In this paper,we investigate an inertial two-neural coupling system with multiple delays.We analyze the number of equilibrium points and demonstrate the corresponding pitchfork bifurcation.Results show that the system...In this paper,we investigate an inertial two-neural coupling system with multiple delays.We analyze the number of equilibrium points and demonstrate the corresponding pitchfork bifurcation.Results show that the system has a unique equilibrium as well as three equilibria for different values of coupling weights.The local asymptotic stability of the equilibrium point is studied using the corresponding characteristic equation.We find that multiple delays can induce the system to exhibit stable switching between the resting state and periodic motion.Stability regions with delay-dependence are exhibited in the parameter plane of the time delays employing the Hopf bifurcation curves.To obtain the global perspective of the system dynamics,stability and periodic activity involving multiple equilibria are investigated by analyzing the intersection points of the pitchfork and Hopf bifurcation curves,called the Bogdanov-Takens(BT)bifurcation.The homoclinic bifurcation and the fold bifurcation of limit cycle are obtained using the BT theoretical results of the third-order normal form.Finally,numerical simulations are provided to support the theoretical analyses.展开更多
A coupled neural system with multiple delays has been investigated. The number of equilibrium points is analyzed. It implies that the neural system exhibits a unique equilibrium and three ones for the different values...A coupled neural system with multiple delays has been investigated. The number of equilibrium points is analyzed. It implies that the neural system exhibits a unique equilibrium and three ones for the different values of coupling weight by employing the pitchfork bifurcation of the trivial equilibrium point. Further, the local asymptotical stability of the trivial equilibrium point is studied by analyzing the corresponding characteristic equation. Some stability criteria involving multiple delays and coupling weight are obtained. The results show that the neural system exhibits the delay-independent and delay-dependent stability. Increasing delay induces stability switching between resting state and periodic motion in some parameter regions of coupling weight. In addition, the criterion for the global stability of the trivial equilibrium is also derived by constructing a suitable Lyapunov functional. Finally, some numerical simulations are taken to support the theoretical results.展开更多
In this paper, we consider a Cohen-Grossberg neural network with three delays. Regard- ing time delays as a parameter, we investigate the effect of time delays on its dynamics. We show that there exist stability switc...In this paper, we consider a Cohen-Grossberg neural network with three delays. Regard- ing time delays as a parameter, we investigate the effect of time delays on its dynamics. We show that there exist stability switches for time delays under certain conditions and the conditions for the existence of periodic oscillations are given by discussing the associated characteristic equation. Numerical simulations are given to illustrate the obtained results and interesting network behaviors are observed, such as multiple stability switches of the network equilibrium and synchronous （asynchronous） oscillations.展开更多
This paper studies the local dynamics of an SDOF system with quadratic and cubic stiffness terms,and with linear delayed velocity feedback.The analysis indicates that for a sufficiently large velocity feedback gain,th...This paper studies the local dynamics of an SDOF system with quadratic and cubic stiffness terms,and with linear delayed velocity feedback.The analysis indicates that for a sufficiently large velocity feedback gain,the equilibrium of the system may undergo a number of stability switches with an increase of time delay,and then becomes unstable forever.At each critical value of time delay for which the system changes its stability,a generic Hopf bifurcation occurs and a periodic motion emerges in a one-sided neighbourhood of the critical time delay.The method of Fredholm alternative is applied to determine the bifurcating periodic motions and their stability.It stresses on the effect of the system parameters on the stable regions and the amplitudes of the bifurcating periodic solutions.展开更多
Interlinked positive feedback loops,an important building block of biochemical systems,can induce bistable switching,leading to long-lasting state changes by brief stimuli.In this work,prevalent mutual activation betw...Interlinked positive feedback loops,an important building block of biochemical systems,can induce bistable switching,leading to long-lasting state changes by brief stimuli.In this work,prevalent mutual activation between two species as another positive feedback is added to a generic interlinked positive-feedback-loop model originating from many realistic biological circuits.A stochastic fluctuation of the positive feedback strength is introduced in a bistable interval of the feedback strength,and bistability appears for the moderate feedback strength at a certain noise level.Stability analysis based on the potential energy landscape is further utilized to explore the noise-induced switching behavior of two stable steady states.展开更多
Time-delay effects on the dynamics of Li^nard type equation with one fast variable and one slow variable are investigated in the present paper. By using the methods of stability switch and geometric singular perturbat...Time-delay effects on the dynamics of Li^nard type equation with one fast variable and one slow variable are investigated in the present paper. By using the methods of stability switch and geometric singular perturbation, time-delay-induced complex oscillations and bursting are investigated, and in several case studies, the mechanism of the generation of the complex oscillations and bursting is illuminated. Numerical results demonstrate the validity of the theoretical results.展开更多
Nanoscale PbxLa1-,Ti1-x/4O3 （PLT） thin film has been fabricated on Pt／Ti／SiO2／Si substrates by chemical solution deposition （CSD） method. Ferroelectricity of the fresh-made PLT thin film has been clearly detect...Nanoscale PbxLa1-,Ti1-x/4O3 （PLT） thin film has been fabricated on Pt／Ti／SiO2／Si substrates by chemical solution deposition （CSD） method. Ferroelectricity of the fresh-made PLT thin film has been clearly detected through piezoelectric force microscopy （PFM） by writing reversible ferroelectric domains. However, PLT thin film also shows off-standard ferroelectric hysteresis loops highly dependent on frequency, indicating large amount of mobile space charges in the film. Subsequent current-voltage （C-V） studies show that sandwich-like Pt／PLT／Pt structure exhibits notable bipolar resistive switching （BRS） characteristics with high stability （〉 103 switching cycles）. It is found that the C-V curves of both high- and low-resistance states have the feature of space-charge-limited current （SCLC） conduction, indicating important roles of defects in the conduction. X-ray photoelectron spectroscopy measurement further verifies that oxygen vacancies based conductive filament mechanism is likely responsible for the observed RS effect. Our demonstration of stable RS effect in the PLT thin film and its possible coupling with ferroelectricity is promising in device development and applications, such as development of ferroelectric-tunable RS memories.展开更多
<em>G</em><sub><em>0</em></sub><em>/G</em><sub><em>1</em></sub> “gaps” joint the <em>S</em> phase and<em> M</em> phase ...<em>G</em><sub><em>0</em></sub><em>/G</em><sub><em>1</em></sub> “gaps” joint the <em>S</em> phase and<em> M</em> phase to form the cell cycle. The dynamics of enzyme reaction to drive the target protein production in <em>M</em> phase is analyzed mathematically. Time delay is introduced since the signal transmission need time in <em>G</em><sub><em>0</em></sub><em>/G</em><sub><em>1</em></sub> “gaps” phase. Hopf bifurcation of DDEs model is analyzed by applying geometrical analytical method. The instability oscillating periodic solutions arise as subcritical Hopf bifurcation occurs. The Hysteresis phenomena of the limit cycle are also observed underlying the saddle-node bifurcation of the limit cycle. Due to stability switching, interestingly, the bifurcating periodical solution dies out near the vicinity of Hopf lines. By Lyapunov-Schmidt reduction scheme, the normal form is computed on the center manifold. Finally, it is verified that the theory analytical results are in coincidence with the numerical simulation.展开更多
In this paper,we propose and analyze a delayed predator-prey model with Holling type III functional response taking into account cooperation behavior in predators.The time delay is introduced in the attack rate to rep...In this paper,we propose and analyze a delayed predator-prey model with Holling type III functional response taking into account cooperation behavior in predators.The time delay is introduced in the attack rate to represent the time necessary to trigger the attack.Each analytical result is followed by an ecological interpretation.We investigate the effect of hunting cooperation on both the number and the level of positive steady states.We observe that the level of the positive equilibrium decreases when increasing the hunting cooperation parameter.Then,we study the impact of the delay as well as the cooperation in hunting on the dynamics of the system.We prove that the presence of delay in the attack rate induces stability switches around the coexisting equilibrium when predators cooperate.In addition,we consider the discrete delay as a bifurcation parameter and prove that the model undergoes a Hopf-bifurcation at the coexisting equilibrium when the delay crosses some critical values.Numerical simulations are presented to confirm our analytical findings.展开更多
In this paper,we study a delayed viral infection model with cellular infection and full logistic proliferations for both healthy and infected cells.The global asymptotic stabil-ities of the equilibria are studied by c...In this paper,we study a delayed viral infection model with cellular infection and full logistic proliferations for both healthy and infected cells.The global asymptotic stabil-ities of the equilibria are studied by constructing Lyapunov functionals.Moreover,we investigated the existence of Hopf bifurcation at the infected equilibrium by regarding the possible combination of the two delays as bifurcation pararmeters.The results show that time delays may destabilize the infected equilibrium and lead to Hopf bifurcation.Finally,numerical simulations are carried out to illustrate the main results and explore the dynamics including Hopf bifurcation and stability switches.展开更多
This paper presents a method for directly analyzing the stability of complex-DDEs on the basis of stability switches. Two novel criteria are developed for the stability of a class of complex- DDEs. These results not o...This paper presents a method for directly analyzing the stability of complex-DDEs on the basis of stability switches. Two novel criteria are developed for the stability of a class of complex- DDEs. These results not only generalize some known results in literature but also greatly reduce the complexity of analysis and computation. To validate the effectiveness of the proposed criteria, the stabilization problem of the extended time delay auto-synchronization （ETDAS） control and n time delay auto-synchronization （NTDAS） control are then further investigated, respectively. The numerical simulations are consistent with the above theoretical analysis.展开更多
Two novel decyloxyphenylquinoxaline-based donor-acceptor （D-A） electroactive monomers bearing dialkoxythiophene as the donor unit are synthesized using Stille coupling reaction. The corresponding polymers, poly[2,3-...Two novel decyloxyphenylquinoxaline-based donor-acceptor （D-A） electroactive monomers bearing dialkoxythiophene as the donor unit are synthesized using Stille coupling reaction. The corresponding polymers, poly[2,3- bis（4-decyloxyphenyl）-5,8-bis（3,4-dimethoxylthiophen-2-yl）quinoxaline] （P1） and poly[2,3-bis（4-decyloxyphenyl）-5,8- bis（2,3-dihydrothieno[3,4-b][1,4]dioxin-5-yl）quinoxaline] （P2）, are directly deposited onto the working electrode surface by electropolymerization. All materials were characterized by nuclear magnetic resonance （NMR）, mass spectrometry （MS）, scanning electron microscopy （SEM）, cyclic voltammetry （CV）, ultraviolet-visible absorption spectrometry （UV-Vis） and spectro-electrochemical measurements. Electrochemical studies demonstrate that both polymers are capable of showing both reasonable n- and p-doping processes, and advanced long-term switching stabilities. 3,4-Ethylenedioxythiophene substituted for 3,4-dimethoxythiophene as a donor unit, which enhances the conjugated double-bond character of the conducting polymer, thus leading to a lower electronic band-gap. Likewise, the neutral state color of the synthesized polymer tuned from blue to blue-green corresponding to the red shift of the maximum absorption wavelengths in the visible region. In addition, kinetics study of P1 revealed 42% （595 nm）, 30% （839 nm） and 69% （1500 nm） transmittance changes （A7%）, while P2 exhibited 32% （740 nm）, 71% （2000 nm） at the dominant wavelengths. It was also observed that both films could switch quickly between the neutral state and oxidation state, with the response time less than 1 s both in visible and near infrared regions.展开更多
In this work, we study the robust observer-driven switching stabilization problem of switched linear sys- tems. Under the condition that each subsystem is completely observable, with the observer-driven switching law ...In this work, we study the robust observer-driven switching stabilization problem of switched linear sys- tems. Under the condition that each subsystem is completely observable, with the observer-driven switching law which makes the system exponentially stable for the nominal system, we prove that the overall system is robust against structural/switching perturbations and is input/output to state stable for unstructural perturbations.展开更多
A predator-prey system with independent harvesting in either species and BeddingtonDeAngelis functional response is investigated. By analyzing characteristic equations and using an iterative technique,we obtain a set ...A predator-prey system with independent harvesting in either species and BeddingtonDeAngelis functional response is investigated. By analyzing characteristic equations and using an iterative technique,we obtain a set of easily verifiable sufficient conditions,which ensure the local and global stability of the nonnegative equilibria of the system. It is also shown that the time delay can cause a stable equilibrium to become unstable and even a switching of stabilities. Numerical simulations are carried out to illustrate the validity of our results.展开更多
In this paper, a hepatitis B viral infection model with a density-dependent proliferation rate of cytotoxic T lymphocyte （CTL） cells and immune response delay is investigated. By analyzing the model, we show that th...In this paper, a hepatitis B viral infection model with a density-dependent proliferation rate of cytotoxic T lymphocyte （CTL） cells and immune response delay is investigated. By analyzing the model, we show that the virus-free equilibrium is globally asymptotically stable, if the basic reproductive ratio is less than one and an endemic equilibrium exists if the basic reproductive ratio is greater than one. By using the stability switches criterion in the delay-differential system with delay-dependent parameters, we present that the stability of endemic equilibrium changes and eventually become stable as time delay increases. This means majority of hepatitis B infection would eventually become a chronic infection due to the immune response time delay is fairly long. Numerical simulations are carried out to explain the mathematical conclusions and biological implications.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.11302126)the State Key Program of National Natural Science of China(Grant No.11032009)+1 种基金the Shanghai Leading Academic Discipline Project(Grant No.B302)Young Teacher Training Program of Colleges and Universities in Shanghai(Grant No.ZZhy12030)
文摘In this paper,we investigate an inertial two-neural coupling system with multiple delays.We analyze the number of equilibrium points and demonstrate the corresponding pitchfork bifurcation.Results show that the system has a unique equilibrium as well as three equilibria for different values of coupling weights.The local asymptotic stability of the equilibrium point is studied using the corresponding characteristic equation.We find that multiple delays can induce the system to exhibit stable switching between the resting state and periodic motion.Stability regions with delay-dependence are exhibited in the parameter plane of the time delays employing the Hopf bifurcation curves.To obtain the global perspective of the system dynamics,stability and periodic activity involving multiple equilibria are investigated by analyzing the intersection points of the pitchfork and Hopf bifurcation curves,called the Bogdanov-Takens(BT)bifurcation.The homoclinic bifurcation and the fold bifurcation of limit cycle are obtained using the BT theoretical results of the third-order normal form.Finally,numerical simulations are provided to support the theoretical analyses.
基金supported by the National Natural Science Foundation of China(Grant Nos.11202068&11572224)the University Key Teacher Foundation for Youths of Henan Province(Grant No.2014GGJS-076)the Key Technologies Research Project of Henan Province(Grant No.152102210089)
文摘A coupled neural system with multiple delays has been investigated. The number of equilibrium points is analyzed. It implies that the neural system exhibits a unique equilibrium and three ones for the different values of coupling weight by employing the pitchfork bifurcation of the trivial equilibrium point. Further, the local asymptotical stability of the trivial equilibrium point is studied by analyzing the corresponding characteristic equation. Some stability criteria involving multiple delays and coupling weight are obtained. The results show that the neural system exhibits the delay-independent and delay-dependent stability. Increasing delay induces stability switching between resting state and periodic motion in some parameter regions of coupling weight. In addition, the criterion for the global stability of the trivial equilibrium is also derived by constructing a suitable Lyapunov functional. Finally, some numerical simulations are taken to support the theoretical results.
文摘In this paper, we consider a Cohen-Grossberg neural network with three delays. Regard- ing time delays as a parameter, we investigate the effect of time delays on its dynamics. We show that there exist stability switches for time delays under certain conditions and the conditions for the existence of periodic oscillations are given by discussing the associated characteristic equation. Numerical simulations are given to illustrate the obtained results and interesting network behaviors are observed, such as multiple stability switches of the network equilibrium and synchronous （asynchronous） oscillations.
基金The project supported by the National Natural Science Foundation of China (19972025)
文摘This paper studies the local dynamics of an SDOF system with quadratic and cubic stiffness terms,and with linear delayed velocity feedback.The analysis indicates that for a sufficiently large velocity feedback gain,the equilibrium of the system may undergo a number of stability switches with an increase of time delay,and then becomes unstable forever.At each critical value of time delay for which the system changes its stability,a generic Hopf bifurcation occurs and a periodic motion emerges in a one-sided neighbourhood of the critical time delay.The method of Fredholm alternative is applied to determine the bifurcating periodic motions and their stability.It stresses on the effect of the system parameters on the stable regions and the amplitudes of the bifurcating periodic solutions.
基金supported by the National Natural Science Foundation of China(Grants 11372017,11272024,and 11371046)the General Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region(Grant NJZY14130)
文摘Interlinked positive feedback loops,an important building block of biochemical systems,can induce bistable switching,leading to long-lasting state changes by brief stimuli.In this work,prevalent mutual activation between two species as another positive feedback is added to a generic interlinked positive-feedback-loop model originating from many realistic biological circuits.A stochastic fluctuation of the positive feedback strength is introduced in a bistable interval of the feedback strength,and bistability appears for the moderate feedback strength at a certain noise level.Stability analysis based on the potential energy landscape is further utilized to explore the noise-induced switching behavior of two stable steady states.
基金supported by the National Natural Science Foundation of China(11102078 and 11032009)Foundation of Jiangxi Education Committee of China(GJJ1169)
文摘Time-delay effects on the dynamics of Li^nard type equation with one fast variable and one slow variable are investigated in the present paper. By using the methods of stability switch and geometric singular perturbation, time-delay-induced complex oscillations and bursting are investigated, and in several case studies, the mechanism of the generation of the complex oscillations and bursting is illuminated. Numerical results demonstrate the validity of the theoretical results.
基金supported by the National Natural Science Foundation of China(51172291,11232015,and 11302267)the Fundamental Research Funds for the Central Universities,NCET in University+3 种基金Research Fund for the Doctoral Program of Higher EducationFok Ying Tung FoundationScience and Technology Innovation Project of Guangdong Provincial Education DepartmentGuangdong Natural Science Funds for Distinguished Young Scholar
文摘Nanoscale PbxLa1-,Ti1-x/4O3 （PLT） thin film has been fabricated on Pt／Ti／SiO2／Si substrates by chemical solution deposition （CSD） method. Ferroelectricity of the fresh-made PLT thin film has been clearly detected through piezoelectric force microscopy （PFM） by writing reversible ferroelectric domains. However, PLT thin film also shows off-standard ferroelectric hysteresis loops highly dependent on frequency, indicating large amount of mobile space charges in the film. Subsequent current-voltage （C-V） studies show that sandwich-like Pt／PLT／Pt structure exhibits notable bipolar resistive switching （BRS） characteristics with high stability （〉 103 switching cycles）. It is found that the C-V curves of both high- and low-resistance states have the feature of space-charge-limited current （SCLC） conduction, indicating important roles of defects in the conduction. X-ray photoelectron spectroscopy measurement further verifies that oxygen vacancies based conductive filament mechanism is likely responsible for the observed RS effect. Our demonstration of stable RS effect in the PLT thin film and its possible coupling with ferroelectricity is promising in device development and applications, such as development of ferroelectric-tunable RS memories.
文摘<em>G</em><sub><em>0</em></sub><em>/G</em><sub><em>1</em></sub> “gaps” joint the <em>S</em> phase and<em> M</em> phase to form the cell cycle. The dynamics of enzyme reaction to drive the target protein production in <em>M</em> phase is analyzed mathematically. Time delay is introduced since the signal transmission need time in <em>G</em><sub><em>0</em></sub><em>/G</em><sub><em>1</em></sub> “gaps” phase. Hopf bifurcation of DDEs model is analyzed by applying geometrical analytical method. The instability oscillating periodic solutions arise as subcritical Hopf bifurcation occurs. The Hysteresis phenomena of the limit cycle are also observed underlying the saddle-node bifurcation of the limit cycle. Due to stability switching, interestingly, the bifurcating periodical solution dies out near the vicinity of Hopf lines. By Lyapunov-Schmidt reduction scheme, the normal form is computed on the center manifold. Finally, it is verified that the theory analytical results are in coincidence with the numerical simulation.
文摘In this paper,we propose and analyze a delayed predator-prey model with Holling type III functional response taking into account cooperation behavior in predators.The time delay is introduced in the attack rate to represent the time necessary to trigger the attack.Each analytical result is followed by an ecological interpretation.We investigate the effect of hunting cooperation on both the number and the level of positive steady states.We observe that the level of the positive equilibrium decreases when increasing the hunting cooperation parameter.Then,we study the impact of the delay as well as the cooperation in hunting on the dynamics of the system.We prove that the presence of delay in the attack rate induces stability switches around the coexisting equilibrium when predators cooperate.In addition,we consider the discrete delay as a bifurcation parameter and prove that the model undergoes a Hopf-bifurcation at the coexisting equilibrium when the delay crosses some critical values.Numerical simulations are presented to confirm our analytical findings.
基金This work was supported by the National Natural Science Foundation of China(#11701445,#11701451 and#11702214)by Natural Science Basic Research Plan in Shaanxi Province of China(2018JQ1057)+1 种基金Scientific Research Program Founded by Shanxi Provincial Education Department(17JK0787)by Young Talent fund of University Association for Science and Technology in Shanxi,China(20180504).
文摘In this paper,we study a delayed viral infection model with cellular infection and full logistic proliferations for both healthy and infected cells.The global asymptotic stabil-ities of the equilibria are studied by constructing Lyapunov functionals.Moreover,we investigated the existence of Hopf bifurcation at the infected equilibrium by regarding the possible combination of the two delays as bifurcation pararmeters.The results show that time delays may destabilize the infected equilibrium and lead to Hopf bifurcation.Finally,numerical simulations are carried out to illustrate the main results and explore the dynamics including Hopf bifurcation and stability switches.
基金This work was supported by National＇Science Foundation for Distinguished Young Scholars under Grant No. 10825207, and in part by Foundation for the Author of National Excellent Doctoral Dissertation of China under Grant No. 200430.
文摘This paper presents a method for directly analyzing the stability of complex-DDEs on the basis of stability switches. Two novel criteria are developed for the stability of a class of complex- DDEs. These results not only generalize some known results in literature but also greatly reduce the complexity of analysis and computation. To validate the effectiveness of the proposed criteria, the stabilization problem of the extended time delay auto-synchronization （ETDAS） control and n time delay auto-synchronization （NTDAS） control are then further investigated, respectively. The numerical simulations are consistent with the above theoretical analysis.
基金financially supported by the National Natural Science Foundation of China(Nos.51473074 and 31400044)the General and Special Program of the Postdoctoral Science Foundation China(Nos.2013M530397 and 2014T70861)+1 种基金the Postgraduate Innovation Project of China University of Petroleum(East China)(No.YCX2015022)the Fundamental Research Funds for the Central Universities(No.15CX06049A)
文摘Two novel decyloxyphenylquinoxaline-based donor-acceptor （D-A） electroactive monomers bearing dialkoxythiophene as the donor unit are synthesized using Stille coupling reaction. The corresponding polymers, poly[2,3- bis（4-decyloxyphenyl）-5,8-bis（3,4-dimethoxylthiophen-2-yl）quinoxaline] （P1） and poly[2,3-bis（4-decyloxyphenyl）-5,8- bis（2,3-dihydrothieno[3,4-b][1,4]dioxin-5-yl）quinoxaline] （P2）, are directly deposited onto the working electrode surface by electropolymerization. All materials were characterized by nuclear magnetic resonance （NMR）, mass spectrometry （MS）, scanning electron microscopy （SEM）, cyclic voltammetry （CV）, ultraviolet-visible absorption spectrometry （UV-Vis） and spectro-electrochemical measurements. Electrochemical studies demonstrate that both polymers are capable of showing both reasonable n- and p-doping processes, and advanced long-term switching stabilities. 3,4-Ethylenedioxythiophene substituted for 3,4-dimethoxythiophene as a donor unit, which enhances the conjugated double-bond character of the conducting polymer, thus leading to a lower electronic band-gap. Likewise, the neutral state color of the synthesized polymer tuned from blue to blue-green corresponding to the red shift of the maximum absorption wavelengths in the visible region. In addition, kinetics study of P1 revealed 42% （595 nm）, 30% （839 nm） and 69% （1500 nm） transmittance changes （A7%）, while P2 exhibited 32% （740 nm）, 71% （2000 nm） at the dominant wavelengths. It was also observed that both films could switch quickly between the neutral state and oxidation state, with the response time less than 1 s both in visible and near infrared regions.
基金supported by the National Natural Science Foundation of China (Nos. 60925013, 60736024, U0735003)
文摘In this work, we study the robust observer-driven switching stabilization problem of switched linear sys- tems. Under the condition that each subsystem is completely observable, with the observer-driven switching law which makes the system exponentially stable for the nominal system, we prove that the overall system is robust against structural/switching perturbations and is input/output to state stable for unstructural perturbations.
基金supported by the Foundation of Fujian Education Bureau (JA08253)the Technology Innovation Platform Project of Fujian Province (2009J1007)
文摘A predator-prey system with independent harvesting in either species and BeddingtonDeAngelis functional response is investigated. By analyzing characteristic equations and using an iterative technique,we obtain a set of easily verifiable sufficient conditions,which ensure the local and global stability of the nonnegative equilibria of the system. It is also shown that the time delay can cause a stable equilibrium to become unstable and even a switching of stabilities. Numerical simulations are carried out to illustrate the validity of our results.
基金Acknowledgments This research is supported by National Natural Science Foundation of China （Nos. 11401117 and 11201236） and the NSF of the Guangxi Higher Education Committee of China （YB2014203） and Guangxi Natural Science Foundation （No. 2012GXNSFAA053011） and Colleges and the Doctoral Fund of Guangxi University of Science and Technology （No. 13Z14）.
文摘In this paper, a hepatitis B viral infection model with a density-dependent proliferation rate of cytotoxic T lymphocyte （CTL） cells and immune response delay is investigated. By analyzing the model, we show that the virus-free equilibrium is globally asymptotically stable, if the basic reproductive ratio is less than one and an endemic equilibrium exists if the basic reproductive ratio is greater than one. By using the stability switches criterion in the delay-differential system with delay-dependent parameters, we present that the stability of endemic equilibrium changes and eventually become stable as time delay increases. This means majority of hepatitis B infection would eventually become a chronic infection due to the immune response time delay is fairly long. Numerical simulations are carried out to explain the mathematical conclusions and biological implications.
