Based on theWorld Health Organization(WHO),Meningitis is a severe infection of the meninges,the membranes covering the brain and spinal cord.It is a devastating disease and remains a significant public health challeng...Based on theWorld Health Organization(WHO),Meningitis is a severe infection of the meninges,the membranes covering the brain and spinal cord.It is a devastating disease and remains a significant public health challenge.This study investigates a bacterial meningitis model through deterministic and stochastic versions.Four-compartment population dynamics explain the concept,particularly the susceptible population,carrier,infected,and recovered.The model predicts the nonnegative equilibrium points and reproduction number,i.e.,the Meningitis-Free Equilibrium(MFE),and Meningitis-Existing Equilibrium(MEE).For the stochastic version of the existing deterministicmodel,the twomethodologies studied are transition probabilities and non-parametric perturbations.Also,positivity,boundedness,extinction,and disease persistence are studiedrigorouslywiththe helpofwell-known theorems.Standard and nonstandard techniques such as EulerMaruyama,stochastic Euler,stochastic Runge Kutta,and stochastic nonstandard finite difference in the sense of delay have been presented for computational analysis of the stochastic model.Unfortunately,standard methods fail to restore the biological properties of the model,so the stochastic nonstandard finite difference approximation is offered as an efficient,low-cost,and independent of time step size.In addition,the convergence,local,and global stability around the equilibria of the nonstandard computational method is studied by assuming the perturbation effect is zero.The simulations and comparison of the methods are presented to support the theoretical results and for the best visualization of results.展开更多
To provide an energy-efficient and slab-demand-compliant rolling delay strategy,the simulation software is utilized to calculate the rolling delay process of the reheating furnace.Based on energy consumption evaluatio...To provide an energy-efficient and slab-demand-compliant rolling delay strategy,the simulation software is utilized to calculate the rolling delay process of the reheating furnace.Based on energy consumption evaluation,two optimization methods were employed.The bisection approach uses the needs of the slab to estimate the rolling delay temperature,and the golden section search method uses the energy consumption analysis of the slab to determine the high-temperature insulation duration.Generally,the slab closest to the discharge position in the control zone is selected as the optimization target.The optimized slab does not show a significant temperature rise after the end of the rolling delay process.When comparing the optimized rolling delay strategies with the traditional ones,the optimized rolling delay strategies not only meet the output requirements for slabs but also offer significant advantages in terms of energy efficiency,and this advantage increases with rolling delay time.展开更多
This paper studies the bandgap characteristics of a locally resonant metamaterial beam with time delays.The dispersion relations are addressed based on transfer matrix method.The governing equations of motion of the b...This paper studies the bandgap characteristics of a locally resonant metamaterial beam with time delays.The dispersion relations are addressed based on transfer matrix method.The governing equations of motion of the beam in the frequency domain are given according to spectral element method.The amplitude-frequency responses of the forced beam are determined by solving linear algebraic equations.The obtained results show that the time-delayed feedback control has great relationships with the location,width and number of the bandgaps.It is interesting that the time delay can change the direction of the movement of the bandgap and give rise to the generation of multiple bandgaps.The influences of different combinations of control parameters on the bandgap properties are shown,such as broadening effects.展开更多
The mathematical method of ZTD(zenith tropospheric delay)spatial prediction is important for precise ZTD derivation and real-time precise point positioning(PPP)augmentation.This paper analyses the performance of the p...The mathematical method of ZTD(zenith tropospheric delay)spatial prediction is important for precise ZTD derivation and real-time precise point positioning(PPP)augmentation.This paper analyses the performance of the popular optimal function coefficient(OFC),sphere cap harmonic analysis(SCHA),kriging and inverse distance weighting(IDW)interpolation in ZTD spatial prediction and Beidou satellite navigation system(BDS)-PPP augmentation over China.For ZTD spatial prediction,the average time consumption of the OFC,kriging,and IDW methods is less than 0.1 s,which is significantly better than that of the SCHA method(63.157 s).The overall ZTD precision of the OFC is 3.44 cm,which outperforms those of the SCHA(9.65 cm),Kriging(10.6 cm),and IDW(11.8 cm)methods.We confirmed that the low performance of kriging and IDW is caused by their weakness in modelling ZTD variation in the vertical direction.To mitigate such deficiencies,an elevation normalization factor(ENF)is introduced into the kriging and IDW models(kriging-ENF and IDW-ENF).The overall ZTD spatial prediction accuracies of IDW-ENF and kriging-ENF are 2.80 cm and 2.01 cm,respectively,which are both superior to those of the OFC and the widely used empirical model GPT3(4.92 cm).For BDS-PPP enhancement,the ZTD provided by the kriging-ENF,IDW-ENF and OFC as prior constraints can effectively reduce the convergence time.Compared with unconstrained BDS-PPP,our proposed kriging-ENF outperforms IDW-ENF and OFC by reducing the horizontal and vertical convergence times by approximately 13.2%and 5.8%in Ningxia and 30.4%and 7.84%in Guangdong,respectively.These results indicate that kriging-ENF is a promising method for ZTD spatial prediction and BDS-PPP enhancement over China.展开更多
The dynamic behaviors of a large-scale ring neural network with a triangular coupling structure are investigated.The characteristic equation of the high-dimensional system using Coate’s flow graph method is calculate...The dynamic behaviors of a large-scale ring neural network with a triangular coupling structure are investigated.The characteristic equation of the high-dimensional system using Coate’s flow graph method is calculated.Time delay is selected as the bifurcation parameter,and sufficient conditions for stability and Hopf bifurcation are derived.It is found that the connection coefficient and time delay play a crucial role in the dynamic behaviors of the model.Furthermore,a phase diagram of multiple equilibrium points with one saddle point and two stable nodes is presented.Finally,the effectiveness of the theory is verified through simulation results.展开更多
Incorporating asymmetric quadratic and cubic stiffnesses into a time-delayed Duffing oscillator provides a more accurate representation of practical systems,where the resulting nonlinearities critically influence subh...Incorporating asymmetric quadratic and cubic stiffnesses into a time-delayed Duffing oscillator provides a more accurate representation of practical systems,where the resulting nonlinearities critically influence subharmonic resonance phenomena,yet comprehensive investigations remain limited.This study employs the generalized harmonic balance(HB)method to conduct an analytical investigation of the subharmonic resonance behavior in asymmetric stiffness nonlinear systems with time delay.To further examine the switching behavior between primary and subharmonic resonances,a numerical continuation approach combining the shooting method and the parameter continuation algorithm is developed.The analytical and numerical continuation solutions are validated through direct numerical integration.Subsequently,the switching behavior and associated bifurcation points are analyzed by means of the numerical continuation results in conjunction with the Floquet theory.Finally,the effects of delay parameters on the existence range of subharmonic responses are discussed in detail,and the influence of initial conditions on system dynamics is explored with basin of attraction plots.This work establishes a comprehensive framework for the analytical and numerical study on time-delayed nonlinear systems with asymmetric stiffness,providing valuable theoretical insights into the stability management of such dynamic systems.展开更多
In 2022,Leukemia is the 13th most common diagnosis of cancer globally as per the source of the International Agency for Research on Cancer(IARC).Leukemia is still a threat and challenge for all regions because of 46.6...In 2022,Leukemia is the 13th most common diagnosis of cancer globally as per the source of the International Agency for Research on Cancer(IARC).Leukemia is still a threat and challenge for all regions because of 46.6%infection in Asia,and 22.1%and 14.7%infection rates in Europe and North America,respectively.To study the dynamics of Leukemia,the population of cells has been divided into three subpopulations of cells susceptible cells,infected cells,and immune cells.To investigate the memory effects and uncertainty in disease progression,leukemia modeling is developed using stochastic fractional delay differential equations(SFDDEs).The feasible properties of positivity,boundedness,and equilibria(i.e.,Leukemia Free Equilibrium(LFE)and Leukemia Present Equilibrium(LPE))of the model were studied rigorously.The local and global stabilities and sensitivity of the parameters around the equilibria under the assumption of reproduction numbers were investigated.To support the theoretical analysis of the model,the Grunwald Letnikov Nonstandard Finite Difference(GL-NSFD)method was used to simulate the results of each subpopulation with memory effect.Also,the positivity and boundedness of the proposed method were studied.Our results show how different methods can help control the cell population and give useful advice to decision-makers on ways to lower leukemia rates in communities.展开更多
Dear Editor,This letter studies finite-time stability (FTS) of impulsive and switched hybrid systems with delay-dependent impulses. Some conditions, based on Lyapunov method, are proposed for ensuring FTS and estimati...Dear Editor,This letter studies finite-time stability (FTS) of impulsive and switched hybrid systems with delay-dependent impulses. Some conditions, based on Lyapunov method, are proposed for ensuring FTS and estimating settling-time function (STF) of the hybrid systems.When switching dynamics are FTS and impulsive dynamics involve destabilizing delay-dependent impulses, the FTS is retained if the impulses occur infrequently.展开更多
This study investigates the transmission dynamics of conjunctivitis using stochastic delay differential equations(SDDEs).A delayed stochastic model is formulated by dividing the population into five distinct compartme...This study investigates the transmission dynamics of conjunctivitis using stochastic delay differential equations(SDDEs).A delayed stochastic model is formulated by dividing the population into five distinct compartments:susceptible,exposed,infected,environmental irritants,and recovered individuals.The model undergoes thorough analytical examination,addressing key dynamical properties including positivity,boundedness,existence,and uniqueness of solutions.Local and global stability around the equilibrium points is studied with respect to the basic reproduction number.The existence of a unique global positive solution for the stochastic delayed model is established.In addition,a stochastic nonstandard finite difference scheme is developed,which is shown to be dynamically consistent and convergent toward the equilibrium states.The scheme preserves the essential qualitative features of the model and demonstrates improved performance when compared to existing numerical methods.Finally,the impact of time delays and stochastic fluctuations on the susceptible and infected populations is analyzed.展开更多
This paper deals with the numerical solution of initial value problems for systems of differential equations with a delay argument. The numerical stability of a linear multistep method is investigated by analysing the...This paper deals with the numerical solution of initial value problems for systems of differential equations with a delay argument. The numerical stability of a linear multistep method is investigated by analysing the solution of the lest equation y’(t)=Ay(t) + By(1-t),where A,B denote constant complex N×N-matrices,and t】0.We investigate carefully the characterization of the stability region.展开更多
The delay compensation method plays an essential role in maintaining the stability and achieving accurate real-time hybrid simulation results. The effectiveness of various compensation methods in different test scenar...The delay compensation method plays an essential role in maintaining the stability and achieving accurate real-time hybrid simulation results. The effectiveness of various compensation methods in different test scenarios, however, needs to be quantitatively evaluated. In this study, four compensation methods （i.e., the polynomial extrapolation, the linear acceleration extrapolation, the inverse compensation and the adaptive inverse compensation） are selected and compared experimentally using a frequency evaluation index （FEI） method. The effectiveness of the FEI method is first verified through comparison with the discrete transfer fimction approach for compensation methods assuming constant delay. Incomparable advantage is further demonstrated for the FEI method when applied to adaptive compensation methods, where the discrete transfer function approach is difficult to implement. Both numerical simulation and laboratory tests with predefined displacements are conducted using sinusoidal signals and random signals as inputs. Findings from numerical simulation and experimental results demonstrate that the FEI method is an efficient and effective approach to compare the performance of different compensation methods, especially for those requiring adaptation of compensation parameters.展开更多
This paper develops the mean-square exponential input-to-state stability（exp-ISS） of the Euler-Maruyama（EM） method for stochastic delay control systems（SDCSs）.The definition of mean-square exp-ISS of numerical m...This paper develops the mean-square exponential input-to-state stability（exp-ISS） of the Euler-Maruyama（EM） method for stochastic delay control systems（SDCSs）.The definition of mean-square exp-ISS of numerical methods is established.The conditions of the exact and EM method for an SDCS with the property of mean-square exp-ISS are obtained without involving control Lyapunov functions or functional.Under the global Lipschitz coefficients and mean-square continuous measurable inputs,it is proved that the mean-square exp-ISS of an SDCS holds if and only if that of the EM method is preserved for a sufficiently small step size.The proposed results are evaluated by using numerical experiments to show their effectiveness.展开更多
A method of source depth estimation based on the multi-path time delay difference is proposed. When the minimum time arrivals in all receiver depths are snapped to a certain time on time delay-depth plane, time delay ...A method of source depth estimation based on the multi-path time delay difference is proposed. When the minimum time arrivals in all receiver depths are snapped to a certain time on time delay-depth plane, time delay arrivals of surface-bottom reflection and bottom-surface reflection intersect at the source depth. Two hydrophones deployed vertically with a certain interval are required at least. If the receiver depths are known, the pair of time delays can be used to estimate the source depth. With the proposed method the source depth can be estimated successfully in a moderate range in the deep ocean without complicated matched-field calculations in the simulations and experiments.展开更多
This paper deals with the stability of linear multistep methods for multidimensional differential systems with distributed delays. The delay-dependent stability of linear multistep methods with compound quadrature rul...This paper deals with the stability of linear multistep methods for multidimensional differential systems with distributed delays. The delay-dependent stability of linear multistep methods with compound quadrature rules is studied. Several new sufficient criteria of delay-dependent stability are obtained by means of the argument principle. An algorithm is provided to check delay-dependent stability. An example that illustrates the effectiveness of the derived theoretical results is given.展开更多
The adapting Runge-Kutta methods with a new interpolation procedure to delay differential equations was introduced by K.J. in't Hout in 1992[1], he proved that the numerical process, satisfies an important asympto...The adapting Runge-Kutta methods with a new interpolation procedure to delay differential equations was introduced by K.J. in't Hout in 1992[1], he proved that the numerical process, satisfies an important asymptotic stability condition. In this paper the convergence of this method under the asymptotic stability and other conditions in theorem 3 is proved.展开更多
This paper focuses on the numerical stability of the block θ methods adapted to differential equations with a delay argument. For the block θ methods, an interpolation procedure is introduced which leads to the nume...This paper focuses on the numerical stability of the block θ methods adapted to differential equations with a delay argument. For the block θ methods, an interpolation procedure is introduced which leads to the numerical processes that satisfy an important asymptotic stability condition related to the class of test problems y′(t)=ay(t)+by(t-τ) with a,b∈C, Re(a)<-|b| and τ>0. We prove that the block θ method is GP stable if and only if the method is A stable for ordinary differential equations. Furthermore, it is proved that the P and GP stability are equivalent for the block θ method.展开更多
An idea of relaxing the effect of delay when computing the Runge-Kutta stages in the current step and a class of two-step continuity Runge-Kutta methods （TSCRK） is presented. Their construction, their order conditio...An idea of relaxing the effect of delay when computing the Runge-Kutta stages in the current step and a class of two-step continuity Runge-Kutta methods （TSCRK） is presented. Their construction, their order conditions and their convergence are studied. The two-step continuity Runge-Kutta methods possess good numerical stability properties and higher stage-order, and keep the explicit process of computing the Runge-Kutta stages. The numerical experiments show that the TSCRK methods are efficient.展开更多
The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was a...The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was analysed for the solution of the generalized system of linear neutral test equations, After the establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, it is shown that a linear multistep method is NGP(G)-stable if and only if it is A-stable.展开更多
This paper presents a Modified Power Series Method (MPSM) for the solution of delay differential equations. Unlike the traditional power series method which is applied to solve only linear differential equations, this...This paper presents a Modified Power Series Method (MPSM) for the solution of delay differential equations. Unlike the traditional power series method which is applied to solve only linear differential equations, this new approach is applicable to both linear and nonlinear problems. The method produces a system of algebraic equations which is solved to determine the coefficients in the trial solution. The method provides the solution in form of a rapid convergent series. The obtained results for numerical examples demonstrate the reliability and efficiency of the method.展开更多
The aim of this paper is to study the asymptotic stability properties of Runge Kutta(R-K) methods for neutral differential equations(NDDEs) when they are applied to the linear test equation of the form: y′(t)=ay(t)...The aim of this paper is to study the asymptotic stability properties of Runge Kutta(R-K) methods for neutral differential equations(NDDEs) when they are applied to the linear test equation of the form: y′(t)=ay(t)+by(t-τ)+cy’(t-τ), t>0, y(t)=g(t), -τ≤t≤0, with a,b,c∈[FK(W+3mm\.3mm][TPP129A,+3mm?3mm,BP], τ>0 and g(t) is a continuous real value function. In this paper we are concerned with the dependence of stability region on a fixed but arbitrary delay τ. In fact, it is one of the N.Guglielmi open problems to investigate the delay dependent stability analysis for NDDEs. The results that the 2,3 stages non natural R-K methods are unstable as Radau IA and Lobatto IIIC are proved. And the s stages Radau IIA methods are unstable, however all Gauss methods are compatible.展开更多
基金Deanship of Research and Graduate Studies at King Khalid University for funding this work through large Research Project under Grant Number RGP2/302/45supported by the Deanship of Scientific Research,Vice Presidency forGraduate Studies and Scientific Research,King Faisal University,Saudi Arabia(Grant Number A426).
文摘Based on theWorld Health Organization(WHO),Meningitis is a severe infection of the meninges,the membranes covering the brain and spinal cord.It is a devastating disease and remains a significant public health challenge.This study investigates a bacterial meningitis model through deterministic and stochastic versions.Four-compartment population dynamics explain the concept,particularly the susceptible population,carrier,infected,and recovered.The model predicts the nonnegative equilibrium points and reproduction number,i.e.,the Meningitis-Free Equilibrium(MFE),and Meningitis-Existing Equilibrium(MEE).For the stochastic version of the existing deterministicmodel,the twomethodologies studied are transition probabilities and non-parametric perturbations.Also,positivity,boundedness,extinction,and disease persistence are studiedrigorouslywiththe helpofwell-known theorems.Standard and nonstandard techniques such as EulerMaruyama,stochastic Euler,stochastic Runge Kutta,and stochastic nonstandard finite difference in the sense of delay have been presented for computational analysis of the stochastic model.Unfortunately,standard methods fail to restore the biological properties of the model,so the stochastic nonstandard finite difference approximation is offered as an efficient,low-cost,and independent of time step size.In addition,the convergence,local,and global stability around the equilibria of the nonstandard computational method is studied by assuming the perturbation effect is zero.The simulations and comparison of the methods are presented to support the theoretical results and for the best visualization of results.
文摘To provide an energy-efficient and slab-demand-compliant rolling delay strategy,the simulation software is utilized to calculate the rolling delay process of the reheating furnace.Based on energy consumption evaluation,two optimization methods were employed.The bisection approach uses the needs of the slab to estimate the rolling delay temperature,and the golden section search method uses the energy consumption analysis of the slab to determine the high-temperature insulation duration.Generally,the slab closest to the discharge position in the control zone is selected as the optimization target.The optimized slab does not show a significant temperature rise after the end of the rolling delay process.When comparing the optimized rolling delay strategies with the traditional ones,the optimized rolling delay strategies not only meet the output requirements for slabs but also offer significant advantages in terms of energy efficiency,and this advantage increases with rolling delay time.
文摘This paper studies the bandgap characteristics of a locally resonant metamaterial beam with time delays.The dispersion relations are addressed based on transfer matrix method.The governing equations of motion of the beam in the frequency domain are given according to spectral element method.The amplitude-frequency responses of the forced beam are determined by solving linear algebraic equations.The obtained results show that the time-delayed feedback control has great relationships with the location,width and number of the bandgaps.It is interesting that the time delay can change the direction of the movement of the bandgap and give rise to the generation of multiple bandgaps.The influences of different combinations of control parameters on the bandgap properties are shown,such as broadening effects.
基金co-supported by the National Nature Science Foundation of China(No.12303071)the Shanghai Science and Technology Plan Project,China(No.23YF1455500)+1 种基金the China Postdoctoral Science Foundation(No.2023M743653)Ministry of Industry and Information Technology of China through the High Precision Timing Service Project(No.TC220A04A-80)。
文摘The mathematical method of ZTD(zenith tropospheric delay)spatial prediction is important for precise ZTD derivation and real-time precise point positioning(PPP)augmentation.This paper analyses the performance of the popular optimal function coefficient(OFC),sphere cap harmonic analysis(SCHA),kriging and inverse distance weighting(IDW)interpolation in ZTD spatial prediction and Beidou satellite navigation system(BDS)-PPP augmentation over China.For ZTD spatial prediction,the average time consumption of the OFC,kriging,and IDW methods is less than 0.1 s,which is significantly better than that of the SCHA method(63.157 s).The overall ZTD precision of the OFC is 3.44 cm,which outperforms those of the SCHA(9.65 cm),Kriging(10.6 cm),and IDW(11.8 cm)methods.We confirmed that the low performance of kriging and IDW is caused by their weakness in modelling ZTD variation in the vertical direction.To mitigate such deficiencies,an elevation normalization factor(ENF)is introduced into the kriging and IDW models(kriging-ENF and IDW-ENF).The overall ZTD spatial prediction accuracies of IDW-ENF and kriging-ENF are 2.80 cm and 2.01 cm,respectively,which are both superior to those of the OFC and the widely used empirical model GPT3(4.92 cm).For BDS-PPP enhancement,the ZTD provided by the kriging-ENF,IDW-ENF and OFC as prior constraints can effectively reduce the convergence time.Compared with unconstrained BDS-PPP,our proposed kriging-ENF outperforms IDW-ENF and OFC by reducing the horizontal and vertical convergence times by approximately 13.2%and 5.8%in Ningxia and 30.4%and 7.84%in Guangdong,respectively.These results indicate that kriging-ENF is a promising method for ZTD spatial prediction and BDS-PPP enhancement over China.
基金Supported by Natural Science Foundation of Shandong Province of China(Grant Nos.ZR2020MF080 and ZR2020MF065).
文摘The dynamic behaviors of a large-scale ring neural network with a triangular coupling structure are investigated.The characteristic equation of the high-dimensional system using Coate’s flow graph method is calculated.Time delay is selected as the bifurcation parameter,and sufficient conditions for stability and Hopf bifurcation are derived.It is found that the connection coefficient and time delay play a crucial role in the dynamic behaviors of the model.Furthermore,a phase diagram of multiple equilibrium points with one saddle point and two stable nodes is presented.Finally,the effectiveness of the theory is verified through simulation results.
基金Project supported by the National Natural Science Foundation of China(Nos.U24B2062,520754285247051087)+1 种基金the Two-chain Fusion High-end Machine Tool Project of Shaanxi Province of China(No.2021LLRh-01-02)the Youth Fund of the National Natural Science Foundation of China(No.52205281)。
文摘Incorporating asymmetric quadratic and cubic stiffnesses into a time-delayed Duffing oscillator provides a more accurate representation of practical systems,where the resulting nonlinearities critically influence subharmonic resonance phenomena,yet comprehensive investigations remain limited.This study employs the generalized harmonic balance(HB)method to conduct an analytical investigation of the subharmonic resonance behavior in asymmetric stiffness nonlinear systems with time delay.To further examine the switching behavior between primary and subharmonic resonances,a numerical continuation approach combining the shooting method and the parameter continuation algorithm is developed.The analytical and numerical continuation solutions are validated through direct numerical integration.Subsequently,the switching behavior and associated bifurcation points are analyzed by means of the numerical continuation results in conjunction with the Floquet theory.Finally,the effects of delay parameters on the existence range of subharmonic responses are discussed in detail,and the influence of initial conditions on system dynamics is explored with basin of attraction plots.This work establishes a comprehensive framework for the analytical and numerical study on time-delayed nonlinear systems with asymmetric stiffness,providing valuable theoretical insights into the stability management of such dynamic systems.
基金supported by the Fundacao para a Ciencia e Tecnologia,FCT,under the project https://doi.org/10.54499/UIDB/04674/2020(accessed on 1 January 2025).
文摘In 2022,Leukemia is the 13th most common diagnosis of cancer globally as per the source of the International Agency for Research on Cancer(IARC).Leukemia is still a threat and challenge for all regions because of 46.6%infection in Asia,and 22.1%and 14.7%infection rates in Europe and North America,respectively.To study the dynamics of Leukemia,the population of cells has been divided into three subpopulations of cells susceptible cells,infected cells,and immune cells.To investigate the memory effects and uncertainty in disease progression,leukemia modeling is developed using stochastic fractional delay differential equations(SFDDEs).The feasible properties of positivity,boundedness,and equilibria(i.e.,Leukemia Free Equilibrium(LFE)and Leukemia Present Equilibrium(LPE))of the model were studied rigorously.The local and global stabilities and sensitivity of the parameters around the equilibria under the assumption of reproduction numbers were investigated.To support the theoretical analysis of the model,the Grunwald Letnikov Nonstandard Finite Difference(GL-NSFD)method was used to simulate the results of each subpopulation with memory effect.Also,the positivity and boundedness of the proposed method were studied.Our results show how different methods can help control the cell population and give useful advice to decision-makers on ways to lower leukemia rates in communities.
基金supported by the National Natural Science Foundation of China(61833005)
文摘Dear Editor,This letter studies finite-time stability (FTS) of impulsive and switched hybrid systems with delay-dependent impulses. Some conditions, based on Lyapunov method, are proposed for ensuring FTS and estimating settling-time function (STF) of the hybrid systems.When switching dynamics are FTS and impulsive dynamics involve destabilizing delay-dependent impulses, the FTS is retained if the impulses occur infrequently.
基金supported by Princess Nourah bint Abdulrahman University Researchers Supporting Project number(PNURSP2025R899)Princess Nourah bint Abdulrahman University,Riyadh,Saudi Arabiasupported by the Deanship of Scientific Research,Vice Presidency for Graduate Studies and Scientific Research,King Faisal University,Saudi Arabia(KFU252831)。
文摘This study investigates the transmission dynamics of conjunctivitis using stochastic delay differential equations(SDDEs).A delayed stochastic model is formulated by dividing the population into five distinct compartments:susceptible,exposed,infected,environmental irritants,and recovered individuals.The model undergoes thorough analytical examination,addressing key dynamical properties including positivity,boundedness,existence,and uniqueness of solutions.Local and global stability around the equilibrium points is studied with respect to the basic reproduction number.The existence of a unique global positive solution for the stochastic delayed model is established.In addition,a stochastic nonstandard finite difference scheme is developed,which is shown to be dynamically consistent and convergent toward the equilibrium states.The scheme preserves the essential qualitative features of the model and demonstrates improved performance when compared to existing numerical methods.Finally,the impact of time delays and stochastic fluctuations on the susceptible and infected populations is analyzed.
文摘This paper deals with the numerical solution of initial value problems for systems of differential equations with a delay argument. The numerical stability of a linear multistep method is investigated by analysing the solution of the lest equation y’(t)=Ay(t) + By(1-t),where A,B denote constant complex N×N-matrices,and t】0.We investigate carefully the characterization of the stability region.
基金National Natural Science Foundation of China under Grant No.51378107the Fundamental Research Funds for the Central Universities and Priority Academic Program Development of Jiangsu Higher Education Institutions under Grant No.KYLX-0158the National Natural Science Foundation under Grant No.CMMI-1227962
文摘The delay compensation method plays an essential role in maintaining the stability and achieving accurate real-time hybrid simulation results. The effectiveness of various compensation methods in different test scenarios, however, needs to be quantitatively evaluated. In this study, four compensation methods （i.e., the polynomial extrapolation, the linear acceleration extrapolation, the inverse compensation and the adaptive inverse compensation） are selected and compared experimentally using a frequency evaluation index （FEI） method. The effectiveness of the FEI method is first verified through comparison with the discrete transfer fimction approach for compensation methods assuming constant delay. Incomparable advantage is further demonstrated for the FEI method when applied to adaptive compensation methods, where the discrete transfer function approach is difficult to implement. Both numerical simulation and laboratory tests with predefined displacements are conducted using sinusoidal signals and random signals as inputs. Findings from numerical simulation and experimental results demonstrate that the FEI method is an efficient and effective approach to compare the performance of different compensation methods, especially for those requiring adaptation of compensation parameters.
基金supported by the National Natural Science Foundation of China(6127312660904032)the Natural Science Foundation of Guangdong Province(10251064101000008)
文摘This paper develops the mean-square exponential input-to-state stability（exp-ISS） of the Euler-Maruyama（EM） method for stochastic delay control systems（SDCSs）.The definition of mean-square exp-ISS of numerical methods is established.The conditions of the exact and EM method for an SDCS with the property of mean-square exp-ISS are obtained without involving control Lyapunov functions or functional.Under the global Lipschitz coefficients and mean-square continuous measurable inputs,it is proved that the mean-square exp-ISS of an SDCS holds if and only if that of the EM method is preserved for a sufficiently small step size.The proposed results are evaluated by using numerical experiments to show their effectiveness.
基金Supported by the National Natural Science Foundation of China under Grant No 11174235
文摘A method of source depth estimation based on the multi-path time delay difference is proposed. When the minimum time arrivals in all receiver depths are snapped to a certain time on time delay-depth plane, time delay arrivals of surface-bottom reflection and bottom-surface reflection intersect at the source depth. Two hydrophones deployed vertically with a certain interval are required at least. If the receiver depths are known, the pair of time delays can be used to estimate the source depth. With the proposed method the source depth can be estimated successfully in a moderate range in the deep ocean without complicated matched-field calculations in the simulations and experiments.
基金Project supported by the National Natural Science Foundation of China(No.11471217)
文摘This paper deals with the stability of linear multistep methods for multidimensional differential systems with distributed delays. The delay-dependent stability of linear multistep methods with compound quadrature rules is studied. Several new sufficient criteria of delay-dependent stability are obtained by means of the argument principle. An algorithm is provided to check delay-dependent stability. An example that illustrates the effectiveness of the derived theoretical results is given.
文摘The adapting Runge-Kutta methods with a new interpolation procedure to delay differential equations was introduced by K.J. in't Hout in 1992[1], he proved that the numerical process, satisfies an important asymptotic stability condition. In this paper the convergence of this method under the asymptotic stability and other conditions in theorem 3 is proved.
文摘This paper focuses on the numerical stability of the block θ methods adapted to differential equations with a delay argument. For the block θ methods, an interpolation procedure is introduced which leads to the numerical processes that satisfy an important asymptotic stability condition related to the class of test problems y′(t)=ay(t)+by(t-τ) with a,b∈C, Re(a)<-|b| and τ>0. We prove that the block θ method is GP stable if and only if the method is A stable for ordinary differential equations. Furthermore, it is proved that the P and GP stability are equivalent for the block θ method.
文摘An idea of relaxing the effect of delay when computing the Runge-Kutta stages in the current step and a class of two-step continuity Runge-Kutta methods （TSCRK） is presented. Their construction, their order conditions and their convergence are studied. The two-step continuity Runge-Kutta methods possess good numerical stability properties and higher stage-order, and keep the explicit process of computing the Runge-Kutta stages. The numerical experiments show that the TSCRK methods are efficient.
文摘The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was analysed for the solution of the generalized system of linear neutral test equations, After the establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, it is shown that a linear multistep method is NGP(G)-stable if and only if it is A-stable.
文摘This paper presents a Modified Power Series Method (MPSM) for the solution of delay differential equations. Unlike the traditional power series method which is applied to solve only linear differential equations, this new approach is applicable to both linear and nonlinear problems. The method produces a system of algebraic equations which is solved to determine the coefficients in the trial solution. The method provides the solution in form of a rapid convergent series. The obtained results for numerical examples demonstrate the reliability and efficiency of the method.
文摘The aim of this paper is to study the asymptotic stability properties of Runge Kutta(R-K) methods for neutral differential equations(NDDEs) when they are applied to the linear test equation of the form: y′(t)=ay(t)+by(t-τ)+cy’(t-τ), t>0, y(t)=g(t), -τ≤t≤0, with a,b,c∈[FK(W+3mm\.3mm][TPP129A,+3mm?3mm,BP], τ>0 and g(t) is a continuous real value function. In this paper we are concerned with the dependence of stability region on a fixed but arbitrary delay τ. In fact, it is one of the N.Guglielmi open problems to investigate the delay dependent stability analysis for NDDEs. The results that the 2,3 stages non natural R-K methods are unstable as Radau IA and Lobatto IIIC are proved. And the s stages Radau IIA methods are unstable, however all Gauss methods are compatible.
