Based on the continuum physics and taking into account variation of the heat dissipation, Helmholtz free ener-gy, internal energy and exothermicity with the thermodynamic process, in this paper, the functional equatio...Based on the continuum physics and taking into account variation of the heat dissipation, Helmholtz free ener-gy, internal energy and exothermicity with the thermodynamic process, in this paper, the functional equations of the general-ized stress and entropy associated ivith the time and temperature are derived for the irreversible process of thermoviscoelastic-plastic materials. As an example, the response functionals of Maxwell viscoelastic materials are obtained.展开更多
This paper examines an epidemic predator-prey model with prey dispersal and Holling type-II functional response. In this model, it is assumed that the predator population suffers a transmissible disease. By analyzing ...This paper examines an epidemic predator-prey model with prey dispersal and Holling type-II functional response. In this model, it is assumed that the predator population suffers a transmissible disease. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria and the existence of Hopf bifurcations at the coexistence equilibrium is addressed. Using Lyapunov functionals and LaSalle's invariance principle, we obtained the sufficient conditions for the global stability of the trivial equilibrium, the predator-extinction equilibrium, the disease-free equilibrium and the coexistence equilibrium, respectively. The paper also includes numerical simulations to illustrate the analytical results.展开更多
A predator-prey model with prey dispersal and Holling type-Ⅱ functional response is investigated.In this model,the time delay due to the gestation of the predator and stagestructure for the predator are considered.By...A predator-prey model with prey dispersal and Holling type-Ⅱ functional response is investigated.In this model,the time delay due to the gestation of the predator and stagestructure for the predator are considered.By analyzing the corresponding characteristic equations,the local stability of each of the nonnegative equilibria is discussed.The existence of Hopf bifurcations at the positive equilibrium is established.By using Lyapunov functionals and LaSalle’s invariance principle,sufficient conditions are obtained for the global stability of the positive equilibrium,the nonnegative boundary equilibrium and the trivial equilibrium of the model,respectively.Numerical simulations are carried out to illustrate the main results.展开更多
In this paper, we study a modified Leslie-Gower predator-prey model with Smith growth subject to homogeneous Neumann boundary condition, in which the functional response is the Crowley-Martin functional response term....In this paper, we study a modified Leslie-Gower predator-prey model with Smith growth subject to homogeneous Neumann boundary condition, in which the functional response is the Crowley-Martin functional response term. Firstly, for ODE model, the local stability of equilibrium point is given. And by using bifurcation theory and selecting suitable bifurcation parameters, we find many kinds of bifurcation phenomena, including Transcritical bifurcation and Hopf bifurcation. For the reaction-diffusion model, we find that Turing instability occurs. Besides, it is proved that Hopf bifurcation exists in the model. Finally, numerical simulations are presented to verify and illustrate the theoretical results.展开更多
By using the continuation theorem of coincidence theory,the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional response x_(1)(t)=x_(1)(t)a_(1)(t...By using the continuation theorem of coincidence theory,the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional response x_(1)(t)=x_(1)(t)a_(1)(t)-b_(1)(t)x_(1)(t)-c_(1)(t)y(t)1+m(t)x_(1)(t)+D_(1)(t)[x_(2)(t)-x_(1)(t)],x_(2)(t)=x_(2)(t)a_(2)(t)-b_(2)(t)x_(2)(t)-c_(2)(t)∫^(0)_(-τ)k(s)x_(2)(t+s)d s+D_(2)(t)[x_(1)(t)-x_(2)(t)],y′(t)=y(t)a_(3)(t)-b_(3)(t)y(t)-c_(3)(t)x_(1)(t)1+m(t)x_(1)(t)is established,where a i(t),b_(i)(t),c_(i)(t)(i=1,2,3),m(t)and D_(i)(t)(i=1,2)are all positive periodic continuous functions with period w>0,τis a nonnegative constant and k(s)is a continuous nonnegative function on[-τ,0].展开更多
Single fiber pull-out testing was conducted to study the origin of the functional responses to loading of carbon fiber reinforced cement-based composites. The variation of electrical resistance with the bonding force ...Single fiber pull-out testing was conducted to study the origin of the functional responses to loading of carbon fiber reinforced cement-based composites. The variation of electrical resistance with the bonding force on the fiber-matrix interface was measured. Single fiber electromechanical testing was also conducted by measuring the electrical resistance under static tension. Comparison of the results shows that the resistance increasing during single fiber pull-out is mainly due to the changes at the interface. The conduction mechanism of the composite can be explained by the tunneling model. The interfacial stress causes the deformation of interfacial structure and the interfacial debonding, which have influences on the tunneling effect and result in the change of resistance.展开更多
Understanding the temperature affecting parasitic efficiency is critical to succeed in utilizing parasitoid as natural enemy in pest management. Laboratory studies were carried out to determine the effects of temperat...Understanding the temperature affecting parasitic efficiency is critical to succeed in utilizing parasitoid as natural enemy in pest management. Laboratory studies were carried out to determine the effects of temperature on parasitoid preference of female Anagrus nilaparvatae Pang et Wang （Hymenoptera：Mymaridae） to the eggs of whitebacked planthopper （WBPH）, Sogatella furcifera Horváth and brown planthopper （BPH）, Nilaparvata lugens Stl to build a composite model describing changes in parasitic response along a temperature gradient （18, 22, 26, 30, 34°C）. The results showed that attack responses of A. nilaparvatae on WBPH and BPH were the best described by a Type II functional response. The two parameters, attack rates （a） and handling times （Th）, of A. nilaparvatae to both eggs were influenced by the temperature. The maximum attack rates to WBPH （1.235） and BPH （1.049） were at 26 and 34°C, respectively, and the shortest handling times to WBPH （0.063） and BPH （0.057） were at 30 and 26°C, respectively. However, the optimal temperature for parasitic efficiency of A. nilaparvatae to WBPH and BPH eggs was both at 26°C, which showed that the present microclimate temperature of the habitat in the paddyfield was beneficial to A. nilaparvatae and indicated that parasitic efficiency of A. nilaparvatae would be impaired by global warming.展开更多
In complex feed structures, there exist main chemical functional groups which are associated with nutrient utilization and availability and functionality. Each functional group has unique molecular structure therefore...In complex feed structures, there exist main chemical functional groups which are associated with nutrient utilization and availability and functionality. Each functional group has unique molecular structure therefore produce unique molecular vibration spectral profile. Feed processing has been used to improve nutrient utilization for many years. However, to date, there was little study on processing-induced changes of feed intrinsic structure and functional groups on a molecular basis within intact tissue. This is because limited research technique is available to study inherent structure on a molecular basis. Recently bioanalytical techniques： such as Synchrotron Infrared Microspectroscopy as well as Diffuse Reflectance Infrared Fourier Transform molecular spectroscopy have been developed. These techniques enable to detect molecular structure change within intact tissues. These techniques can prevent destruction or alteration of the intrinsic protein structures during processing for analysis. However, these techniques have not been used in animal feed and nutrition research. The objective of this review was show that with the advanced technique, sensitivity and responses of functional groups to feed processing on a molecular basis could be detected in my research team. These functional groups are highly associated with nutrient utilization in animals.展开更多
In this paper,we consider a nonlinear size-structured population model with functional response,which describes the dynamics of a predator-prey system living in a common habitat.We present a kind of functional respons...In this paper,we consider a nonlinear size-structured population model with functional response,which describes the dynamics of a predator-prey system living in a common habitat.We present a kind of functional response for the prey being a plant or algae,and explain its biological meanings.When the vital rates depend both on the individual's size and on the total population or only depend on the former,we obtain the existence of equilibrium solutions.展开更多
This paper deals with the questio n of global stability of the positive locally asymptotically stable equilibrium in a class of predator\|prey system of Gause\|typ e with Holling Ⅲ functional response. The Dulac'...This paper deals with the questio n of global stability of the positive locally asymptotically stable equilibrium in a class of predator\|prey system of Gause\|typ e with Holling Ⅲ functional response. The Dulac's criterion is applied and lia punov functions are constructed to establish the global stability.展开更多
The effect of a protection zone on a diffusion predator-prey model with Ivlev-type functional response is considered.We discuss the existence and non-existence of positive steady state solutions by using the bifurcati...The effect of a protection zone on a diffusion predator-prey model with Ivlev-type functional response is considered.We discuss the existence and non-existence of positive steady state solutions by using the bifurcation theory.It is shown that the protection zone for prey has beneficial effects on the coexistence of the two species when the growth rate of predator is positive.Moreover,we examine the dependence of the coexistence region on the efficiency of the predator capture of the prey and the protection zone.展开更多
The main purpose of this paper is to study the persistence of the general multispecies competition predator-pray system with Holling Ⅲ type functional response. In this system, the competition among predator species ...The main purpose of this paper is to study the persistence of the general multispecies competition predator-pray system with Holling Ⅲ type functional response. In this system, the competition among predator species and among prey species are simultaneously considered. By using the comparison theory and qualitative analysis, the sufficient conditions for uniform strong persistence are obtained.展开更多
Hyper-and multi-spectral image fusion is an important technology to produce hyper-spectral and hyper-resolution images,which always depends on the spectral response function andthe point spread function.However,few wo...Hyper-and multi-spectral image fusion is an important technology to produce hyper-spectral and hyper-resolution images,which always depends on the spectral response function andthe point spread function.However,few works have been payed on the estimation of the two degra-dation functions.To learn the two functions from image pairs to be fused,we propose a Dirichletnetwork,where both functions are properly constrained.Specifically,the spatial response function isconstrained with positivity,while the Dirichlet distribution along with a total variation is imposedon the point spread function.To the best of our knowledge,the neural network and the Dirichlet regularization are exclusively investigated,for the first time,to estimate the degradation functions.Both image degradation and fusion experiments demonstrate the effectiveness and superiority of theproposed Dirichlet network.展开更多
In recent years,rumor spreading has caused widespread public panic and affected the whole social harmony and stability.Consequently,how to control the rumor spreading effectively and reduce its negative influence urge...In recent years,rumor spreading has caused widespread public panic and affected the whole social harmony and stability.Consequently,how to control the rumor spreading effectively and reduce its negative influence urgently needs people to pay much attention.In this paper,we mainly study the near-optimal control of a stochastic rumor spreading model with Holling II functional response function and imprecise parameters.Firstly,the science knowledge propagation and the refutation mechanism as the control strategies are introduced into a stochastic rumor spreading model.Then,some sufficient and necessary conditions for the near-optimal control of the stochastic rumor spreading model are discussed respectively.Finally,through some numerical simulations,the validity and availability of theoretical analysis is verified.Meanwhile,it shows the significance and effectiveness of the proposed control strategies on controlling rumor spreading,and demonstrates the influence of stochastic disturbance and imprecise parameters on the process of rumor spreading.展开更多
In this study, the impulsive predator-prey dynamic systems on time scales calculus are studied. When the system has periodic solution is investigated, and three different conditions have been found, which are necessar...In this study, the impulsive predator-prey dynamic systems on time scales calculus are studied. When the system has periodic solution is investigated, and three different conditions have been found, which are necessary for the periodic solution of the predator-prey dynamic systems with Beddington-DeAngelis type functional response. For this study the main tools are time scales calculus and coincidence degree theory. Also the findings are beneficial for continuous case, discrete case and the unification of both these cases. Additionally, unification of continuous and discrete case is a good example for the modeling of the life cycle of insects.展开更多
Allam and Tantawy [1] presented an analytical solu- tion for stress distribution and perturbations of the magnetic field vector in FGM hollow structures made from viscoelas- tic composite materials .While studying thi...Allam and Tantawy [1] presented an analytical solu- tion for stress distribution and perturbations of the magnetic field vector in FGM hollow structures made from viscoelas- tic composite materials .While studying this article, the dis- cusser noticed a confusion in regarding Maxwell＇s electro- magnetic stress expression展开更多
This paper investigates the existence of periodic solutions of a three-species food-chain diffusive system with Beddington-DeAngelis functional responses and time delays in a two-patch environment on time scales. By u...This paper investigates the existence of periodic solutions of a three-species food-chain diffusive system with Beddington-DeAngelis functional responses and time delays in a two-patch environment on time scales. By using a continuation theorem based on coincidence degree theory, we obtain sufficient criteria for the existence of periodic solutions for the system. Moreover, when the time scale T is chosen as R or Z, the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the method is unified to provide the existence of the desired solutions for continuous differential equations and discrete difference equations.展开更多
In this paper,we consider the positive steady state solutions of a predator-prey model with Holling type Ⅱfunctional response and cross-diffusion,where two cross-diffusion rates represent the tendency of prey to keep...In this paper,we consider the positive steady state solutions of a predator-prey model with Holling type Ⅱfunctional response and cross-diffusion,where two cross-diffusion rates represent the tendency of prey to keep away from its predator and the tendency of the predator to chase its prey,respectively.Applying the fixed point index theory,some sufficient conditions for the existence of positive steady state solutions are established.Furthermore,the non-existence of positive steady state solutions is studied.展开更多
A predator-prey diffusion system with a Bazykin functional response is studied. The existence of equilibrium points, the stability of normal number equilibrium points and the existence of Hopf bifurcationes are invest...A predator-prey diffusion system with a Bazykin functional response is studied. The existence of equilibrium points, the stability of normal number equilibrium points and the existence of Hopf bifurcationes are investigated for the proposed system, the existence of positive solutions in the system is discussed under Neumann boundary conditions, and the stability of constant equilibrium points is focused on under the condition of Hurwitz criterion. The results show that there exist positive equilibrium points in the system under Neumann boundary conditions, and the normal number equilibrium points are stable when specific conditions are satisfied, and the bifurcation points of Hopf bifurcationes and their orders are given.展开更多
To investigate the effects of self-memory diffusion on predator-prey models, we consider a predator-prey model with Bazykin functional response of self- memory diffusion. The uniqueness, boundedness, positivity, exist...To investigate the effects of self-memory diffusion on predator-prey models, we consider a predator-prey model with Bazykin functional response of self- memory diffusion. The uniqueness, boundedness, positivity, existence and stability of equilibrium point of the model are studied. In this paper, the uniqueness of the solution is discussed under the non-negative initial function and Neumann boundary conditions satisfying a specific space. The boundness of the solution is proved by the comparison principle of parabolic equations, and the positivity of the solution is proved by the strong maximum principle of parabolic equations. Hurwitz criterion and Lyapunov function construction are used to analyze the local stability and global stability of feasible equilibrium points. The results show that the system solution is unique non-negative and bounded. The model is unstable at the trivial equilibrium point E0 and the boundary equilibrium point E1, and the condition of whether the positive equilibrium point E2 is stable under certain conditions is given.展开更多
文摘Based on the continuum physics and taking into account variation of the heat dissipation, Helmholtz free ener-gy, internal energy and exothermicity with the thermodynamic process, in this paper, the functional equations of the general-ized stress and entropy associated ivith the time and temperature are derived for the irreversible process of thermoviscoelastic-plastic materials. As an example, the response functionals of Maxwell viscoelastic materials are obtained.
基金Supported by the Social Science Foundation of Hebei Province(Grant No.HB23TJ003)the Science Research Project of Hebei Education Department(Grant No.BJK2024197)。
文摘This paper examines an epidemic predator-prey model with prey dispersal and Holling type-II functional response. In this model, it is assumed that the predator population suffers a transmissible disease. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria and the existence of Hopf bifurcations at the coexistence equilibrium is addressed. Using Lyapunov functionals and LaSalle's invariance principle, we obtained the sufficient conditions for the global stability of the trivial equilibrium, the predator-extinction equilibrium, the disease-free equilibrium and the coexistence equilibrium, respectively. The paper also includes numerical simulations to illustrate the analytical results.
基金Supported by the Social Science Foundation of Hebei Province(HB23TJO03)。
文摘A predator-prey model with prey dispersal and Holling type-Ⅱ functional response is investigated.In this model,the time delay due to the gestation of the predator and stagestructure for the predator are considered.By analyzing the corresponding characteristic equations,the local stability of each of the nonnegative equilibria is discussed.The existence of Hopf bifurcations at the positive equilibrium is established.By using Lyapunov functionals and LaSalle’s invariance principle,sufficient conditions are obtained for the global stability of the positive equilibrium,the nonnegative boundary equilibrium and the trivial equilibrium of the model,respectively.Numerical simulations are carried out to illustrate the main results.
文摘In this paper, we study a modified Leslie-Gower predator-prey model with Smith growth subject to homogeneous Neumann boundary condition, in which the functional response is the Crowley-Martin functional response term. Firstly, for ODE model, the local stability of equilibrium point is given. And by using bifurcation theory and selecting suitable bifurcation parameters, we find many kinds of bifurcation phenomena, including Transcritical bifurcation and Hopf bifurcation. For the reaction-diffusion model, we find that Turing instability occurs. Besides, it is proved that Hopf bifurcation exists in the model. Finally, numerical simulations are presented to verify and illustrate the theoretical results.
基金Supported by the National Natural Science Foundation of China(19531070)the Major and Youth Project Foundation of Hubei Province Education Department(2001Z06003)(2002B00002).
文摘By using the continuation theorem of coincidence theory,the existence of a positive periodic solution for a two patches competition system with diffusion and time delay and functional response x_(1)(t)=x_(1)(t)a_(1)(t)-b_(1)(t)x_(1)(t)-c_(1)(t)y(t)1+m(t)x_(1)(t)+D_(1)(t)[x_(2)(t)-x_(1)(t)],x_(2)(t)=x_(2)(t)a_(2)(t)-b_(2)(t)x_(2)(t)-c_(2)(t)∫^(0)_(-τ)k(s)x_(2)(t+s)d s+D_(2)(t)[x_(1)(t)-x_(2)(t)],y′(t)=y(t)a_(3)(t)-b_(3)(t)y(t)-c_(3)(t)x_(1)(t)1+m(t)x_(1)(t)is established,where a i(t),b_(i)(t),c_(i)(t)(i=1,2,3),m(t)and D_(i)(t)(i=1,2)are all positive periodic continuous functions with period w>0,τis a nonnegative constant and k(s)is a continuous nonnegative function on[-τ,0].
基金the National Natural Science Foundation of China Key Project(No.50238040)
文摘Single fiber pull-out testing was conducted to study the origin of the functional responses to loading of carbon fiber reinforced cement-based composites. The variation of electrical resistance with the bonding force on the fiber-matrix interface was measured. Single fiber electromechanical testing was also conducted by measuring the electrical resistance under static tension. Comparison of the results shows that the resistance increasing during single fiber pull-out is mainly due to the changes at the interface. The conduction mechanism of the composite can be explained by the tunneling model. The interfacial stress causes the deformation of interfacial structure and the interfacial debonding, which have influences on the tunneling effect and result in the change of resistance.
基金supported by the Special Fund for Agro-Scientific Research in the Public Interest, China (200903051 and 200803003)
文摘Understanding the temperature affecting parasitic efficiency is critical to succeed in utilizing parasitoid as natural enemy in pest management. Laboratory studies were carried out to determine the effects of temperature on parasitoid preference of female Anagrus nilaparvatae Pang et Wang （Hymenoptera：Mymaridae） to the eggs of whitebacked planthopper （WBPH）, Sogatella furcifera Horváth and brown planthopper （BPH）, Nilaparvata lugens Stl to build a composite model describing changes in parasitic response along a temperature gradient （18, 22, 26, 30, 34°C）. The results showed that attack responses of A. nilaparvatae on WBPH and BPH were the best described by a Type II functional response. The two parameters, attack rates （a） and handling times （Th）, of A. nilaparvatae to both eggs were influenced by the temperature. The maximum attack rates to WBPH （1.235） and BPH （1.049） were at 26 and 34°C, respectively, and the shortest handling times to WBPH （0.063） and BPH （0.057） were at 30 and 26°C, respectively. However, the optimal temperature for parasitic efficiency of A. nilaparvatae to WBPH and BPH eggs was both at 26°C, which showed that the present microclimate temperature of the habitat in the paddyfield was beneficial to A. nilaparvatae and indicated that parasitic efficiency of A. nilaparvatae would be impaired by global warming.
基金supported by grants from the Natural Sciences and Engineering Research Council of Canada (NSERC)SaskCanola Funding+1 种基金Saskatchewan Agricultural Development Fund (ADF)Ministry of Agriculture Strategic Research Chair Fund (Saskatchewan,Canada)
文摘In complex feed structures, there exist main chemical functional groups which are associated with nutrient utilization and availability and functionality. Each functional group has unique molecular structure therefore produce unique molecular vibration spectral profile. Feed processing has been used to improve nutrient utilization for many years. However, to date, there was little study on processing-induced changes of feed intrinsic structure and functional groups on a molecular basis within intact tissue. This is because limited research technique is available to study inherent structure on a molecular basis. Recently bioanalytical techniques： such as Synchrotron Infrared Microspectroscopy as well as Diffuse Reflectance Infrared Fourier Transform molecular spectroscopy have been developed. These techniques enable to detect molecular structure change within intact tissues. These techniques can prevent destruction or alteration of the intrinsic protein structures during processing for analysis. However, these techniques have not been used in animal feed and nutrition research. The objective of this review was show that with the advanced technique, sensitivity and responses of functional groups to feed processing on a molecular basis could be detected in my research team. These functional groups are highly associated with nutrient utilization in animals.
基金Supported by the National Natural Science Foundation of China(10471108)
文摘In this paper,we consider a nonlinear size-structured population model with functional response,which describes the dynamics of a predator-prey system living in a common habitat.We present a kind of functional response for the prey being a plant or algae,and explain its biological meanings.When the vital rates depend both on the individual's size and on the total population or only depend on the former,we obtain the existence of equilibrium solutions.
基金Supported by the National Natural Science Foundation of China(195 310 70 )
文摘This paper deals with the questio n of global stability of the positive locally asymptotically stable equilibrium in a class of predator\|prey system of Gause\|typ e with Holling Ⅲ functional response. The Dulac's criterion is applied and lia punov functions are constructed to establish the global stability.
基金Supported by the National Natural Science Foundation of China(11761063).
文摘The effect of a protection zone on a diffusion predator-prey model with Ivlev-type functional response is considered.We discuss the existence and non-existence of positive steady state solutions by using the bifurcation theory.It is shown that the protection zone for prey has beneficial effects on the coexistence of the two species when the growth rate of predator is positive.Moreover,we examine the dependence of the coexistence region on the efficiency of the predator capture of the prey and the protection zone.
基金Supported by the National Natural Science Foundation of China (10701020)
文摘The main purpose of this paper is to study the persistence of the general multispecies competition predator-pray system with Holling Ⅲ type functional response. In this system, the competition among predator species and among prey species are simultaneously considered. By using the comparison theory and qualitative analysis, the sufficient conditions for uniform strong persistence are obtained.
基金the Postdoctoral ScienceFoundation of China(No.2023M730156)the NationalNatural Foundation of China(No.62301012).
文摘Hyper-and multi-spectral image fusion is an important technology to produce hyper-spectral and hyper-resolution images,which always depends on the spectral response function andthe point spread function.However,few works have been payed on the estimation of the two degra-dation functions.To learn the two functions from image pairs to be fused,we propose a Dirichletnetwork,where both functions are properly constrained.Specifically,the spatial response function isconstrained with positivity,while the Dirichlet distribution along with a total variation is imposedon the point spread function.To the best of our knowledge,the neural network and the Dirichlet regularization are exclusively investigated,for the first time,to estimate the degradation functions.Both image degradation and fusion experiments demonstrate the effectiveness and superiority of theproposed Dirichlet network.
基金Project supported by the Program for Professor of Special Appointment(Eastern Scholar)at Shanghai Institutions of Higher Learningthe Project for the Natural Science Foundation of Shanghai,China(Grant No.21ZR1444100)the Project for the National Natural Science Foundation of China(Grant Nos.72174121,71774111,71871144,and 71804047)。
文摘In recent years,rumor spreading has caused widespread public panic and affected the whole social harmony and stability.Consequently,how to control the rumor spreading effectively and reduce its negative influence urgently needs people to pay much attention.In this paper,we mainly study the near-optimal control of a stochastic rumor spreading model with Holling II functional response function and imprecise parameters.Firstly,the science knowledge propagation and the refutation mechanism as the control strategies are introduced into a stochastic rumor spreading model.Then,some sufficient and necessary conditions for the near-optimal control of the stochastic rumor spreading model are discussed respectively.Finally,through some numerical simulations,the validity and availability of theoretical analysis is verified.Meanwhile,it shows the significance and effectiveness of the proposed control strategies on controlling rumor spreading,and demonstrates the influence of stochastic disturbance and imprecise parameters on the process of rumor spreading.
文摘In this study, the impulsive predator-prey dynamic systems on time scales calculus are studied. When the system has periodic solution is investigated, and three different conditions have been found, which are necessary for the periodic solution of the predator-prey dynamic systems with Beddington-DeAngelis type functional response. For this study the main tools are time scales calculus and coincidence degree theory. Also the findings are beneficial for continuous case, discrete case and the unification of both these cases. Additionally, unification of continuous and discrete case is a good example for the modeling of the life cycle of insects.
文摘Allam and Tantawy [1] presented an analytical solu- tion for stress distribution and perturbations of the magnetic field vector in FGM hollow structures made from viscoelas- tic composite materials .While studying this article, the dis- cusser noticed a confusion in regarding Maxwell＇s electro- magnetic stress expression
基金Supported by the Foundation for subjects development of Harbin University(No.HXK200716)
文摘This paper investigates the existence of periodic solutions of a three-species food-chain diffusive system with Beddington-DeAngelis functional responses and time delays in a two-patch environment on time scales. By using a continuation theorem based on coincidence degree theory, we obtain sufficient criteria for the existence of periodic solutions for the system. Moreover, when the time scale T is chosen as R or Z, the existence of the periodic solutions of the corresponding continuous and discrete models follows. Therefore, the method is unified to provide the existence of the desired solutions for continuous differential equations and discrete difference equations.
基金Supported by the National Natural Science Foundation of China(Grant No.11761063).
文摘In this paper,we consider the positive steady state solutions of a predator-prey model with Holling type Ⅱfunctional response and cross-diffusion,where two cross-diffusion rates represent the tendency of prey to keep away from its predator and the tendency of the predator to chase its prey,respectively.Applying the fixed point index theory,some sufficient conditions for the existence of positive steady state solutions are established.Furthermore,the non-existence of positive steady state solutions is studied.
文摘A predator-prey diffusion system with a Bazykin functional response is studied. The existence of equilibrium points, the stability of normal number equilibrium points and the existence of Hopf bifurcationes are investigated for the proposed system, the existence of positive solutions in the system is discussed under Neumann boundary conditions, and the stability of constant equilibrium points is focused on under the condition of Hurwitz criterion. The results show that there exist positive equilibrium points in the system under Neumann boundary conditions, and the normal number equilibrium points are stable when specific conditions are satisfied, and the bifurcation points of Hopf bifurcationes and their orders are given.
文摘To investigate the effects of self-memory diffusion on predator-prey models, we consider a predator-prey model with Bazykin functional response of self- memory diffusion. The uniqueness, boundedness, positivity, existence and stability of equilibrium point of the model are studied. In this paper, the uniqueness of the solution is discussed under the non-negative initial function and Neumann boundary conditions satisfying a specific space. The boundness of the solution is proved by the comparison principle of parabolic equations, and the positivity of the solution is proved by the strong maximum principle of parabolic equations. Hurwitz criterion and Lyapunov function construction are used to analyze the local stability and global stability of feasible equilibrium points. The results show that the system solution is unique non-negative and bounded. The model is unstable at the trivial equilibrium point E0 and the boundary equilibrium point E1, and the condition of whether the positive equilibrium point E2 is stable under certain conditions is given.
