Many discrete systems have more distinctive dynamical behaviors compared to continuous ones,which has led lots of researchers to investigate them.The discrete predatorprey model with two different functional responses...Many discrete systems have more distinctive dynamical behaviors compared to continuous ones,which has led lots of researchers to investigate them.The discrete predatorprey model with two different functional responses(Holling type I and II functional responses)is discussed in this paper,which depicts a complex population relationship.The local dynamical behaviors of the interior fixed point of this system are studied.The detailed analysis reveals this system undergoes flip bifurcation and Neimark-Sacker bifurcation.Especially,we prove the existence of Marotto's chaos by analytical method.In addition,the hybrid control method is applied to control the chaos of this system.Numerical simulations are presented to support our research and demonstrate new dynamical behaviors,such as period-10,19,29,39,48 orbits and chaos in the sense of Li-Yorke.展开更多
This work studies the stability and metastability of stationary patterns in a diffusionchemotaxis model without cell proliferation.We first establish the interval of unstable wave modes of the homogeneous steady state...This work studies the stability and metastability of stationary patterns in a diffusionchemotaxis model without cell proliferation.We first establish the interval of unstable wave modes of the homogeneous steady state,and show that the chemotactic flux is the key mechanism for pattern formation.Then,we treat the chemotaxis coefficient as a bifurcation parameter to obtain the asymptotic expressions of steady states.Based on this,we derive the sufficient conditions for the stability of one-step pattern,and prove the metastability of two or more step patterns.All the analytical results are demonstrated by numerical simulations.展开更多
We consider in this research an age-structured alcoholism model.The global behavior of the model is investigated.It is proved that the system has a threshold dynamics in terms of the basic reproduction number(BRN),whe...We consider in this research an age-structured alcoholism model.The global behavior of the model is investigated.It is proved that the system has a threshold dynamics in terms of the basic reproduction number(BRN),where we obtained that alcohol-free equilibrium(AFE)is globally asymptotically stable(GAS)in the case R_(0)≤1,but for R_(0)>1 we found that the system persists and the nontrivial equilibrium(EE)is GAS.Furthermore,the effects of the susceptible drinkers rate and the repulse rate of the recovers to alcoholics are investigated,which allow us to provide a proper strategy for reducing the spread of alcohol use in the studied populations.The obtained mathematical results are tested numerically next to its biological relevance.展开更多
This paper proposes fractional-order systems for Hopfield Neural Network(HNN).The so-called Predictor Corrector Adams Bashforth Moulton Method(PCABMM)has been implemented for solving such systems.Graphical comparisons...This paper proposes fractional-order systems for Hopfield Neural Network(HNN).The so-called Predictor Corrector Adams Bashforth Moulton Method(PCABMM)has been implemented for solving such systems.Graphical comparisons between the PCABMM and the Runge-Kutla Method(RKM)solutions for the classical HNN reveal that the proposed technique is one of the powerful tools for handling these systems.To determine all Lyapunov exponents for them,the Benettin-Wolf algorithm has been involved in the PCABMM.leased on such algorithm,the Lyapunov exponents as a function of a given parameter and as another function of the fractional-order have been described,the intermittent chaos for these systems has been explored.A new result related to the Mittag-Leffler stability of some nonlinear Fractional-order Hopfield Neural Network(FoHNN)systems has been shown.Besides,the description and the dynamic analysis of those phenomena have been discussed and verified theoretically and numerically via illustrating the phase portraits and the Lyapunov exponents'diagrams.展开更多
A new mathematical model of chronic hepatitis C virus(HCV)infection incorporating humoral and cell-mediated immune responscs,distinct cell proliferation rates for both uninfected and infected hepatocytes,and antiviral...A new mathematical model of chronic hepatitis C virus(HCV)infection incorporating humoral and cell-mediated immune responscs,distinct cell proliferation rates for both uninfected and infected hepatocytes,and antiviral treatment all at once,is formulated and analyzed meticulously.Analysis of the model elucidates the existence of multiple equilibrium states.Moreover,the model has a locally asymptotically stable disease-free equilibrium(DFE)whenever the basic reproduction number is less than unity.Local sensitivity analysis(L.SA)result exhibits that the most influential(negatively sensitive)parameters on the epidemic threshold are the drug efficacy of blocking virus production and the drug efficacy of removing infection.However,LSA does not accurately assess uncertainty and scnsitivity in the system and may mislead us since by default this technique holds all other parameters fixed at baseline values.To overcome this pitfall,one of the most robust and efficient global sensitivity analysis(GSA)methods,which is Latin hypercube sampling-partial rank correlation coefficient technique,elucidates that the proliferation rate of infected hepatocytes and the drug efficacy of killing infected hep-atocytes are highly sensitive parameters that affect the transmission dynamics of HCV in any population.Our study suggests that cell proliferation of the infected hepatocytes can be very crucial in controlling disease outbreak.Thus,a future HCV drug that boosts cell-mediated immune response is expected to be quite effective in controlling disease outbreak.展开更多
In this paper,we study the Hopf bifurcation of predator-prey system with two delays and disease transmission.Furthermore,the global existence of bifurcated periodic solution was studied,the influence of disease transm...In this paper,we study the Hopf bifurcation of predator-prey system with two delays and disease transmission.Furthermore,the global existence of bifurcated periodic solution was studied,the influence of disease transmission is given.At last,some simulations are given to support our result.展开更多
In this paper, we are concerned with the existence of an entire solution in a delayed nonlocal dispersal competitive system. This entire solution converges to two monotone fronts with different speeds, which approach ...In this paper, we are concerned with the existence of an entire solution in a delayed nonlocal dispersal competitive system. This entire solution converges to two monotone fronts with different speeds, which approach each other from both sides of the x-axis, as t converge to-∞ and then converge to (1,0) as t converges to +∞. Its global dynamic shows the superior species invade the inferior ones from both sides of the x-axis and then the inferior ones become extinct, which is a new invading way. In fact, our conclusions extend this invading way into a more general competitive system. Furthermore, we show several properties of this entire solution.展开更多
The stability of the predator-prey model subject to the Allee effect is an interesting topic in recent times.In this paper,we investigate the impact of weak Allee effect on the stability of a discrete-time predator-pr...The stability of the predator-prey model subject to the Allee effect is an interesting topic in recent times.In this paper,we investigate the impact of weak Allee effect on the stability of a discrete-time predator-prey model with Holling type-IV functional response.The mathematical features of the proposed model are analyzed with the help of equilibrium analysis,stability analysis,and bifurcation theory.We provide sufficient conditions for the flip bifurcation by considering Allee parameter as the bifurcation parameter.We observe that the model becomes stable from chaotic dynamics as the Allee parameter increases.Further,we observe bi-stability behavior of the model between only prey existence equilibrium and the coexistence equilibrium.Our analytical findings are illustrated through numerical simulations.展开更多
In the present paper,an epidemic model with Z-type control mechanism has been pro- posed and analyzed to explore the disease control strategy on an infectious disease outbreak.The uncontrolled model can have a disease...In the present paper,an epidemic model with Z-type control mechanism has been pro- posed and analyzed to explore the disease control strategy on an infectious disease outbreak.The uncontrolled model can have a disease-free equilibrium and an endemic equilibrium.The expression of the basic reproduction number and the conditions for the stability of the equilibria are derived.It is also observed that the disease-free equilibrium is globally asymptotically stable if R0<1,whereas the endemic equilibrium is globally asymptotically stable if R0>1.The model is further improved by considering Z-control mechanism and investigated.Disease can be controlled by using Z-control while the basic reproduction of the uncontrolled system is greater than unity.The positivity conditions of the solutions are derived and the basin of attraction for successful implementation of Z-control mechanism is also investigated.To verify the analytical findings,extensive numerical simulations on the model are carried out.展开更多
In this paper, we derive a time-delayed and diffusive echinococcosis transmission model. We first address the well-posedness to the initial-value problem for the model and give the basic reproduction number TO0. In th...In this paper, we derive a time-delayed and diffusive echinococcosis transmission model. We first address the well-posedness to the initial-value problem for the model and give the basic reproduction number TO0. In the case of a bounded spatial domain, we establish the local stability as well as the global stability of the disease-free and disease equilibria of the model. The methods to prove the local and the global stability are to analyze the corresponding characteristic equations and construct Lyapunov functionals, respectively. In the case of an unbounded spatial domain, by applying Schauder＇s fixed point theorem and the limiting arguments, we show that when R0 〉 1, there exists a constant c＊ 〉 0 such that the model admits positive traveling wave solutions connecting the disease-free and endemic equilibrium for c 〉 c＊, and when R0 〉 1 and c 〈 c＊, the model has no positive traveling wave solutions connecting them.展开更多
In this paper, we concern a class of the generalized delayed stochastic predator-prey models with feedback coutrols based on discrete observations. The existence of global positive solution is given first. Then we dis...In this paper, we concern a class of the generalized delayed stochastic predator-prey models with feedback coutrols based on discrete observations. The existence of global positive solution is given first. Then we discuss the deterministic model briefly, and establish the necessary conditions and the sufficient conditions for almost-sure extinction and persistence in mean for the stochastic system, where we show that the feedback controls can change the properties of the population systems significantly. Finally, numerical simulations are introduced to support the main results.展开更多
In this paper, we have considered a delayed stage-structured diffusive prey-predator model, in which predator is assumed to undergo exploitation. By using the theory of partial functional differential equations, the l...In this paper, we have considered a delayed stage-structured diffusive prey-predator model, in which predator is assumed to undergo exploitation. By using the theory of partial functional differential equations, the local stability of an interior equilibrium is established and the existence of Hopf bifurcations at the interior equilibrium is also discussed. By applying the normal form and the center manifold theory, an explicit algorithm to determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived. Finally, the complex dynamics are obtained and numerical simulations substantiate the analytical results.展开更多
Astrocytes have potential to break synchrony between neurons. Authors＇ recent researches reveal that astrocytes vary the synchronization threshold and provide an appropriate feedback control in stabilizing neural act...Astrocytes have potential to break synchrony between neurons. Authors＇ recent researches reveal that astrocytes vary the synchronization threshold and provide an appropriate feedback control in stabilizing neural activities. In this study, we propose an astrocyte-inspired controller for desynchronization of two coupled limit-cycle oscillators as a minimal network model. The design procedure consists of two parts. First, based on the astrocyte model, the structure of the dynamic controller is suggested. Then, to have an emcient controller, parameters of controller are tuned through an optimization algo- rithm. The proposed bio-inspired controller takes advantages of three important proper- ties： （1） the controller desynchronizes the oscillators without any undesirable effects （e.g. stopping, annihilating or starting divergent oscillations）; （2） it consumes little effort to preserve the desirable desynchronized state; and （3） the controller is robust with respect to parameters＇ variations. Simulation results reveal the ability of the proposed controller.展开更多
This study examines an optimal contraception control problem for a nonlinear competitive vermin population model that is dependent on size structure and spatial diffusion in a polluted environment.The control variable...This study examines an optimal contraception control problem for a nonlinear competitive vermin population model that is dependent on size structure and spatial diffusion in a polluted environment.The control variables are the average number of female sterilant and the input rate of exogenous toxicant.It has a good guiding effect on curbing environmental pollution and controlling the number of vermin.These results provide a theoretical basis for controlling and preventing vermin and curbing environmental pollution.The hybrid system belongs to the class of separable models,and its solution is separable in terms of size and spatial location.Therefore,we transform the system into two subsystems and prove the existence and uniqueness of non-negative solutions via the comparison principle and fixed point theorem,respectively.The necessary conditions for the optimal contraception strategy are derived by constructing an adjoint system and using tangent-normal cones.The method of characteristics and the finite difference method approximate the non-negative solutions of the two subsystems,and some numerical examples illustrate the theoretical results.展开更多
In this paper,a new mosquito population suppression model with stage and sex structure is constructed,which is composed of two sub-models switching each other.Sterile mosquitoes are released with period T and remain s...In this paper,a new mosquito population suppression model with stage and sex structure is constructed,which is composed of two sub-models switching each other.Sterile mosquitoes are released with period T and remain sexually active for time T.For the case T<T,three thresholds T^(*),m^(*)and c^(*)are determined for the release period T and release amount c.According to the values of T and c in different ranges determined by these thresholds,we study the dynamical behavior of the system for different release strategies,mainly including the existence and stability of the mosquito-extinction equilibrium and positive periodic solutions.Finally,some numerical simulations are performed to illustrate our results.展开更多
Phytoplanktons are drifting plants in an aquatic system.They provide food for marine animals and are compared to terrestrial plants in that having chlorophyll and carrying out photosynthesis.Zooplanktons are drifting ...Phytoplanktons are drifting plants in an aquatic system.They provide food for marine animals and are compared to terrestrial plants in that having chlorophyll and carrying out photosynthesis.Zooplanktons are drifting animals found inside the aquatic bodies.For stable aquatic ecosystem,the growth of both Zooplankton and Phytoplankton should be in steady state but in previous eras,there has been a universal explosion in destructive Plankton or algal blooms.Many investigators used various mathematical methodologies to try to explain the bloom phenomenon.So,in this paper,a discretized two-dimensional Phytoplankton-Zooplankton model is investigated.The results for the existence and uniqueness,and conditions for local stability with topological classifications of the equilibrium solutions are determined.It is also exhibited that at trivial and semitrivial equilibrium solutions,discrete model does not undergo fip bifurcation,but it undergoes Neimark-Sacker bifurcation at interior equilibrium solution under certain conditions.Further,state feedback method is deployed to control the chaos in the under consideration system.The extensive numerical simulations are provided to demonstrate theoretical results.展开更多
In this paper,we develop a three-dimensional fractional-order cancer model.The proposed model involves the interaction among tumor cells,healthy tissue cells and activated effector cells.The detailed analysis of the e...In this paper,we develop a three-dimensional fractional-order cancer model.The proposed model involves the interaction among tumor cells,healthy tissue cells and activated effector cells.The detailed analysis of the equilibrium points is studied.Also,the existence and uniqueness of the solution are investigated.The fractional derivative is considered in the Caputo sense.Numerical simulations are performed to illustrate the effectiveness of the obtained theoretical results.The outcome of the study reveals that the order of the fractional derivative has a significant effect on the dynamic process.Further,the calculated Lyapunov exponents give the existence of chaotic behavior of the proposed model.Also,it is observed from the obtained results that decrease in fractional-order p increases the chaotic behavior of the model.展开更多
The citrate secreted by the rice(Oryza sativa L.)roots will promote the absorption of phosphate,and this process is described by the Kirk model.In our work,the Kirk model is divided into citrate sub-model and phosphat...The citrate secreted by the rice(Oryza sativa L.)roots will promote the absorption of phosphate,and this process is described by the Kirk model.In our work,the Kirk model is divided into citrate sub-model and phosphate sub-model.In the citrate sub-model,we obtain the analytical solution of citrate with the Laplace transform,inverse Laplace transform and convolution theorem.The citrate solution is substituted into the phosphate sub-model,and the analytical solution of phosphate is obtained by the separation variable method.The existence of the solutions can be proved by the comparison test,the Weierstrass M-test and the Abel discriminating method.展开更多
In this paper,we study a deterministic model with non-autonomous system for mixed cultivars to assess the effect of cultivar susceptibility and seasonal variation on banana Xanthomonas wilt(BXW)disease dynamics.A spec...In this paper,we study a deterministic model with non-autonomous system for mixed cultivars to assess the effect of cultivar susceptibility and seasonal variation on banana Xanthomonas wilt(BXW)disease dynamics.A special case of two cultivars classified as highly susceptible for inflorescence infection(ABB)and less susceptible(AAA)cultivar is considered.The basic reproduction number corresponding to the non-autonomous system is derived and numerically computed to determine disease dynamics.Results showed that the disease dies out whenever the periodic basic reproduction number is less than unity and a periodic solution is obtained when it is greater than one.Results further showed that for both cultivars,the basic reproduction number increases with increasing values of the transmission rates and declines exponentially with increasing values of roguing rates.The critical roguing rate of ABB-genome cultivar was higher than that of AAA-genome cultivars.The peaks in disease prevalence indicate the importance of effective implementation of controls during the rainy season.We conclude that highly susceptible cultivars play an important role in the spread of BXW and control measures should be effectively implemented during the rainy season if BXW is to be eradicated.展开更多
基金supported by the National Natural Science Foundation of China(No.12001503)the Project of Beijing Municipal Commission of Education(KM 202110015001)。
文摘Many discrete systems have more distinctive dynamical behaviors compared to continuous ones,which has led lots of researchers to investigate them.The discrete predatorprey model with two different functional responses(Holling type I and II functional responses)is discussed in this paper,which depicts a complex population relationship.The local dynamical behaviors of the interior fixed point of this system are studied.The detailed analysis reveals this system undergoes flip bifurcation and Neimark-Sacker bifurcation.Especially,we prove the existence of Marotto's chaos by analytical method.In addition,the hybrid control method is applied to control the chaos of this system.Numerical simulations are presented to support our research and demonstrate new dynamical behaviors,such as period-10,19,29,39,48 orbits and chaos in the sense of Li-Yorke.
基金Manjun Ma was supported by the National Natural Science Foundation of China(Nos.12071434 and 11671359).
文摘This work studies the stability and metastability of stationary patterns in a diffusionchemotaxis model without cell proliferation.We first establish the interval of unstable wave modes of the homogeneous steady state,and show that the chemotactic flux is the key mechanism for pattern formation.Then,we treat the chemotaxis coefficient as a bifurcation parameter to obtain the asymptotic expressions of steady states.Based on this,we derive the sufficient conditions for the stability of one-step pattern,and prove the metastability of two or more step patterns.All the analytical results are demonstrated by numerical simulations.
基金supported by DGESTR of Algeria No.COOL03UN130120200004.
文摘We consider in this research an age-structured alcoholism model.The global behavior of the model is investigated.It is proved that the system has a threshold dynamics in terms of the basic reproduction number(BRN),where we obtained that alcohol-free equilibrium(AFE)is globally asymptotically stable(GAS)in the case R_(0)≤1,but for R_(0)>1 we found that the system persists and the nontrivial equilibrium(EE)is GAS.Furthermore,the effects of the susceptible drinkers rate and the repulse rate of the recovers to alcoholics are investigated,which allow us to provide a proper strategy for reducing the spread of alcohol use in the studied populations.The obtained mathematical results are tested numerically next to its biological relevance.
基金supporting this work by the University Ajman Grant:2Q20-COVID-19-08.
文摘This paper proposes fractional-order systems for Hopfield Neural Network(HNN).The so-called Predictor Corrector Adams Bashforth Moulton Method(PCABMM)has been implemented for solving such systems.Graphical comparisons between the PCABMM and the Runge-Kutla Method(RKM)solutions for the classical HNN reveal that the proposed technique is one of the powerful tools for handling these systems.To determine all Lyapunov exponents for them,the Benettin-Wolf algorithm has been involved in the PCABMM.leased on such algorithm,the Lyapunov exponents as a function of a given parameter and as another function of the fractional-order have been described,the intermittent chaos for these systems has been explored.A new result related to the Mittag-Leffler stability of some nonlinear Fractional-order Hopfield Neural Network(FoHNN)systems has been shown.Besides,the description and the dynamic analysis of those phenomena have been discussed and verified theoretically and numerically via illustrating the phase portraits and the Lyapunov exponents'diagrams.
文摘A new mathematical model of chronic hepatitis C virus(HCV)infection incorporating humoral and cell-mediated immune responscs,distinct cell proliferation rates for both uninfected and infected hepatocytes,and antiviral treatment all at once,is formulated and analyzed meticulously.Analysis of the model elucidates the existence of multiple equilibrium states.Moreover,the model has a locally asymptotically stable disease-free equilibrium(DFE)whenever the basic reproduction number is less than unity.Local sensitivity analysis(L.SA)result exhibits that the most influential(negatively sensitive)parameters on the epidemic threshold are the drug efficacy of blocking virus production and the drug efficacy of removing infection.However,LSA does not accurately assess uncertainty and scnsitivity in the system and may mislead us since by default this technique holds all other parameters fixed at baseline values.To overcome this pitfall,one of the most robust and efficient global sensitivity analysis(GSA)methods,which is Latin hypercube sampling-partial rank correlation coefficient technique,elucidates that the proliferation rate of infected hepatocytes and the drug efficacy of killing infected hep-atocytes are highly sensitive parameters that affect the transmission dynamics of HCV in any population.Our study suggests that cell proliferation of the infected hepatocytes can be very crucial in controlling disease outbreak.Thus,a future HCV drug that boosts cell-mediated immune response is expected to be quite effective in controlling disease outbreak.
文摘In this paper,we study the Hopf bifurcation of predator-prey system with two delays and disease transmission.Furthermore,the global existence of bifurcated periodic solution was studied,the influence of disease transmission is given.At last,some simulations are given to support our result.
基金Y. Wang partially supported by the Natural Science Foundation of Shanxi Province (201801D221008)G. Liu partially supported by the NSFC (11471197)+2 种基金Natural Science Foundation of Shanxi Province (2014011005-1)X.Li partially supported by the NSFC (11571041)the Fundamental Research Funds for the Central Universities.
文摘In this paper, we are concerned with the existence of an entire solution in a delayed nonlocal dispersal competitive system. This entire solution converges to two monotone fronts with different speeds, which approach each other from both sides of the x-axis, as t converge to-∞ and then converge to (1,0) as t converges to +∞. Its global dynamic shows the superior species invade the inferior ones from both sides of the x-axis and then the inferior ones become extinct, which is a new invading way. In fact, our conclusions extend this invading way into a more general competitive system. Furthermore, we show several properties of this entire solution.
文摘The stability of the predator-prey model subject to the Allee effect is an interesting topic in recent times.In this paper,we investigate the impact of weak Allee effect on the stability of a discrete-time predator-prey model with Holling type-IV functional response.The mathematical features of the proposed model are analyzed with the help of equilibrium analysis,stability analysis,and bifurcation theory.We provide sufficient conditions for the flip bifurcation by considering Allee parameter as the bifurcation parameter.We observe that the model becomes stable from chaotic dynamics as the Allee parameter increases.Further,we observe bi-stability behavior of the model between only prey existence equilibrium and the coexistence equilibrium.Our analytical findings are illustrated through numerical simulations.
文摘In the present paper,an epidemic model with Z-type control mechanism has been pro- posed and analyzed to explore the disease control strategy on an infectious disease outbreak.The uncontrolled model can have a disease-free equilibrium and an endemic equilibrium.The expression of the basic reproduction number and the conditions for the stability of the equilibria are derived.It is also observed that the disease-free equilibrium is globally asymptotically stable if R0<1,whereas the endemic equilibrium is globally asymptotically stable if R0>1.The model is further improved by considering Z-control mechanism and investigated.Disease can be controlled by using Z-control while the basic reproduction of the uncontrolled system is greater than unity.The positivity conditions of the solutions are derived and the basin of attraction for successful implementation of Z-control mechanism is also investigated.To verify the analytical findings,extensive numerical simulations on the model are carried out.
文摘In this paper, we derive a time-delayed and diffusive echinococcosis transmission model. We first address the well-posedness to the initial-value problem for the model and give the basic reproduction number TO0. In the case of a bounded spatial domain, we establish the local stability as well as the global stability of the disease-free and disease equilibria of the model. The methods to prove the local and the global stability are to analyze the corresponding characteristic equations and construct Lyapunov functionals, respectively. In the case of an unbounded spatial domain, by applying Schauder＇s fixed point theorem and the limiting arguments, we show that when R0 〉 1, there exists a constant c＊ 〉 0 such that the model admits positive traveling wave solutions connecting the disease-free and endemic equilibrium for c 〉 c＊, and when R0 〉 1 and c 〈 c＊, the model has no positive traveling wave solutions connecting them.
文摘In this paper, we concern a class of the generalized delayed stochastic predator-prey models with feedback coutrols based on discrete observations. The existence of global positive solution is given first. Then we discuss the deterministic model briefly, and establish the necessary conditions and the sufficient conditions for almost-sure extinction and persistence in mean for the stochastic system, where we show that the feedback controls can change the properties of the population systems significantly. Finally, numerical simulations are introduced to support the main results.
文摘In this paper, we have considered a delayed stage-structured diffusive prey-predator model, in which predator is assumed to undergo exploitation. By using the theory of partial functional differential equations, the local stability of an interior equilibrium is established and the existence of Hopf bifurcations at the interior equilibrium is also discussed. By applying the normal form and the center manifold theory, an explicit algorithm to determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived. Finally, the complex dynamics are obtained and numerical simulations substantiate the analytical results.
文摘Astrocytes have potential to break synchrony between neurons. Authors＇ recent researches reveal that astrocytes vary the synchronization threshold and provide an appropriate feedback control in stabilizing neural activities. In this study, we propose an astrocyte-inspired controller for desynchronization of two coupled limit-cycle oscillators as a minimal network model. The design procedure consists of two parts. First, based on the astrocyte model, the structure of the dynamic controller is suggested. Then, to have an emcient controller, parameters of controller are tuned through an optimization algo- rithm. The proposed bio-inspired controller takes advantages of three important proper- ties： （1） the controller desynchronizes the oscillators without any undesirable effects （e.g. stopping, annihilating or starting divergent oscillations）; （2） it consumes little effort to preserve the desirable desynchronized state; and （3） the controller is robust with respect to parameters＇ variations. Simulation results reveal the ability of the proposed controller.
基金supported by the National Natural Science Foundation of China(No.11561041)the Young Doctor Support Foundation of Gansu Education Department(No.2023QB-077)the Start-Up Foundation of Doctoral Research of Hexi University(No.KYQD2023011).
文摘This study examines an optimal contraception control problem for a nonlinear competitive vermin population model that is dependent on size structure and spatial diffusion in a polluted environment.The control variables are the average number of female sterilant and the input rate of exogenous toxicant.It has a good guiding effect on curbing environmental pollution and controlling the number of vermin.These results provide a theoretical basis for controlling and preventing vermin and curbing environmental pollution.The hybrid system belongs to the class of separable models,and its solution is separable in terms of size and spatial location.Therefore,we transform the system into two subsystems and prove the existence and uniqueness of non-negative solutions via the comparison principle and fixed point theorem,respectively.The necessary conditions for the optimal contraception strategy are derived by constructing an adjoint system and using tangent-normal cones.The method of characteristics and the finite difference method approximate the non-negative solutions of the two subsystems,and some numerical examples illustrate the theoretical results.
基金This work is supported by the National Natural Science Foundation of China(12071407,11901502)Training plan for young backbone teachers in Henan Province(2019GGJS157)+2 种基金Program for Science&Technology Innovation Talents in Universities of Henan Province(21HASTIT026)Program for Innovative Research Team(in Science and Technology)in the University of Henan Province(21IRTSTHN014)Natural Science Foundation of Henan Province(222300420016).
文摘In this paper,a new mosquito population suppression model with stage and sex structure is constructed,which is composed of two sub-models switching each other.Sterile mosquitoes are released with period T and remain sexually active for time T.For the case T<T,three thresholds T^(*),m^(*)and c^(*)are determined for the release period T and release amount c.According to the values of T and c in different ranges determined by these thresholds,we study the dynamical behavior of the system for different release strategies,mainly including the existence and stability of the mosquito-extinction equilibrium and positive periodic solutions.Finally,some numerical simulations are performed to illustrate our results.
基金The research of A.Q.Khan and F.Nazir is partially supported by the Higher Education Commission of Pakistan.
文摘Phytoplanktons are drifting plants in an aquatic system.They provide food for marine animals and are compared to terrestrial plants in that having chlorophyll and carrying out photosynthesis.Zooplanktons are drifting animals found inside the aquatic bodies.For stable aquatic ecosystem,the growth of both Zooplankton and Phytoplankton should be in steady state but in previous eras,there has been a universal explosion in destructive Plankton or algal blooms.Many investigators used various mathematical methodologies to try to explain the bloom phenomenon.So,in this paper,a discretized two-dimensional Phytoplankton-Zooplankton model is investigated.The results for the existence and uniqueness,and conditions for local stability with topological classifications of the equilibrium solutions are determined.It is also exhibited that at trivial and semitrivial equilibrium solutions,discrete model does not undergo fip bifurcation,but it undergoes Neimark-Sacker bifurcation at interior equilibrium solution under certain conditions.Further,state feedback method is deployed to control the chaos in the under consideration system.The extensive numerical simulations are provided to demonstrate theoretical results.
基金supported by grants from the China Postdoctoral Science Foundation(Grant Nos.2019M663653 and 2014M560755)the National Natural Science Foundation of China(Grant Nos.11971375,11571272,11201368 and 11631012)+1 种基金the National Science and Technology major project of China(Grant No.2018ZX10721202)grant from the Natural Science Foundation of Shaanxi Province(Grant No.2019JM-273).
文摘In this paper,we develop a three-dimensional fractional-order cancer model.The proposed model involves the interaction among tumor cells,healthy tissue cells and activated effector cells.The detailed analysis of the equilibrium points is studied.Also,the existence and uniqueness of the solution are investigated.The fractional derivative is considered in the Caputo sense.Numerical simulations are performed to illustrate the effectiveness of the obtained theoretical results.The outcome of the study reveals that the order of the fractional derivative has a significant effect on the dynamic process.Further,the calculated Lyapunov exponents give the existence of chaotic behavior of the proposed model.Also,it is observed from the obtained results that decrease in fractional-order p increases the chaotic behavior of the model.
基金support of the Natural Science Foundations.of China(11671085,11501111 and 11771082)Leading project in Fujian Province(2015Y0054)Nonlinear Analysis and Its Applications(19120/Z1607219016,IRTL1206).
文摘The citrate secreted by the rice(Oryza sativa L.)roots will promote the absorption of phosphate,and this process is described by the Kirk model.In our work,the Kirk model is divided into citrate sub-model and phosphate sub-model.In the citrate sub-model,we obtain the analytical solution of citrate with the Laplace transform,inverse Laplace transform and convolution theorem.The citrate solution is substituted into the phosphate sub-model,and the analytical solution of phosphate is obtained by the separation variable method.The existence of the solutions can be proved by the comparison test,the Weierstrass M-test and the Abel discriminating method.
基金Mcknight Foundation Grant No.12-508 with additional support from the Roots,Tubers and Banana(RTB)program and Bioversity International.
文摘In this paper,we study a deterministic model with non-autonomous system for mixed cultivars to assess the effect of cultivar susceptibility and seasonal variation on banana Xanthomonas wilt(BXW)disease dynamics.A special case of two cultivars classified as highly susceptible for inflorescence infection(ABB)and less susceptible(AAA)cultivar is considered.The basic reproduction number corresponding to the non-autonomous system is derived and numerically computed to determine disease dynamics.Results showed that the disease dies out whenever the periodic basic reproduction number is less than unity and a periodic solution is obtained when it is greater than one.Results further showed that for both cultivars,the basic reproduction number increases with increasing values of the transmission rates and declines exponentially with increasing values of roguing rates.The critical roguing rate of ABB-genome cultivar was higher than that of AAA-genome cultivars.The peaks in disease prevalence indicate the importance of effective implementation of controls during the rainy season.We conclude that highly susceptible cultivars play an important role in the spread of BXW and control measures should be effectively implemented during the rainy season if BXW is to be eradicated.
