformly asymptotical stability for nonautonomous difference equations are given in this paper. The classical Liapunov asymptotical stability theorem of nonautonomous difference equations relies on the existence of a positive definite Liapunov function that has an indefinitely small upper bound and whose variation along a given nonautonomous difference equations is negative definite. In this paper, we consider the case that the Liapunov function is only positive definite and its variation is semi-negative definite. At these weaker conditions, we put forward a new asymptotical stability theorem of nonautonomous difference equations by adding to extra conditions on the variation. After that, in addition to the hypotheses of our new asymptotical stability theorem, we obtain a new uniformly asymptotical stability theorem of nonautonomous difference equations provided that the Liapunov function has an indefinitely small upper bound. Example is given to verify our results in the last.展开更多
A three-species ratio-dependent predator-prey diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and sufficient conditions axe obta...A three-species ratio-dependent predator-prey diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and sufficient conditions axe obtained for the global stability of the positive equilibrium of the system.展开更多
Distinctness, Uniformity and Stability (DUS) testing is the technical base of Plant Variety Protection (PVP) and the scientific basis for the approval of Plant Breeder's Rights (PBR). DUS Test Guidelines are no...Distinctness, Uniformity and Stability (DUS) testing is the technical base of Plant Variety Protection (PVP) and the scientific basis for the approval of Plant Breeder's Rights (PBR). DUS Test Guidelines are not only the technical manuals for the DUS testing authorities to conduct the testing, but also the technical standards for the competent authorities to examine the DUS of new varieties of plants. Tea plant, originated from Yunnan Province, China, is a very important woody cash species in the world. The International Union for the Protection of New Varieties of Plants (UPOV) DUS Test Guidelines for tea plant is the first Test Guidelines prepared by China for the UPOV. In this article, the subject, selection, and determination of characteristics, states of expression of characteristics and the selection of example varieties, assessment of the UPOV DUS Test Guidelines for tea plant were elucidated in detail. Finally, the proposal of PVP for tea plant in China was also proposed. The preparation of UPOV DUS Test Guidelines for tea plant will have important significance both for promoting the development of PVP and increasing the status of international PVP fields for China.展开更多
A delayed three-species ratio-dependent predator-prey food-chain model without dominating instantaneous negative feedback is investigated. It is shown that the system is permanent under some appropriate conditions,and...A delayed three-species ratio-dependent predator-prey food-chain model without dominating instantaneous negative feedback is investigated. It is shown that the system is permanent under some appropriate conditions,and sufficient conditions are obtained for the local asymptotic stability of a positive equilibrium of the system.展开更多
In the area of control theory the time-delay systems have been investigated. It's well known that delays often result in instability, therefore, stability analysis of time-delay systems is an important subject in ...In the area of control theory the time-delay systems have been investigated. It's well known that delays often result in instability, therefore, stability analysis of time-delay systems is an important subject in control theory. As a result, many criteria for testing the stability of linear time-delay systems have been proposed. Significant progress has been made in the theory of impulsive systems and impulsive delay systems in recent years. However, the corresponding theory for uncertain impulsive systems and uncertain impulsive delay systems has not been fully developed. In this paper, robust stability criteria are established for uncertain linear delay impulsive systems by using Lyapunov function, Razumikhin techniques and the results obtained. Some examples are given to illustrate our theory.展开更多
Some sufficient, conditions for boundedness and persistence and global asymptotic stability of solutions for a class of delay difference equations with higher order are obtained, which partly solve G. Ladas' two o...Some sufficient, conditions for boundedness and persistence and global asymptotic stability of solutions for a class of delay difference equations with higher order are obtained, which partly solve G. Ladas' two open problems and extend some known results.展开更多
In order to develop a basic electrode with low fume and good usability, a uew slag system has been designed after analyzing several basic electrode slag systems. Then in view of uniform design method, arranging the ex...In order to develop a basic electrode with low fume and good usability, a uew slag system has been designed after analyzing several basic electrode slag systems. Then in view of uniform design method, arranging the experiment points by it, the influenced laws of the uew system coating compouents on the arc stability had been searched. In the formula, niue coating compouents were taken as independent variables and they were divided into six levels in all twenty-four experiments. The arc stability was taken as function and taken down the data when welding and then put them into the computer to be processed statistically. The analysis results give the mathematical model and trend diagrams between independent variables and the function. They indicate that the effects of many coating compouents on the arc stability are in the mutual form. The mutual effects between CaCO3 and BaF2, BaF2 and BaCO3 , increases the arc stability separately. While the mutual effects between CaF2 and iron powder, the square item of iron powder itself decreases the arc stability separately.展开更多
Single-walled carbon nanotubes(SWCNTs)are receiving immense research attention due to their tremendous thermal,electrical,structural and mechanical properties.In this paper,an exact solution of the dynamic response of...Single-walled carbon nanotubes(SWCNTs)are receiving immense research attention due to their tremendous thermal,electrical,structural and mechanical properties.In this paper,an exact solution of the dynamic response of SWCNT with a moving uniformly distributed load is presented.The SWCNT is modelled via the theories of Bernoulli-Euler-thermal elasticity mechanics and solved using Integral transforms.The developed closed-form solution in the present work is compared with existing results and excellent agreements are established.The parametric studies show that as the magnitude of the pressure distribution at the surface increases,the deflection associated with the single walled nanotube increases at any mode whilst a corresponding increase in temperature and foundation parameter have an attenuating effect on deflection.Moreover,an increase in the Winkler parameter,as well as a decrease in the SWCNT mass increases its frequency of vibration.Furthermore,an increase in the speed of the external agent decreases the total external pressure as a result of the removal of dead loads.The present work is envisaged to improve the application of SWCNT as nanodevices for structural,electrical and mechanical systems.展开更多
Stability, boundedness and persistence are three important aspects for an ecological model. In this paper, a further analysis of a class of anaerobic digestion ecological models is performed. Based on the Liupunov Met...Stability, boundedness and persistence are three important aspects for an ecological model. In this paper, a further analysis of a class of anaerobic digestion ecological models is performed. Based on the Liupunov Method, the local stability of all equilibria in the system is got. According to the vector fields described by the system, the proof of the boundedness of the solution on the anaerobic digestion processes is completed in three steps. The method proposed in the discussion on the boundedness can be generalized to the similar problems. Results in this paper give information on how to run the ecological system well by adjusting the system parameters.展开更多
In this paper the perturbed neutral differential equation with positive and negative coefficientsddt[x(t)-C(t)x(t-r)]+P(t)x(t-τ)-Q(t)x(t-σ)=f(t,x(t)), t≥t 0is considered. Sufficient conditions for the zero soluti...In this paper the perturbed neutral differential equation with positive and negative coefficientsddt[x(t)-C(t)x(t-r)]+P(t)x(t-τ)-Q(t)x(t-σ)=f(t,x(t)), t≥t 0is considered. Sufficient conditions for the zero solution of this equation to be uniformly stable as well as asymptotically stable are obtained.展开更多
An attempt has been made to apply Arnold type nonlinear stability criteria to the diagnostic study of the persistence (stability) or breakdown (instability) of the atmospheric flows. In the case of the blocking high, ...An attempt has been made to apply Arnold type nonlinear stability criteria to the diagnostic study of the persistence (stability) or breakdown (instability) of the atmospheric flows. In the case of the blocking high, the cut-off low and the zonal flow, the relationships of the geostrophic stream function versus the potential vorticity of the observed atmosphere are analyzed, which indicates that Arnold second type nonlinear stability theorem is more relevant to the observed atmosphere than the first one. For both the stable and unstable zonal flows, Arnold second type nonlinear stability criteria are applied to the diagnosis. The primary results show that our analyses correspond well to the evolution of the atmospheric motions. The synoptically stable zonal flows satisfy Arnol′d second type nonlinear stability criteria; while the synoptically unstable ones violate the nonlinear stability criteria.展开更多
The AHP-GDM model is used for the assessment of structural stability, with the Bohai Sea area as an exam- ple. In this model, the credit degree of each expert is calculated through the assessment matrix based on the s...The AHP-GDM model is used for the assessment of structural stability, with the Bohai Sea area as an exam- ple. In this model, the credit degree of each expert is calculated through the assessment matrix based on the similarity and diversity of vector. The comprehensive opinions of expert panel are quantitatively obtained by considering the effect ofcredit degree. According to the geological structural setting, the Bohai Sea is di- vided into twelve assessment zones of structural stability by non-uniform element method. The structural stability grade of each zone is obtained on the basis of the latest geophysical data, earthquake statistical data, and the information of fault activities, current stress field and crustal deformation. The results show that there are one relatively stable area, three relatively sub-stable areas, six relatively sub-unstable areas and two relatively unstable areas. The assessment results of non-uniform element method are very close with those of uniform grid method with size of 0.25 in longitude direction and 0.14 in latitude direction. However the workload of non-uniform element method is only 1 / 16 of the latter. Compared with traditional assessment methods of structural stability, a more objective and reliable assessment result can be obtained by combining non-uniform element method and AHP-GDM model.展开更多
In this paper,the author investigates uuiform stability,asymptotic stability,and uniform asymptotic stability forthe zero solution of neutral functional differentialequations.Some well-known results are improved.
Consider the neutral differential equation with positive and negative coefficients and unbounded delay ddt[x(t)-P(t)x(h(t))]+Q(t)x(q(t))-R(t)x(r(t))=0, t≥t 0, where P(t)∈C([t 0, ∞), R), Q(t), R(t)∈C([t 0, ∞...Consider the neutral differential equation with positive and negative coefficients and unbounded delay ddt[x(t)-P(t)x(h(t))]+Q(t)x(q(t))-R(t)x(r(t))=0, t≥t 0, where P(t)∈C([t 0, ∞), R), Q(t), R(t)∈C([t 0, ∞), [WTHZ]R +), and h, q, r: [t 0, ∞)→R are continuously differentiable and strictly increasing, h(t)<t, q(t)<t, r(t)<t for all t≥t 0. In this paper, the authors obtain sufficient conditions for the zero solution of this equation with unbounded delay to be uniformly stable as well as asymptotically stable. [WTH1X]展开更多
The paper deals with the problem of the asymptotic stability for general continuous nonlinear networked control systems (NCSs). Based on Lyapunov stability theorem combined with improved Razumikhin technique, the su...The paper deals with the problem of the asymptotic stability for general continuous nonlinear networked control systems (NCSs). Based on Lyapunov stability theorem combined with improved Razumikhin technique, the sufficient conditions of asymptotic stability for the system are derived. With the proposed method, the estimate of maximum allowable delay bound (MADB) for linear networked control system is also given. Compared to the other methods, the proposed method gives a much less conservative MADB and more general results. Numerical examples and some simulations are worked out to demonstrate the effectiveness and performance of the proposed method.展开更多
Based on the theory of fractional calculus, the contraction mapping principle, Krasnoselskii fixed point theorem and the inequality technique, a class of Caputo fractional-order BAM neural networks with delays in the ...Based on the theory of fractional calculus, the contraction mapping principle, Krasnoselskii fixed point theorem and the inequality technique, a class of Caputo fractional-order BAM neural networks with delays in the leakage terms is investigated in this paper. Some new sufficient conditions are established to guarantee the existence and uniqueness of the nontrivial solution. Moreover, uniform stability of such networks is proposed in fixed time intervals. Finally, an illustrative example is also given to demonstrate the effectiveness of the obtained results.展开更多
In this paper the stability of nonlinear nonautonomous systems under the frequently-acting perturbation is studied. This study is a forward development of the study of the stability in the Liapunov sense; furthermore,...In this paper the stability of nonlinear nonautonomous systems under the frequently-acting perturbation is studied. This study is a forward development of the study of the stability in the Liapunov sense; furthermore, it is of significance in practice since perturbations are often not single in the time domain. Malkin proved a general theorem about thesubject. To apply the theorem, however, the user has to construct a Liapunov function which satisfies specified conditions and it is difficult to find such a function for nonlinear nonautonomous systems. In the light of the principle of Liapunov's indirect method, which is an effective method to decide the stability of nonlinear systems in the Liapunov sense, the authors have achieved several important conclusions expressed in the form of theorems to determine the stability of nonlinear nonautonomous systems under the frequently-acting perturbation.展开更多
In this article, an infectious model with saturation effect is considered. By using compound matrix theory and a series of theorems associated to qualitative theory of differential equations which are introduced by Mu...In this article, an infectious model with saturation effect is considered. By using compound matrix theory and a series of theorems associated to qualitative theory of differential equations which are introduced by Muldowney and Micheal Li, we study globally stable problem of the model.展开更多
In this paper,by applying Comparison Theorem of differential equation,Continuation Theorem of coincidence degree theory,Barbalat Lemma and Lyapunov Function,a diffusion system with distributive time delay and ratio-de...In this paper,by applying Comparison Theorem of differential equation,Continuation Theorem of coincidence degree theory,Barbalat Lemma and Lyapunov Function,a diffusion system with distributive time delay and ratio-dependence functional response is studied.It is proved that the system is uniformly persistent under appropriate conditions.Further,if the system is a periodic one,it can have a strictly positive periodic solution which is globally asymptotically stable under appropriations.Some new results are obtained.展开更多
Let X and Y be real Banach spaces. The stability of Hyers Ulam Rassias approximate isometries on restricted domains S (unbounded or bounded) for into mapping f: S→Y satisfying ‖ f(x)-f(y)‖-‖x-y‖≤ε(x,y) for al...Let X and Y be real Banach spaces. The stability of Hyers Ulam Rassias approximate isometries on restricted domains S (unbounded or bounded) for into mapping f: S→Y satisfying ‖ f(x)-f(y)‖-‖x-y‖≤ε(x,y) for all x,y∈S is studied in case that the target space Y is uniformly convex Banach space of the modulus of convexity of power type q ≥2 or Y is the L q(Ω,,μ) (1<q <+∞) space or Y is a Hilbert space. Furthermore, the stability of approximate isometries for the case that (x,y)=‖x‖ p+‖y‖ p or (x,y)=‖x-y‖ p for p ≠1 is investigated.展开更多
文摘New theorems of asymptotical stability and uniformly asymptotical stability for nonautonomous difference equations are given in this paper. The classical Liapunov asymptotical stability theorem of nonautonomous difference equations relies on the existence of a positive definite Liapunov function that has an indefinitely small upper bound and whose variation along a given nonautonomous difference equations is negative definite. In this paper, we consider the case that the Liapunov function is only positive definite and its variation is semi-negative definite. At these weaker conditions, we put forward a new asymptotical stability theorem of nonautonomous difference equations by adding to extra conditions on the variation. After that, in addition to the hypotheses of our new asymptotical stability theorem, we obtain a new uniformly asymptotical stability theorem of nonautonomous difference equations provided that the Liapunov function has an indefinitely small upper bound. Example is given to verify our results in the last.
文摘A three-species ratio-dependent predator-prey diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and sufficient conditions axe obtained for the global stability of the positive equilibrium of the system.
文摘Distinctness, Uniformity and Stability (DUS) testing is the technical base of Plant Variety Protection (PVP) and the scientific basis for the approval of Plant Breeder's Rights (PBR). DUS Test Guidelines are not only the technical manuals for the DUS testing authorities to conduct the testing, but also the technical standards for the competent authorities to examine the DUS of new varieties of plants. Tea plant, originated from Yunnan Province, China, is a very important woody cash species in the world. The International Union for the Protection of New Varieties of Plants (UPOV) DUS Test Guidelines for tea plant is the first Test Guidelines prepared by China for the UPOV. In this article, the subject, selection, and determination of characteristics, states of expression of characteristics and the selection of example varieties, assessment of the UPOV DUS Test Guidelines for tea plant were elucidated in detail. Finally, the proposal of PVP for tea plant in China was also proposed. The preparation of UPOV DUS Test Guidelines for tea plant will have important significance both for promoting the development of PVP and increasing the status of international PVP fields for China.
文摘A delayed three-species ratio-dependent predator-prey food-chain model without dominating instantaneous negative feedback is investigated. It is shown that the system is permanent under some appropriate conditions,and sufficient conditions are obtained for the local asymptotic stability of a positive equilibrium of the system.
基金This project was supported by the National Natural Science Foundation of China (60274007) NSERC-Canada.
文摘In the area of control theory the time-delay systems have been investigated. It's well known that delays often result in instability, therefore, stability analysis of time-delay systems is an important subject in control theory. As a result, many criteria for testing the stability of linear time-delay systems have been proposed. Significant progress has been made in the theory of impulsive systems and impulsive delay systems in recent years. However, the corresponding theory for uncertain impulsive systems and uncertain impulsive delay systems has not been fully developed. In this paper, robust stability criteria are established for uncertain linear delay impulsive systems by using Lyapunov function, Razumikhin techniques and the results obtained. Some examples are given to illustrate our theory.
文摘Some sufficient, conditions for boundedness and persistence and global asymptotic stability of solutions for a class of delay difference equations with higher order are obtained, which partly solve G. Ladas' two open problems and extend some known results.
基金Supported by Research Project of Heilongjiang Education Science and Technology (11521051)
文摘In order to develop a basic electrode with low fume and good usability, a uew slag system has been designed after analyzing several basic electrode slag systems. Then in view of uniform design method, arranging the experiment points by it, the influenced laws of the uew system coating compouents on the arc stability had been searched. In the formula, niue coating compouents were taken as independent variables and they were divided into six levels in all twenty-four experiments. The arc stability was taken as function and taken down the data when welding and then put them into the computer to be processed statistically. The analysis results give the mathematical model and trend diagrams between independent variables and the function. They indicate that the effects of many coating compouents on the arc stability are in the mutual form. The mutual effects between CaCO3 and BaF2, BaF2 and BaCO3 , increases the arc stability separately. While the mutual effects between CaF2 and iron powder, the square item of iron powder itself decreases the arc stability separately.
文摘Single-walled carbon nanotubes(SWCNTs)are receiving immense research attention due to their tremendous thermal,electrical,structural and mechanical properties.In this paper,an exact solution of the dynamic response of SWCNT with a moving uniformly distributed load is presented.The SWCNT is modelled via the theories of Bernoulli-Euler-thermal elasticity mechanics and solved using Integral transforms.The developed closed-form solution in the present work is compared with existing results and excellent agreements are established.The parametric studies show that as the magnitude of the pressure distribution at the surface increases,the deflection associated with the single walled nanotube increases at any mode whilst a corresponding increase in temperature and foundation parameter have an attenuating effect on deflection.Moreover,an increase in the Winkler parameter,as well as a decrease in the SWCNT mass increases its frequency of vibration.Furthermore,an increase in the speed of the external agent decreases the total external pressure as a result of the removal of dead loads.The present work is envisaged to improve the application of SWCNT as nanodevices for structural,electrical and mechanical systems.
基金Supported by the National Natural Science Foundation of China (No.60372012) and NSF of Chongqing (No.0831)
文摘Stability, boundedness and persistence are three important aspects for an ecological model. In this paper, a further analysis of a class of anaerobic digestion ecological models is performed. Based on the Liupunov Method, the local stability of all equilibria in the system is got. According to the vector fields described by the system, the proof of the boundedness of the solution on the anaerobic digestion processes is completed in three steps. The method proposed in the discussion on the boundedness can be generalized to the similar problems. Results in this paper give information on how to run the ecological system well by adjusting the system parameters.
文摘In this paper the perturbed neutral differential equation with positive and negative coefficientsddt[x(t)-C(t)x(t-r)]+P(t)x(t-τ)-Q(t)x(t-σ)=f(t,x(t)), t≥t 0is considered. Sufficient conditions for the zero solution of this equation to be uniformly stable as well as asymptotically stable are obtained.
文摘An attempt has been made to apply Arnold type nonlinear stability criteria to the diagnostic study of the persistence (stability) or breakdown (instability) of the atmospheric flows. In the case of the blocking high, the cut-off low and the zonal flow, the relationships of the geostrophic stream function versus the potential vorticity of the observed atmosphere are analyzed, which indicates that Arnold second type nonlinear stability theorem is more relevant to the observed atmosphere than the first one. For both the stable and unstable zonal flows, Arnold second type nonlinear stability criteria are applied to the diagnosis. The primary results show that our analyses correspond well to the evolution of the atmospheric motions. The synoptically stable zonal flows satisfy Arnol′d second type nonlinear stability criteria; while the synoptically unstable ones violate the nonlinear stability criteria.
基金The National High Technology Research and Development Program of China(863Program)under contract Nos 2009AA093401 and 2010AA09Z302the National Natural Science Foundation of China(Key Program)under contract No.90814011+1 种基金Special Funds for Postdoctoral Innovative Projects of Shandong Province under contract No.201102008the Fundamental Research Funds for the Central Universities under contract No.11CX04037A
文摘The AHP-GDM model is used for the assessment of structural stability, with the Bohai Sea area as an exam- ple. In this model, the credit degree of each expert is calculated through the assessment matrix based on the similarity and diversity of vector. The comprehensive opinions of expert panel are quantitatively obtained by considering the effect ofcredit degree. According to the geological structural setting, the Bohai Sea is di- vided into twelve assessment zones of structural stability by non-uniform element method. The structural stability grade of each zone is obtained on the basis of the latest geophysical data, earthquake statistical data, and the information of fault activities, current stress field and crustal deformation. The results show that there are one relatively stable area, three relatively sub-stable areas, six relatively sub-unstable areas and two relatively unstable areas. The assessment results of non-uniform element method are very close with those of uniform grid method with size of 0.25 in longitude direction and 0.14 in latitude direction. However the workload of non-uniform element method is only 1 / 16 of the latter. Compared with traditional assessment methods of structural stability, a more objective and reliable assessment result can be obtained by combining non-uniform element method and AHP-GDM model.
文摘Consider the neutral differential equation with positive and negative coefficients and unbounded delay ddt[x(t)-P(t)x(h(t))]+Q(t)x(q(t))-R(t)x(r(t))=0, t≥t 0, where P(t)∈C([t 0, ∞), R), Q(t), R(t)∈C([t 0, ∞), [WTHZ]R +), and h, q, r: [t 0, ∞)→R are continuously differentiable and strictly increasing, h(t)<t, q(t)<t, r(t)<t for all t≥t 0. In this paper, the authors obtain sufficient conditions for the zero solution of this equation with unbounded delay to be uniformly stable as well as asymptotically stable. [WTH1X]
基金supported by Hi-Tech Research and Development (863) Program of China (No.2006AA04Z207)Research Fund for Doctorial Programof Higher Education of China (No.20060006018)+1 种基金International Cooperation Program of Science and Technology of China (No.2007DFA11530)the National Natural Science Foundation of China (No.60875072)
文摘The paper deals with the problem of the asymptotic stability for general continuous nonlinear networked control systems (NCSs). Based on Lyapunov stability theorem combined with improved Razumikhin technique, the sufficient conditions of asymptotic stability for the system are derived. With the proposed method, the estimate of maximum allowable delay bound (MADB) for linear networked control system is also given. Compared to the other methods, the proposed method gives a much less conservative MADB and more general results. Numerical examples and some simulations are worked out to demonstrate the effectiveness and performance of the proposed method.
文摘Based on the theory of fractional calculus, the contraction mapping principle, Krasnoselskii fixed point theorem and the inequality technique, a class of Caputo fractional-order BAM neural networks with delays in the leakage terms is investigated in this paper. Some new sufficient conditions are established to guarantee the existence and uniqueness of the nontrivial solution. Moreover, uniform stability of such networks is proposed in fixed time intervals. Finally, an illustrative example is also given to demonstrate the effectiveness of the obtained results.
文摘In this paper the stability of nonlinear nonautonomous systems under the frequently-acting perturbation is studied. This study is a forward development of the study of the stability in the Liapunov sense; furthermore, it is of significance in practice since perturbations are often not single in the time domain. Malkin proved a general theorem about thesubject. To apply the theorem, however, the user has to construct a Liapunov function which satisfies specified conditions and it is difficult to find such a function for nonlinear nonautonomous systems. In the light of the principle of Liapunov's indirect method, which is an effective method to decide the stability of nonlinear systems in the Liapunov sense, the authors have achieved several important conclusions expressed in the form of theorems to determine the stability of nonlinear nonautonomous systems under the frequently-acting perturbation.
基金The NNSF (10171010) of China Major Project of Education Ministry (01061) of China, Key Library for Vegetation Ecology, Education Ministry of China.
文摘In this article, an infectious model with saturation effect is considered. By using compound matrix theory and a series of theorems associated to qualitative theory of differential equations which are introduced by Muldowney and Micheal Li, we study globally stable problem of the model.
文摘In this paper,by applying Comparison Theorem of differential equation,Continuation Theorem of coincidence degree theory,Barbalat Lemma and Lyapunov Function,a diffusion system with distributive time delay and ratio-dependence functional response is studied.It is proved that the system is uniformly persistent under appropriate conditions.Further,if the system is a periodic one,it can have a strictly positive periodic solution which is globally asymptotically stable under appropriations.Some new results are obtained.
文摘Let X and Y be real Banach spaces. The stability of Hyers Ulam Rassias approximate isometries on restricted domains S (unbounded or bounded) for into mapping f: S→Y satisfying ‖ f(x)-f(y)‖-‖x-y‖≤ε(x,y) for all x,y∈S is studied in case that the target space Y is uniformly convex Banach space of the modulus of convexity of power type q ≥2 or Y is the L q(Ω,,μ) (1<q <+∞) space or Y is a Hilbert space. Furthermore, the stability of approximate isometries for the case that (x,y)=‖x‖ p+‖y‖ p or (x,y)=‖x-y‖ p for p ≠1 is investigated.