For high-steep slopes in hydropower engineering, damage can be induced or accumulated due to a seriesof human or natural activities, including excavation, dam construction, earthquake, rainstorm, rapid riseor drop of ...For high-steep slopes in hydropower engineering, damage can be induced or accumulated due to a seriesof human or natural activities, including excavation, dam construction, earthquake, rainstorm, rapid riseor drop of water level in the service lifetime of slopes. According to the concept that the progressivedamage （microseismicity） of rock slope is the essence of the precursor of slope instability, a microseismicmonitoring system for high-steep rock slopes is established. Positioning accuracy of the monitoringsystem is tested by fixed-position blasting method. Based on waveform and cluster analyses of microseismicevents recorded during test, the tempo-spatial distribution of microseismic events is analyzed.The deformation zone in the deep rock masses induced by the microseismic events is preliminarilydelimited. Based on the physical information measured by in situ microseismic monitoring, an evaluationmethod for the dynamic stability of rock slopes is proposed and preliminarily implemented bycombining microseismic monitoring and numerical modeling. Based on the rock mass damage modelobtained by back analysis of microseismic information, the rock mass elements within the microseismicdamage zone are automatically searched by finite element program. Then the stiffness and strengthreductions are performed on these damaged elements accordingly. Attempts are made to establish thecorrelation between microseismic event, strength deterioration and slope dynamic instability, so as toquantitatively evaluate the dynamic stability of slope. The case studies about two practical slopes indicatethat the proposed method can reflect the factor of safety of rock slope more objectively. Numericalanalysis can help to understand the characteristics and modes of the monitored microseismic events inrock slopes. Microseismic monitoring data and simulation results can be used to mutually modify thesensitive rock parameters and calibrate the model. Combination of microseismic monitoring and numericalsimulation provides a more objective basis for the numerical model and parameters and a solidmechanical foundation for the microseismic monitoring.展开更多
Hybrid-driven underwater glider is a new type of tmmanned underwater vehicle, which combines the advantages of autonomous underwater vehicles and traditional underwater gliders. The autonomous underwater vehicles have...Hybrid-driven underwater glider is a new type of tmmanned underwater vehicle, which combines the advantages of autonomous underwater vehicles and traditional underwater gliders. The autonomous underwater vehicles have good maneuverability and can travel with a high speed, while the traditional underwater gliders are highlighted by low power consumption, long voyage, long endurance and good stealth characteristics. The hybrid-driven underwater gliders can realize variable motion profiles by their own buoyancy-driven and propeller propulsion systems. Stability of the mechanical system determines the performance of the system. In this paper, the Petrel-II hybrid-driven underwater glider developed by Tianjin University is selected as the research object and the stability of hybrid-driven underwater glider unitedly controlled by buoyancy and propeller has been targeted and evidenced. The dimensionless equations of the hybrid-driven underwater glider are obtained when the propeller is working. Then, the steady speed and steady glide path angle under steady-state motion have also been achieved. The steady-state operating conditions can be calculated when the hybrid-driven underwater glider reaches the desired steady-state motion. And the steady- state operating conditions are relatively conservative at the lower bound of the velocity range compared with the range of the velocity derived from the method of the composite Lyapunov function. By calculating the hydrodynamic coefficients of the Petrel-II hybrid-driven underwater glider, the simulation analysis has been conducted. In addition, the results of the field trials conducted in the South China Sea and the Danjiangkou Reservoir of China have been presented to illustrate the validity of the analysis and simulations.and to show the feasibility of the method of the composite Lyapunov function which verifies the stability of the Petrel-II hybrid-driven underwater glider.展开更多
The volume of influence of excavation at the right bank slope of Dagangshan Hydropower Station, southwest China, is essentially determined from microseismic monitoring, numerical modeling and conventional measurements...The volume of influence of excavation at the right bank slope of Dagangshan Hydropower Station, southwest China, is essentially determined from microseismic monitoring, numerical modeling and conventional measurements as well as in situ observations. Microseismic monitoring is a new application technique for investigating microcrackings in rock slopes. A micro- seismic monitoring network has been systematically used to monitor rock masses unloading relaxation due to continuous exca- vation of rock slope and stress redistribution caused by dam impoundment later on, and to identify and delineate the potential slippage regions since May, 2010. An important database of seismic source locations is available. The analysis of microseismic events showed a particular tempo-spatial distribution. Seismic events predominantly occurred around the upstream slope of 1180 m elevation, especially focusing on the hanging wall of fault XL316-1. Such phenomenon was interpreted by numerical modeling using RFPA-SRM code （realistic failure process analysis-strength reduction method）. By comparing microseismic activity and results of numerical simulation with in site observation and conventional measurements results, a strong correlation can he obtained between seismic source locations and excavation-induced stress distribution in the working areas. The volume of influence of the rock slope is thus determined. Engineering practices show microseismic monitoring can accurately diagnose magnitude, intensity and associated tempo-spatial characteristics of tectonic activities such as faults and unloading zones. The integrated technique combining seismic monitoring with numerical modeling, as well as in site observation and conventional surveying, leads to a better understanding of the internal effect and relationship between microseismic activity and stress field in the right bank slope from different perspectives.展开更多
The long-term stability of large-span soft rock tunnel is influenced greatly by the creep effect of surrounding rock.The development of a new type of foam concrete which has the property of high compressibility and lo...The long-term stability of large-span soft rock tunnel is influenced greatly by the creep effect of surrounding rock.The development of a new type of foam concrete which has the property of high compressibility and low ductility was introduced.And it was made as filling material of reserved deformation layer between the first lining and the second lining used in large-span soft rock tunnel.The effect of the new type of foam concrete was simulated as filling material of reserved deformation layer using numerical simulation.Through the comparison with the common large-span soft rock tunnel,the vault settlement and surrounding convergence are reduced by about 61% and 45%,respectively,after creep of 100 a.And in the second lining,the plastic zone reduces apparently and the maximum equivalent plastic strain decreases relatively.So,it can be found that the application of the new type of foam concrete as the filling material of reserved deformation layer can relieve the excessive force in second lining induced by rock creep,reduce its deformation and improve the stability of tunnel.展开更多
In order to study the safety factor and instability process of cohesive soil slope, the discrete element method(DEM) was applied. DEM software PFC2 D was used to simulate the triaxial test to study the influence of th...In order to study the safety factor and instability process of cohesive soil slope, the discrete element method(DEM) was applied. DEM software PFC2 D was used to simulate the triaxial test to study the influence of the particle micro parameters on the macroscopic characteristics of cohesive soil and calibrate the micro parameters of DEM model on this basis. Embankment slope stability analysis was carried out by strength reduction and gravity increase method, it is shown that the safety factor obtained by strength reduction method is more conservative, and the arc-shaped feature of the sliding surface under the gravity increase method is more obvious. Throughout the progressive failure process, the failure trends, maximum displacements, and velocity changes obtained by the two methods were consistent. When slope was destroyed, the upper part was cracked, the middle part was sheared, and the lower part was destroyed by extrusion. The conclusions of this paper can be applied to the safety factor calculation of cohesive soil slopes and the analysis of the instability process.展开更多
In underground mining by sublevel caving method, the deformation and damage of the surface induced by subsidence are the major challenging issues. The dynamic and soft backflling body increases the safety risks in the...In underground mining by sublevel caving method, the deformation and damage of the surface induced by subsidence are the major challenging issues. The dynamic and soft backflling body increases the safety risks in the subsiding area. In this paper, taking Zhangfushan iron mine as an example, the ore body and the general layout are focused on the safety of backflling of mined-out area. Then, we use the ANSYS software to construct a three-dimensional(3D) model for the mining area in the Zhangfushan iron mine. According to the simulation results of the initial mining stages, the ore body is stoped step by step as suggested in the design. The stability of the backflling is back analyzed based on the monitored displacements, considering the stress distribution to optimize the stoping sequence. The simulations show that a reasonable stoping sequence can minimize the concentration of high compressive stress and ensure the safety of stoping of the ore body.展开更多
Zhangmu Town in Tibet of China,which lies in the southern piedmont of the median Himalayas,is a small but strategically important port of trade exchange between China and Nepal.Many rockfall events have occurred in Zh...Zhangmu Town in Tibet of China,which lies in the southern piedmont of the median Himalayas,is a small but strategically important port of trade exchange between China and Nepal.Many rockfall events have occurred in Zhangmu since 1970,resulting in huge economic losses and serious influence on the bilateral trade.We conducted a detailed field investigation on the high and steep slope in Zhangmu Town,and analyzed the distribution features,stability,failure modes and evolution of dangerous rocks of potential rockfalls.Then we numerically simulated the movement path,velocity and accumulation forms of the rockfall with PFC^(3D)program.The results indicated that the dangerous rock belt could be divided into three sections,namely,unstable section,slightly stable section and basically stable section.It was estimated that the rock debris and single dangerous rock would be unstable in the case of earthquakes or rainstorms.Due to the terrain constraints,the fallen rocks would scatter near the mouth of the Zhangmu ditch and in the Buqu River through multiple times of rolling,collision-induced diversion and bouncing.Without reinforcement,the rockfall could cause serious damage to the car parks,gas stations and National Highway 318 along the line from Zhangmu Town to Zhangmu ditch.Based on the field survey and numerical simulation,we recommended rockfall removal and interception as the major prevention measures,and protective sheds as auxiliary measure.展开更多
In this paper,we consider the numerical implementation of the 2D wave equation in isotropic-heterogeneous media.The stability analysis of the scheme using the von Neumann stability method has been studied.We conducted...In this paper,we consider the numerical implementation of the 2D wave equation in isotropic-heterogeneous media.The stability analysis of the scheme using the von Neumann stability method has been studied.We conducted a study on modeling the propagation of acoustic waves in a heterogeneous medium and performed numerical simulations in various heterogeneous media at different time steps.Developed parallel code using Compute Unified Device Architecture(CUDA)technology and tested on domains of various sizes.Performance analysis showed that our parallel approach showed significant speedup compared to sequential code on the Central Processing Unit(CPU).The proposed parallel visualization simulator can be an important tool for numerous wave control systems in engineering practice.展开更多
To investigate the strong random nature of the geometric interfaces between soil and rock, a rock-soil slope is considered as a two-phase random medium. A nonlinear translation of a Gaussian field is utilized to simul...To investigate the strong random nature of the geometric interfaces between soil and rock, a rock-soil slope is considered as a two-phase random medium. A nonlinear translation of a Gaussian field is utilized to simulate the two-phase random media, such that the soil(or rock) volume fraction and the inclination of the soil layer can be examined. The finite element method with random media incorporated as the material properties is used to determine the factor of safety of the rock-soil slope. Monte-Carlo simulations are used to estimate the statistical characteristics of the factor of safety. The failure mode of the rock-soil slope is examined by observing the maximum principal plastic strain at incipient slope failure. It is found that the critical surface of a rock-soil slope is fairly irregular, and it significantly differs from that of a pure soil slope. The factor of safety is sensitive to the soil volume faction, but it is predictable. The average factor of safety could be well predicted by the weighted harmonic average between the strength of soil and rock; the prediction model is practical and simple. Parametric studies on the inclination of the soil layer demonstrate that the most instable scenario occurs when the slope angle is consistent with the inclination of the soil layer.展开更多
In this paper, we discuss feedback control of a class of delay chaotic maps. Our aim is to drive the chaotic maps to its initially unstable fixed points by using linear and nonlinear state feedback control. The contro...In this paper, we discuss feedback control of a class of delay chaotic maps. Our aim is to drive the chaotic maps to its initially unstable fixed points by using linear and nonlinear state feedback control. The control is achieved by using small, bounded perturbations. Some numerical simulations are given to demonstrate the effectiveness of the proposed control method.展开更多
In this paper,we investigate the dynamic behaviour of a mathematical model of cancer that includes immune cells,tumor cells,and normal cells,and ex-plore the effects of the introduction of a delayed term of targeted t...In this paper,we investigate the dynamic behaviour of a mathematical model of cancer that includes immune cells,tumor cells,and normal cells,and ex-plore the effects of the introduction of a delayed term of targeted therapy on the model.This model was first proposed by Anusmita Das etal.,numerous studies have attempted to model the interaction between tumours and the im-mune system using deterministic delay differential equations(DDEs)so a de-lay term was added,in this paper,on the basis to make the model more real-istic.Also,the local and global stability of the equilibrium point of the model is analyzed by linearization and Lyapunov method,and the numerical simu-lation of MATLAB is used to verify the analysis results.展开更多
We propose a mathematical model of the coronavirus disease 2019(COVID-19)to investigate the transmission and control mechanism of the disease in the community of Nigeria.Using stability theory of differential equation...We propose a mathematical model of the coronavirus disease 2019(COVID-19)to investigate the transmission and control mechanism of the disease in the community of Nigeria.Using stability theory of differential equations,the qualitative behavior of model is studied.The pandemic indicator represented by basic reproductive number R0 is obtained from the largest eigenvalue of the next-generation matrix.Local as well as global asymptotic stability conditions for the disease-free and pandemic equilibrium are obtained which determines the conditions to stabilize the exponential spread of the disease.Further,we examined this model by using Atangana–Baleanu fractional derivative operator and existence criteria of solution for the operator is established.We consider the data of reported infection cases from April 1,2020,till April 30,2020,and parameterized the model.We have used one of the reliable and efficient method known as iterative Laplace transform to obtain numerical simulations.The impacts of various biological parameters on transmission dynamics of COVID-19 is examined.These results are based on different values of the fractional parameter and serve as a control parameter to identify the significant strategies for the control of the disease.In the end,the obtained results are demonstrated graphically to justify our theoretical findings.展开更多
基金supported by grants from the National Basic Research Program of China (Grant Nos. 2011CB013503, 2014CB047103)the National Natural Science Foundation of China (Grant Nos. 51279024, 51209127)
文摘For high-steep slopes in hydropower engineering, damage can be induced or accumulated due to a seriesof human or natural activities, including excavation, dam construction, earthquake, rainstorm, rapid riseor drop of water level in the service lifetime of slopes. According to the concept that the progressivedamage （microseismicity） of rock slope is the essence of the precursor of slope instability, a microseismicmonitoring system for high-steep rock slopes is established. Positioning accuracy of the monitoringsystem is tested by fixed-position blasting method. Based on waveform and cluster analyses of microseismicevents recorded during test, the tempo-spatial distribution of microseismic events is analyzed.The deformation zone in the deep rock masses induced by the microseismic events is preliminarilydelimited. Based on the physical information measured by in situ microseismic monitoring, an evaluationmethod for the dynamic stability of rock slopes is proposed and preliminarily implemented bycombining microseismic monitoring and numerical modeling. Based on the rock mass damage modelobtained by back analysis of microseismic information, the rock mass elements within the microseismicdamage zone are automatically searched by finite element program. Then the stiffness and strengthreductions are performed on these damaged elements accordingly. Attempts are made to establish thecorrelation between microseismic event, strength deterioration and slope dynamic instability, so as toquantitatively evaluate the dynamic stability of slope. The case studies about two practical slopes indicatethat the proposed method can reflect the factor of safety of rock slope more objectively. Numericalanalysis can help to understand the characteristics and modes of the monitored microseismic events inrock slopes. Microseismic monitoring data and simulation results can be used to mutually modify thesensitive rock parameters and calibrate the model. Combination of microseismic monitoring and numericalsimulation provides a more objective basis for the numerical model and parameters and a solidmechanical foundation for the microseismic monitoring.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51475319 and 51722508)the National Key R&D Plan(Grant No.2016YFC0301100)Aoshan Talents Program of Qingdao National Laboratory for Marine Science and Technology
文摘Hybrid-driven underwater glider is a new type of tmmanned underwater vehicle, which combines the advantages of autonomous underwater vehicles and traditional underwater gliders. The autonomous underwater vehicles have good maneuverability and can travel with a high speed, while the traditional underwater gliders are highlighted by low power consumption, long voyage, long endurance and good stealth characteristics. The hybrid-driven underwater gliders can realize variable motion profiles by their own buoyancy-driven and propeller propulsion systems. Stability of the mechanical system determines the performance of the system. In this paper, the Petrel-II hybrid-driven underwater glider developed by Tianjin University is selected as the research object and the stability of hybrid-driven underwater glider unitedly controlled by buoyancy and propeller has been targeted and evidenced. The dimensionless equations of the hybrid-driven underwater glider are obtained when the propeller is working. Then, the steady speed and steady glide path angle under steady-state motion have also been achieved. The steady-state operating conditions can be calculated when the hybrid-driven underwater glider reaches the desired steady-state motion. And the steady- state operating conditions are relatively conservative at the lower bound of the velocity range compared with the range of the velocity derived from the method of the composite Lyapunov function. By calculating the hydrodynamic coefficients of the Petrel-II hybrid-driven underwater glider, the simulation analysis has been conducted. In addition, the results of the field trials conducted in the South China Sea and the Danjiangkou Reservoir of China have been presented to illustrate the validity of the analysis and simulations.and to show the feasibility of the method of the composite Lyapunov function which verifies the stability of the Petrel-II hybrid-driven underwater glider.
基金supported by the National Natural Science Foundation of China (Nos. 50820125405, 50909013 and 50804006)the National Basic Research Program (973) of China (No. 2007CB209404)
文摘The volume of influence of excavation at the right bank slope of Dagangshan Hydropower Station, southwest China, is essentially determined from microseismic monitoring, numerical modeling and conventional measurements as well as in situ observations. Microseismic monitoring is a new application technique for investigating microcrackings in rock slopes. A micro- seismic monitoring network has been systematically used to monitor rock masses unloading relaxation due to continuous exca- vation of rock slope and stress redistribution caused by dam impoundment later on, and to identify and delineate the potential slippage regions since May, 2010. An important database of seismic source locations is available. The analysis of microseismic events showed a particular tempo-spatial distribution. Seismic events predominantly occurred around the upstream slope of 1180 m elevation, especially focusing on the hanging wall of fault XL316-1. Such phenomenon was interpreted by numerical modeling using RFPA-SRM code （realistic failure process analysis-strength reduction method）. By comparing microseismic activity and results of numerical simulation with in site observation and conventional measurements results, a strong correlation can he obtained between seismic source locations and excavation-induced stress distribution in the working areas. The volume of influence of the rock slope is thus determined. Engineering practices show microseismic monitoring can accurately diagnose magnitude, intensity and associated tempo-spatial characteristics of tectonic activities such as faults and unloading zones. The integrated technique combining seismic monitoring with numerical modeling, as well as in site observation and conventional surveying, leads to a better understanding of the internal effect and relationship between microseismic activity and stress field in the right bank slope from different perspectives.
基金Projects(41072238,51009133)supported by the National Natural Science Foundation of China
文摘The long-term stability of large-span soft rock tunnel is influenced greatly by the creep effect of surrounding rock.The development of a new type of foam concrete which has the property of high compressibility and low ductility was introduced.And it was made as filling material of reserved deformation layer between the first lining and the second lining used in large-span soft rock tunnel.The effect of the new type of foam concrete was simulated as filling material of reserved deformation layer using numerical simulation.Through the comparison with the common large-span soft rock tunnel,the vault settlement and surrounding convergence are reduced by about 61% and 45%,respectively,after creep of 100 a.And in the second lining,the plastic zone reduces apparently and the maximum equivalent plastic strain decreases relatively.So,it can be found that the application of the new type of foam concrete as the filling material of reserved deformation layer can relieve the excessive force in second lining induced by rock creep,reduce its deformation and improve the stability of tunnel.
基金Project(51808116) supported by the National Natural Science Foundation of ChinaProject(BK20180404) supported by the Natural Science Foundation of Jiangsu Province, China+1 种基金Project(KFJ170106) supported by the Changsha University of Science & Technology via Open Fund of National Engineering Laboratory of Highway Maintenance Technology,ChinaProject(242020R40133) supported by Fundamental Research Funds for the Central Universities, China。
文摘In order to study the safety factor and instability process of cohesive soil slope, the discrete element method(DEM) was applied. DEM software PFC2 D was used to simulate the triaxial test to study the influence of the particle micro parameters on the macroscopic characteristics of cohesive soil and calibrate the micro parameters of DEM model on this basis. Embankment slope stability analysis was carried out by strength reduction and gravity increase method, it is shown that the safety factor obtained by strength reduction method is more conservative, and the arc-shaped feature of the sliding surface under the gravity increase method is more obvious. Throughout the progressive failure process, the failure trends, maximum displacements, and velocity changes obtained by the two methods were consistent. When slope was destroyed, the upper part was cracked, the middle part was sheared, and the lower part was destroyed by extrusion. The conclusions of this paper can be applied to the safety factor calculation of cohesive soil slopes and the analysis of the instability process.
文摘In underground mining by sublevel caving method, the deformation and damage of the surface induced by subsidence are the major challenging issues. The dynamic and soft backflling body increases the safety risks in the subsiding area. In this paper, taking Zhangfushan iron mine as an example, the ore body and the general layout are focused on the safety of backflling of mined-out area. Then, we use the ANSYS software to construct a three-dimensional(3D) model for the mining area in the Zhangfushan iron mine. According to the simulation results of the initial mining stages, the ore body is stoped step by step as suggested in the design. The stability of the backflling is back analyzed based on the monitored displacements, considering the stress distribution to optimize the stoping sequence. The simulations show that a reasonable stoping sequence can minimize the concentration of high compressive stress and ensure the safety of stoping of the ore body.
基金the National Key Research and Development Program(Grant No.2019YFC1509704)National Natural Science Foundation of China(Grant No.U1704243)。
文摘Zhangmu Town in Tibet of China,which lies in the southern piedmont of the median Himalayas,is a small but strategically important port of trade exchange between China and Nepal.Many rockfall events have occurred in Zhangmu since 1970,resulting in huge economic losses and serious influence on the bilateral trade.We conducted a detailed field investigation on the high and steep slope in Zhangmu Town,and analyzed the distribution features,stability,failure modes and evolution of dangerous rocks of potential rockfalls.Then we numerically simulated the movement path,velocity and accumulation forms of the rockfall with PFC^(3D)program.The results indicated that the dangerous rock belt could be divided into three sections,namely,unstable section,slightly stable section and basically stable section.It was estimated that the rock debris and single dangerous rock would be unstable in the case of earthquakes or rainstorms.Due to the terrain constraints,the fallen rocks would scatter near the mouth of the Zhangmu ditch and in the Buqu River through multiple times of rolling,collision-induced diversion and bouncing.Without reinforcement,the rockfall could cause serious damage to the car parks,gas stations and National Highway 318 along the line from Zhangmu Town to Zhangmu ditch.Based on the field survey and numerical simulation,we recommended rockfall removal and interception as the major prevention measures,and protective sheds as auxiliary measure.
基金funded by the Committee of Science of the Ministry of Science and Higher Education of the Republic of Kazakhstan(Grants No.AP14972032)NT is also supported by the Beatriu de Pinós programme and by AGAUR(Generalitat de Catalunya)grant 2021 SGR 00087.
文摘In this paper,we consider the numerical implementation of the 2D wave equation in isotropic-heterogeneous media.The stability analysis of the scheme using the von Neumann stability method has been studied.We conducted a study on modeling the propagation of acoustic waves in a heterogeneous medium and performed numerical simulations in various heterogeneous media at different time steps.Developed parallel code using Compute Unified Device Architecture(CUDA)technology and tested on domains of various sizes.Performance analysis showed that our parallel approach showed significant speedup compared to sequential code on the Central Processing Unit(CPU).The proposed parallel visualization simulator can be an important tool for numerous wave control systems in engineering practice.
基金supported by the International Science and Technology Cooperation Programme of Hainan Province,China (Grant No.ZDYF2016226)the National Natural Science Foundation of China(Grant No.51879203)
文摘To investigate the strong random nature of the geometric interfaces between soil and rock, a rock-soil slope is considered as a two-phase random medium. A nonlinear translation of a Gaussian field is utilized to simulate the two-phase random media, such that the soil(or rock) volume fraction and the inclination of the soil layer can be examined. The finite element method with random media incorporated as the material properties is used to determine the factor of safety of the rock-soil slope. Monte-Carlo simulations are used to estimate the statistical characteristics of the factor of safety. The failure mode of the rock-soil slope is examined by observing the maximum principal plastic strain at incipient slope failure. It is found that the critical surface of a rock-soil slope is fairly irregular, and it significantly differs from that of a pure soil slope. The factor of safety is sensitive to the soil volume faction, but it is predictable. The average factor of safety could be well predicted by the weighted harmonic average between the strength of soil and rock; the prediction model is practical and simple. Parametric studies on the inclination of the soil layer demonstrate that the most instable scenario occurs when the slope angle is consistent with the inclination of the soil layer.
基金the National Natural Science Foundation of China.
文摘In this paper, we discuss feedback control of a class of delay chaotic maps. Our aim is to drive the chaotic maps to its initially unstable fixed points by using linear and nonlinear state feedback control. The control is achieved by using small, bounded perturbations. Some numerical simulations are given to demonstrate the effectiveness of the proposed control method.
文摘In this paper,we investigate the dynamic behaviour of a mathematical model of cancer that includes immune cells,tumor cells,and normal cells,and ex-plore the effects of the introduction of a delayed term of targeted therapy on the model.This model was first proposed by Anusmita Das etal.,numerous studies have attempted to model the interaction between tumours and the im-mune system using deterministic delay differential equations(DDEs)so a de-lay term was added,in this paper,on the basis to make the model more real-istic.Also,the local and global stability of the equilibrium point of the model is analyzed by linearization and Lyapunov method,and the numerical simu-lation of MATLAB is used to verify the analysis results.
文摘We propose a mathematical model of the coronavirus disease 2019(COVID-19)to investigate the transmission and control mechanism of the disease in the community of Nigeria.Using stability theory of differential equations,the qualitative behavior of model is studied.The pandemic indicator represented by basic reproductive number R0 is obtained from the largest eigenvalue of the next-generation matrix.Local as well as global asymptotic stability conditions for the disease-free and pandemic equilibrium are obtained which determines the conditions to stabilize the exponential spread of the disease.Further,we examined this model by using Atangana–Baleanu fractional derivative operator and existence criteria of solution for the operator is established.We consider the data of reported infection cases from April 1,2020,till April 30,2020,and parameterized the model.We have used one of the reliable and efficient method known as iterative Laplace transform to obtain numerical simulations.The impacts of various biological parameters on transmission dynamics of COVID-19 is examined.These results are based on different values of the fractional parameter and serve as a control parameter to identify the significant strategies for the control of the disease.In the end,the obtained results are demonstrated graphically to justify our theoretical findings.
