In this paper,the stability and Hopf bifurcation of multiple sclerosis model with time delay and saturation function reaction are studied.At first,the stability condition of trivial equilibrium point is given,and the ...In this paper,the stability and Hopf bifurcation of multiple sclerosis model with time delay and saturation function reaction are studied.At first,the stability condition of trivial equilibrium point is given,and the stability of nonnegative equilibrium point is discussed.Then,the existence condition of Hopf bifurcation is given by choosing the added time delay τ as the bifurcation parameter.The direction of Hopf bifurcation and the stability of its periodic solution are analyzed by using canonical form theory and central manifold theorem.Finally,the conclusion is drawn by numerical analysis.展开更多
By using the so-called SP-stable polynomials, this paper reconsiders the problem of global stabilization of linear systems with input saturation. Firstly, a new nonlinear feedback law consisting of parallel connection...By using the so-called SP-stable polynomials, this paper reconsiders the problem of global stabilization of linear systems with input saturation. Firstly, a new nonlinear feedback law consisting of parallel connections of saturation functions by means of the so-called state-dependent saturation function is proposed for global stabilization of chains of integrators system. The state-dependent saturation function allows increasing the control energy when some of the states are badly scaled and can improve significantly the transient performances of the closed-loop system. Secondly, this type of global stabilization nonlinear feedback laws is extended to a class of linear systems that can be globally stabilized by bounded controls. Numerical examples show the effectiveness of the proposed approach.展开更多
All harmonics of the non-linear standing wave tend to saturate when the excitation is strong enough. In the present work, saturation functions are found from the experimental laws of saturation, so that the physical ...All harmonics of the non-linear standing wave tend to saturate when the excitation is strong enough. In the present work, saturation functions are found from the experimental laws of saturation, so that the physical significance thereof may be investigated展开更多
Mathematical modelling has been extensively used to measure intervention strategies for the control of contagious conditions.Alignment between different models is pivotal for furnishing strong substantiation for polic...Mathematical modelling has been extensively used to measure intervention strategies for the control of contagious conditions.Alignment between different models is pivotal for furnishing strong substantiation for policymakers because the differences in model features can impact their prognostications.Mathematical modelling has been widely used in order to better understand the transmission,treatment,and prevention of infectious diseases.Herein,we study the dynamics of a human immunodeficiency virus(HIV)infection model with four variables:S(t),I(t),C(t),and A(t)the susceptible individuals;HIV infected individuals(with no clinical symptoms of AIDS);HIV infected individuals(under ART with a viral load remaining low),and HIV infected individuals with two different incidence functions(bilinear and saturated incidence functions).A novel numerical scheme called the continuous Galerkin-Petrov method is implemented for the solution of themodel.The influence of different clinical parameters on the dynamical behavior of S(t),I(t),C(t)and A(t)is described and analyzed.All the results are depicted graphically.On the other hand,we explore the time-dependent movement of nanofluid in porous media on an extending sheet under the influence of thermal radiation,heat flux,hall impact,variable heat source,and nanomaterial.The flow is considered to be 2D,boundary layer,viscous,incompressible,laminar,and unsteady.Sufficient transformations turn governing connected PDEs intoODEs,which are solved using the proposed scheme.To justify the envisaged problem,a comparison of the current work with previous literature is presented.展开更多
To realize the continuous and variable gait transition for a new type of arthropod robot, a multi-level gait transition model is studied in this paper. The model is composed of central pattern generator （CPG） and sa...To realize the continuous and variable gait transition for a new type of arthropod robot, a multi-level gait transition model is studied in this paper. The model is composed of central pattern generator （CPG） and saturation function. The CPG consists of four pairs of oscillators which can ex- hibit rhythmic activity when given stimulation signal S that lies in the range of saturation function. All oscillators receive the same S, but each pair of oscillators has different saturation functions. Multi- level gait transition can be realized when S changes regularly, as the oscillators start or stop oscilla- ting at different times. After computer simulation, the gait transition model is implemented in the ar- thropod robot. The experimental results show that ideal gait transition for the arthropod robot can be realized with the multi-level gait transition model.展开更多
In this paper,we study a network-based SIR epidemic model with a saturated treatment function in which a parameterαis introduced to measure the extent of the effect of the infected being delayed for treatment.Our aim...In this paper,we study a network-based SIR epidemic model with a saturated treatment function in which a parameterαis introduced to measure the extent of the effect of the infected being delayed for treatment.Our aim is to present a global analysis and to investigate how the parameterαaffects the spreading of diseases.Our main results are as follows:(1)In the case of the threshold value R_(0)<1,there exist two values of α:α_(c) and α_(0),such that the disease-free equilibrium is globally asymptotically stable when α≤α_(0) and multiple endemic equilibria exist when α≥α_(0).This means that the parameterαhas an essential infuence on the spreading of the disease.(2)In the case of the threshold value R_(0)>1,if the model has only one endemic equilibrium,then the unique endemic equilibrium is globally attractive.In this case,it is also proved that if α≤α_(c),then the endemic equilibrium has only one,so is globally attractive,In addition,numerical simulation is performed to illustrate our theoretical results.展开更多
Many autoimmune diseases exhibit an alternating pattern of relapses and remissions in which the apparent self-tolerance phase is interrupted by periodic autoimmune episodes. In this paper, we introduce a class of term...Many autoimmune diseases exhibit an alternating pattern of relapses and remissions in which the apparent self-tolerance phase is interrupted by periodic autoimmune episodes. In this paper, we introduce a class of terminally differentiated effector T cells to an existing model of autoimmune disease and investigate the stability and Hopf branching phenomenon in a model of multiple sclerosis with a saturable functional response. First, we explore the local asymptotic stability of the equilibrium point and propose conditions for the existence of Hopf branching. Finally, with the help of canonical type theory and the central manifold theorem, we analyze the direction of Hopf branching and the stability of branching periodic solutions.展开更多
Petrophysicists and reservoir engineers utilise the capillary pressure and saturation-height function for calculating the water saturation of any reservoir,at a given height above the free water level.The results have...Petrophysicists and reservoir engineers utilise the capillary pressure and saturation-height function for calculating the water saturation of any reservoir,at a given height above the free water level.The results have a big impact on reserve estimation.The majority of capillary pressure studies are carried out in labs with core data.Cores,on the other hand,are usually altered from their original state before being delivered to laboratories.Moreover,the accuracy of discrete sets of core data in describing entire reservoir parameters,is still up for debate.Prediction of the capillary pressure curve in reservoir condition is an important subject that is challenging to perform.The use of nuclear magnetic resonance(NMR)logs for oil and gas exploration has grown in popularity over the last few decades.However,most of the time the utilization of the data is limited for evaluating porosity-permeability,distributions and computation of irreducible water saturation.After the advent of fluid substitution methods,NMR T_(2)distributions may now be used to synthesize core equivalent capillary pressure curves.Using fluid substitution workflow,our study introduces a better approach for obtaining capillary pressure curves from the NMR T_(2)distribution.The available core data has been used to calculate calibration parameters for better saturation height modelling.The workflow introduces a novel approach in resistivity independent saturation computation.In the exploratory wells of our study area,computed water saturation derived from the saturation height function exhibits encouraging agreement with resistivity based water saturation from multi-mineral model.The NMR based saturation height modelling approach has been included in study area for the first time so far.展开更多
An SIS epidemic model with the standard incidence rate and saturated treatment func- tion is proposed. The dynamics of the system are discussed, and the effect of the capacity for treatment and the recruitment of the ...An SIS epidemic model with the standard incidence rate and saturated treatment func- tion is proposed. The dynamics of the system are discussed, and the effect of the capacity for treatment and the recruitment of the population are also studied. We find that the effect of the maximum recovery per unit of time and the recruitment rate of the popula- tion over some level are two factors which lead to the backward bifurcation, and in some cases, the model may undergo the saddle-node bifurcation or Bogdanov-Takens bifurca- tion. It is shown that the disease-free equilibrium is globally asymptotically stable under some conditions, Numerical simulations are consistent with our obtained results in the- orems, which show that improving the efficiency and capacity of treatment is important for control of disease.展开更多
A mathematical model describing the epidemic interactions between humans and blackflies in the transmission of onchocerciasis is considered.In this model,the onchocerciasis infected human individuals are divided into ...A mathematical model describing the epidemic interactions between humans and blackflies in the transmission of onchocerciasis is considered.In this model,the onchocerciasis infected human individuals are divided into two classes of infected humans with high and low microfilarial output incorporating saturated treatment function,which caters for high saturation of onchocerciasis disease.We analyze the model feasible region and obtain the basic reproduction number(R_(hb))using the next generation matrix method.Also,we obtain the onchocerciasis-free and onchocerciasis endemic equilibrium solutions and show that if R_(hb) is less than unity,the onchocerciasis-free equilibrium is locally and globally asymptotically stable.Furthermore,we employed a Lyapunov function to analyze the global asymptotic stability of the onchocerciasis—endemic equilibrium whenever Rhb is greater than unity.In addition,data on mass drug distribution of ivermectin drug to combat onchocerciasis prevalence in Ekiti state of Nigeria were fitted to the model.Graphical results reveal that consistent annual or bi-annual distribution of ivermectin drug in the region is effective in reducing the disease menace.Further simulations also show that public health control measures are needed to minimize infectious contact between humans and blackflies which leads to onchocerciasis infections and visual blindness.展开更多
文摘In this paper,the stability and Hopf bifurcation of multiple sclerosis model with time delay and saturation function reaction are studied.At first,the stability condition of trivial equilibrium point is given,and the stability of nonnegative equilibrium point is discussed.Then,the existence condition of Hopf bifurcation is given by choosing the added time delay τ as the bifurcation parameter.The direction of Hopf bifurcation and the stability of its periodic solution are analyzed by using canonical form theory and central manifold theorem.Finally,the conclusion is drawn by numerical analysis.
基金supported in part by the National Natural Science Foundation of China under Grant Nos. 60904007 and 61074111the China Postdoctoral Science Foundation under Grant No.20100480059+2 种基金the Heilongjiang Postdoctoral Foundation of China under Grant No.LRB10-194the Foundation for Innovative Research Group of the National Natural Science Foundation of China under Grant No.601021002the Development Program for Outstanding Young Teachers at the Harbin Institute of Technology under Grant No. HITQNJS.2009.054
文摘By using the so-called SP-stable polynomials, this paper reconsiders the problem of global stabilization of linear systems with input saturation. Firstly, a new nonlinear feedback law consisting of parallel connections of saturation functions by means of the so-called state-dependent saturation function is proposed for global stabilization of chains of integrators system. The state-dependent saturation function allows increasing the control energy when some of the states are badly scaled and can improve significantly the transient performances of the closed-loop system. Secondly, this type of global stabilization nonlinear feedback laws is extended to a class of linear systems that can be globally stabilized by bounded controls. Numerical examples show the effectiveness of the proposed approach.
文摘All harmonics of the non-linear standing wave tend to saturate when the excitation is strong enough. In the present work, saturation functions are found from the experimental laws of saturation, so that the physical significance thereof may be investigated
文摘Mathematical modelling has been extensively used to measure intervention strategies for the control of contagious conditions.Alignment between different models is pivotal for furnishing strong substantiation for policymakers because the differences in model features can impact their prognostications.Mathematical modelling has been widely used in order to better understand the transmission,treatment,and prevention of infectious diseases.Herein,we study the dynamics of a human immunodeficiency virus(HIV)infection model with four variables:S(t),I(t),C(t),and A(t)the susceptible individuals;HIV infected individuals(with no clinical symptoms of AIDS);HIV infected individuals(under ART with a viral load remaining low),and HIV infected individuals with two different incidence functions(bilinear and saturated incidence functions).A novel numerical scheme called the continuous Galerkin-Petrov method is implemented for the solution of themodel.The influence of different clinical parameters on the dynamical behavior of S(t),I(t),C(t)and A(t)is described and analyzed.All the results are depicted graphically.On the other hand,we explore the time-dependent movement of nanofluid in porous media on an extending sheet under the influence of thermal radiation,heat flux,hall impact,variable heat source,and nanomaterial.The flow is considered to be 2D,boundary layer,viscous,incompressible,laminar,and unsteady.Sufficient transformations turn governing connected PDEs intoODEs,which are solved using the proposed scheme.To justify the envisaged problem,a comparison of the current work with previous literature is presented.
基金Supported by the Ministerial Level Advanced Research Foundation(65822576)
文摘To realize the continuous and variable gait transition for a new type of arthropod robot, a multi-level gait transition model is studied in this paper. The model is composed of central pattern generator （CPG） and saturation function. The CPG consists of four pairs of oscillators which can ex- hibit rhythmic activity when given stimulation signal S that lies in the range of saturation function. All oscillators receive the same S, but each pair of oscillators has different saturation functions. Multi- level gait transition can be realized when S changes regularly, as the oscillators start or stop oscilla- ting at different times. After computer simulation, the gait transition model is implemented in the ar- thropod robot. The experimental results show that ideal gait transition for the arthropod robot can be realized with the multi-level gait transition model.
基金The research was supported in part by the NNSFC(grant 12071058)the Applied Basic Research Program of Department of Science and Technology of Liaoning Province of China(grant 2023JH2/101300095).
文摘In this paper,we study a network-based SIR epidemic model with a saturated treatment function in which a parameterαis introduced to measure the extent of the effect of the infected being delayed for treatment.Our aim is to present a global analysis and to investigate how the parameterαaffects the spreading of diseases.Our main results are as follows:(1)In the case of the threshold value R_(0)<1,there exist two values of α:α_(c) and α_(0),such that the disease-free equilibrium is globally asymptotically stable when α≤α_(0) and multiple endemic equilibria exist when α≥α_(0).This means that the parameterαhas an essential infuence on the spreading of the disease.(2)In the case of the threshold value R_(0)>1,if the model has only one endemic equilibrium,then the unique endemic equilibrium is globally attractive.In this case,it is also proved that if α≤α_(c),then the endemic equilibrium has only one,so is globally attractive,In addition,numerical simulation is performed to illustrate our theoretical results.
文摘Many autoimmune diseases exhibit an alternating pattern of relapses and remissions in which the apparent self-tolerance phase is interrupted by periodic autoimmune episodes. In this paper, we introduce a class of terminally differentiated effector T cells to an existing model of autoimmune disease and investigate the stability and Hopf branching phenomenon in a model of multiple sclerosis with a saturable functional response. First, we explore the local asymptotic stability of the equilibrium point and propose conditions for the existence of Hopf branching. Finally, with the help of canonical type theory and the central manifold theorem, we analyze the direction of Hopf branching and the stability of branching periodic solutions.
基金The authors gratefully appreciate the support of Oil and Natural Gas Corporation,for providing data and permission to carry out the work under the CoEOGE project:RD/0120-PSUCE19-001.
文摘Petrophysicists and reservoir engineers utilise the capillary pressure and saturation-height function for calculating the water saturation of any reservoir,at a given height above the free water level.The results have a big impact on reserve estimation.The majority of capillary pressure studies are carried out in labs with core data.Cores,on the other hand,are usually altered from their original state before being delivered to laboratories.Moreover,the accuracy of discrete sets of core data in describing entire reservoir parameters,is still up for debate.Prediction of the capillary pressure curve in reservoir condition is an important subject that is challenging to perform.The use of nuclear magnetic resonance(NMR)logs for oil and gas exploration has grown in popularity over the last few decades.However,most of the time the utilization of the data is limited for evaluating porosity-permeability,distributions and computation of irreducible water saturation.After the advent of fluid substitution methods,NMR T_(2)distributions may now be used to synthesize core equivalent capillary pressure curves.Using fluid substitution workflow,our study introduces a better approach for obtaining capillary pressure curves from the NMR T_(2)distribution.The available core data has been used to calculate calibration parameters for better saturation height modelling.The workflow introduces a novel approach in resistivity independent saturation computation.In the exploratory wells of our study area,computed water saturation derived from the saturation height function exhibits encouraging agreement with resistivity based water saturation from multi-mineral model.The NMR based saturation height modelling approach has been included in study area for the first time so far.
文摘An SIS epidemic model with the standard incidence rate and saturated treatment func- tion is proposed. The dynamics of the system are discussed, and the effect of the capacity for treatment and the recruitment of the population are also studied. We find that the effect of the maximum recovery per unit of time and the recruitment rate of the popula- tion over some level are two factors which lead to the backward bifurcation, and in some cases, the model may undergo the saddle-node bifurcation or Bogdanov-Takens bifurca- tion. It is shown that the disease-free equilibrium is globally asymptotically stable under some conditions, Numerical simulations are consistent with our obtained results in the- orems, which show that improving the efficiency and capacity of treatment is important for control of disease.
文摘A mathematical model describing the epidemic interactions between humans and blackflies in the transmission of onchocerciasis is considered.In this model,the onchocerciasis infected human individuals are divided into two classes of infected humans with high and low microfilarial output incorporating saturated treatment function,which caters for high saturation of onchocerciasis disease.We analyze the model feasible region and obtain the basic reproduction number(R_(hb))using the next generation matrix method.Also,we obtain the onchocerciasis-free and onchocerciasis endemic equilibrium solutions and show that if R_(hb) is less than unity,the onchocerciasis-free equilibrium is locally and globally asymptotically stable.Furthermore,we employed a Lyapunov function to analyze the global asymptotic stability of the onchocerciasis—endemic equilibrium whenever Rhb is greater than unity.In addition,data on mass drug distribution of ivermectin drug to combat onchocerciasis prevalence in Ekiti state of Nigeria were fitted to the model.Graphical results reveal that consistent annual or bi-annual distribution of ivermectin drug in the region is effective in reducing the disease menace.Further simulations also show that public health control measures are needed to minimize infectious contact between humans and blackflies which leads to onchocerciasis infections and visual blindness.
