对机械运动中多自由度线性定常系统的运动稳定性分析有多种方法,但是这些方法不是受到使用条件的限制就是数学分析繁杂。本文利用劳斯-赫尔维茨判据(Routh-Hurw itz C riterion)对机械系统中离心转速调节器的运动稳定性进行了分析,这种...对机械运动中多自由度线性定常系统的运动稳定性分析有多种方法,但是这些方法不是受到使用条件的限制就是数学分析繁杂。本文利用劳斯-赫尔维茨判据(Routh-Hurw itz C riterion)对机械系统中离心转速调节器的运动稳定性进行了分析,这种分析方法的优点就在于:建立系统运动微分方程的特征方程后,不必求解特征方程的根,只需知道根的符号就可判断系统的零解稳定性。结果表明使用Routh-Hurw itz方法分析运动稳定性问题更为简捷,实用。展开更多
Cases of COVID-19 and its variant omicron are raised all across the world.The most lethal form and effect of COVID-19 are the omicron version,which has been reported in tens of thousands of cases daily in numerous nat...Cases of COVID-19 and its variant omicron are raised all across the world.The most lethal form and effect of COVID-19 are the omicron version,which has been reported in tens of thousands of cases daily in numerous nations.Following WHO(World health organization)records on 30 December 2021,the cases of COVID-19 were found to be maximum for which boarding individuals were found 1,524,266,active,recovered,and discharge were found to be 82,402 and 34,258,778,respectively.While there were 160,989 active cases,33,614,434 cured cases,456,386 total deaths,and 605,885,769 total samples tested.So far,1,438,322,742 individuals have been vaccinated.The coronavirus or COVID-19 is inciting panic for several reasons.It is a new virus that has affected the whole world.Scientists have introduced certain ways to prevent the virus.One can lower the danger of infection by reducing the contact rate with other persons.Avoiding crowded places and social events withmany people reduces the chance of one being exposed to the virus.The deadly COVID-19 spreads speedily.It is thought that the upcoming waves of this pandemicwill be evenmore dreadful.Mathematicians have presented severalmathematical models to study the pandemic and predict future dangers.The need of the hour is to restrict the mobility to control the infection from spreading.Moreover,separating affected individuals from healthy people is essential to control the infection.We consider the COVID-19 model in which the population is divided into five compartments.The present model presents the population’s diffusion effects on all susceptible,exposed,infected,isolated,and recovered compartments.The reproductive number,which has a key role in the infectious models,is discussed.The equilibrium points and their stability is presented.For numerical simulations,finite difference(FD)schemes like nonstandard finite difference(NSFD),forward in time central in space(FTCS),and Crank Nicolson(CN)schemes are implemented.Some core characteristics of schemes like stability and consistency are calculated.展开更多
Based on the Routh-Hurwitz criterion, this paper investigates the stability of a new chaotic system. State feedback controllers are designed to control the chaotic system to the unsteady equilibrium points and limit c...Based on the Routh-Hurwitz criterion, this paper investigates the stability of a new chaotic system. State feedback controllers are designed to control the chaotic system to the unsteady equilibrium points and limit cycle. Theoretical analyses give the range of value of control parameters to stabilize the unsteady equilibrium points of the chaotic system and its critical parameter for generating Hopf bifurcation. Certain nP periodic orbits can be stabilized by parameter adjustment. Numerical simulations indicate that the method can effectively guide the system trajectories to unsteady equilibrium points and periodic orbits.展开更多
In this paper, it is shown that for low-order uncertain systems, there is no need to calculate all the minimum and maximum values of the coefficients for a perturbed system which is expressed in terms of polynomials a...In this paper, it is shown that for low-order uncertain systems, there is no need to calculate all the minimum and maximum values of the coefficients for a perturbed system which is expressed in terms of polynomials and hence no need to formulate and test all the four Kharitonov＇s polynomials. Furthermore, for higher-order systems such as n ≥ 5, the usual four Kharitonov＇s polynomials need not be tested initially for sufficient condition of perturbed systems; rather, the necessary condition can be checked before going for sufficient condition. In order to show the effectiveness of the proposed method, numerical examples are shown and computational efficiency is highlighted.展开更多
In this manuscript, Local dynamic behaviors including stability and Hopf bifurcation of a new four-dimensional quadratic autonomous system are studied both analytically and numerically. Determining conditions of equil...In this manuscript, Local dynamic behaviors including stability and Hopf bifurcation of a new four-dimensional quadratic autonomous system are studied both analytically and numerically. Determining conditions of equilibrium points on different parameters are derived. Next, the stability conditions are investigated by using Routh-Hurwitz criterion and bifurcation conditions are investigated by using Hopf bifurcation theory, respectively. It is found that Hopf bifurcation on the initial point is supercritical in this four-dimensional autonomous system. The theoretical results are verified by numerical simulation. Besides, the new four-dimensional autonomous system under the parametric conditions of hyperchaos is studied in detail. It is also found that the system can enter hyperchaos, first through Hopf bifurcation and then through periodic bifurcation.展开更多
This paper presents a criterion for a polynomial to be non-unstable and for the calculation of the number of eigenvalues which have zero real parts and negative real parts.It generalizes the Routh-Hurwitz criterion an...This paper presents a criterion for a polynomial to be non-unstable and for the calculation of the number of eigenvalues which have zero real parts and negative real parts.It generalizes the Routh-Hurwitz criterion and is very convenient in many applications.展开更多
文摘对机械运动中多自由度线性定常系统的运动稳定性分析有多种方法,但是这些方法不是受到使用条件的限制就是数学分析繁杂。本文利用劳斯-赫尔维茨判据(Routh-Hurw itz C riterion)对机械系统中离心转速调节器的运动稳定性进行了分析,这种分析方法的优点就在于:建立系统运动微分方程的特征方程后,不必求解特征方程的根,只需知道根的符号就可判断系统的零解稳定性。结果表明使用Routh-Hurw itz方法分析运动稳定性问题更为简捷,实用。
基金supported by the research grants Seed ProjectPrince Sultan UniversitySaudi Arabia SEED-2022-CHS-100.
文摘Cases of COVID-19 and its variant omicron are raised all across the world.The most lethal form and effect of COVID-19 are the omicron version,which has been reported in tens of thousands of cases daily in numerous nations.Following WHO(World health organization)records on 30 December 2021,the cases of COVID-19 were found to be maximum for which boarding individuals were found 1,524,266,active,recovered,and discharge were found to be 82,402 and 34,258,778,respectively.While there were 160,989 active cases,33,614,434 cured cases,456,386 total deaths,and 605,885,769 total samples tested.So far,1,438,322,742 individuals have been vaccinated.The coronavirus or COVID-19 is inciting panic for several reasons.It is a new virus that has affected the whole world.Scientists have introduced certain ways to prevent the virus.One can lower the danger of infection by reducing the contact rate with other persons.Avoiding crowded places and social events withmany people reduces the chance of one being exposed to the virus.The deadly COVID-19 spreads speedily.It is thought that the upcoming waves of this pandemicwill be evenmore dreadful.Mathematicians have presented severalmathematical models to study the pandemic and predict future dangers.The need of the hour is to restrict the mobility to control the infection from spreading.Moreover,separating affected individuals from healthy people is essential to control the infection.We consider the COVID-19 model in which the population is divided into five compartments.The present model presents the population’s diffusion effects on all susceptible,exposed,infected,isolated,and recovered compartments.The reproductive number,which has a key role in the infectious models,is discussed.The equilibrium points and their stability is presented.For numerical simulations,finite difference(FD)schemes like nonstandard finite difference(NSFD),forward in time central in space(FTCS),and Crank Nicolson(CN)schemes are implemented.Some core characteristics of schemes like stability and consistency are calculated.
基金Project supported by the National Natural Science Foundation of China (Grant No 10672053)
文摘Based on the Routh-Hurwitz criterion, this paper investigates the stability of a new chaotic system. State feedback controllers are designed to control the chaotic system to the unsteady equilibrium points and limit cycle. Theoretical analyses give the range of value of control parameters to stabilize the unsteady equilibrium points of the chaotic system and its critical parameter for generating Hopf bifurcation. Certain nP periodic orbits can be stabilized by parameter adjustment. Numerical simulations indicate that the method can effectively guide the system trajectories to unsteady equilibrium points and periodic orbits.
文摘In this paper, it is shown that for low-order uncertain systems, there is no need to calculate all the minimum and maximum values of the coefficients for a perturbed system which is expressed in terms of polynomials and hence no need to formulate and test all the four Kharitonov＇s polynomials. Furthermore, for higher-order systems such as n ≥ 5, the usual four Kharitonov＇s polynomials need not be tested initially for sufficient condition of perturbed systems; rather, the necessary condition can be checked before going for sufficient condition. In order to show the effectiveness of the proposed method, numerical examples are shown and computational efficiency is highlighted.
文摘In this manuscript, Local dynamic behaviors including stability and Hopf bifurcation of a new four-dimensional quadratic autonomous system are studied both analytically and numerically. Determining conditions of equilibrium points on different parameters are derived. Next, the stability conditions are investigated by using Routh-Hurwitz criterion and bifurcation conditions are investigated by using Hopf bifurcation theory, respectively. It is found that Hopf bifurcation on the initial point is supercritical in this four-dimensional autonomous system. The theoretical results are verified by numerical simulation. Besides, the new four-dimensional autonomous system under the parametric conditions of hyperchaos is studied in detail. It is also found that the system can enter hyperchaos, first through Hopf bifurcation and then through periodic bifurcation.
文摘This paper presents a criterion for a polynomial to be non-unstable and for the calculation of the number of eigenvalues which have zero real parts and negative real parts.It generalizes the Routh-Hurwitz criterion and is very convenient in many applications.
