There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works conc...There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works concern with system which includes more than two terms. In this paper, system which includes four nonlinear terms are studies. We obtain the global asymptotic stability of zero solution, and discard the condition which require the Liapunov function trends to infinity, and only require that the positive orbit is bounded.展开更多
The concept of edge polynomials with variable length is introduced. Stability of such polynomials is analyzed. Under the condition that one extreme of the edge is stable, the stability radius of edge polynomials with ...The concept of edge polynomials with variable length is introduced. Stability of such polynomials is analyzed. Under the condition that one extreme of the edge is stable, the stability radius of edge polynomials with variable length is characterized in terms of the real spectral radius of the matrix H -1 ( f 0) H (g) , where both H (f 0) and H (g) are Hurwitz like matrices. Based on this result, stability radius of control systems with interval type plants and first order controllers are determined.展开更多
Two dimensional parabolic stability equations (PSE) are numerically solved using expansions in orthogonal functions in the normal direction.The Chebyshev polynomials approximation,which is a very useful form of ortho...Two dimensional parabolic stability equations (PSE) are numerically solved using expansions in orthogonal functions in the normal direction.The Chebyshev polynomials approximation,which is a very useful form of orthogonal expansions, is applied to solving parabolic stability equations. It is shown that results of great accuracy are effectively obtained.The availability of using Chebyshev approximations in parabolic stability equations is confirmed.展开更多
The performances of a well-known GHR car-following model was investigated by using numerical simulations in describing the acceleration and deceleration process induced by the motion of a leading car. It is shown that...The performances of a well-known GHR car-following model was investigated by using numerical simulations in describing the acceleration and deceleration process induced by the motion of a leading car. It is shown that in GHR model vehicle is allowed to run arbitrarily close together if their speed are identical,and it waves aside even though the separation is larger than its desired distance. Based on these investigations, a modified GHR model which features a new nonlinear term which attempts to adjust the inter-vehicle spacing to a certain desired value was proposed accordingly to overcome these deficiencies. In addition, the analysis of the additive nonlinear term and steady-state flow of the new model were studied to prove its rationality.展开更多
Using the theory of polynomials,this paper gives a new necessary and sufficient condition for a polynomial to be Hurwitz polynomial,a simple proof of the stability criterion of Liénard and Chipart is also obtained.
Background:Athletes have been shown to exhibit better balance compared to non-athletes(NON).However,few studies have investigated how the surface on which athletes train affects the strategies adopted to maintain bala...Background:Athletes have been shown to exhibit better balance compared to non-athletes(NON).However,few studies have investigated how the surface on which athletes train affects the strategies adopted to maintain balance.Two distinct athlete groups who experience different types of sport-specific balance training are stable surface athletes(SSA) such as basketball players and those who train on unstable surfaces(USA) such as surfers.The purpose of this study was to investigate the effects of training surface on dynamic balance in athletes compared to NON.Methods:Eight NON,eight SSA,and eight USA performed five 20-s trials in each of five experimental conditions including a static condition and four dynamic conditions in which the support surface translated in the anteroposterior(AP) or mediolateral(ML) planes using positive or negative feedback paradigms.Approximate entropy(Ap En) and root mean square distance(RMS) of the center of pressure(Co P) were calculated for the AP and ML directions.Four 3 × 5(group × condition) repeated measures ANOVAs were used to determine significant effects of group and condition on variables of interest.Results:USA exhibited smaller Ap En values than SSA in the AP signals while no significant differences were observed in the ML Co P signals.Generally,the negative feedback conditions were associated with significantly greater RMS values than the positive feedback conditions.Conclusion:USA exhibit unique postural strategies compared to SSA.These unique strategies seemingly exhibit a direction-specific attribute and may be associated with divergent motor control strategies.展开更多
文摘There are many works on the asymptotic stability of second dimensional nonlinear differential equation. In particular, these results only concern with the system which includes one or two terms, whereas few works concern with system which includes more than two terms. In this paper, system which includes four nonlinear terms are studies. We obtain the global asymptotic stability of zero solution, and discard the condition which require the Liapunov function trends to infinity, and only require that the positive orbit is bounded.
文摘The concept of edge polynomials with variable length is introduced. Stability of such polynomials is analyzed. Under the condition that one extreme of the edge is stable, the stability radius of edge polynomials with variable length is characterized in terms of the real spectral radius of the matrix H -1 ( f 0) H (g) , where both H (f 0) and H (g) are Hurwitz like matrices. Based on this result, stability radius of control systems with interval type plants and first order controllers are determined.
文摘Two dimensional parabolic stability equations (PSE) are numerically solved using expansions in orthogonal functions in the normal direction.The Chebyshev polynomials approximation,which is a very useful form of orthogonal expansions, is applied to solving parabolic stability equations. It is shown that results of great accuracy are effectively obtained.The availability of using Chebyshev approximations in parabolic stability equations is confirmed.
基金Key Foundation Project of Shanghai (No.032912066)
文摘The performances of a well-known GHR car-following model was investigated by using numerical simulations in describing the acceleration and deceleration process induced by the motion of a leading car. It is shown that in GHR model vehicle is allowed to run arbitrarily close together if their speed are identical,and it waves aside even though the separation is larger than its desired distance. Based on these investigations, a modified GHR model which features a new nonlinear term which attempts to adjust the inter-vehicle spacing to a certain desired value was proposed accordingly to overcome these deficiencies. In addition, the analysis of the additive nonlinear term and steady-state flow of the new model were studied to prove its rationality.
文摘Using the theory of polynomials,this paper gives a new necessary and sufficient condition for a polynomial to be Hurwitz polynomial,a simple proof of the stability criterion of Liénard and Chipart is also obtained.
文摘Background:Athletes have been shown to exhibit better balance compared to non-athletes(NON).However,few studies have investigated how the surface on which athletes train affects the strategies adopted to maintain balance.Two distinct athlete groups who experience different types of sport-specific balance training are stable surface athletes(SSA) such as basketball players and those who train on unstable surfaces(USA) such as surfers.The purpose of this study was to investigate the effects of training surface on dynamic balance in athletes compared to NON.Methods:Eight NON,eight SSA,and eight USA performed five 20-s trials in each of five experimental conditions including a static condition and four dynamic conditions in which the support surface translated in the anteroposterior(AP) or mediolateral(ML) planes using positive or negative feedback paradigms.Approximate entropy(Ap En) and root mean square distance(RMS) of the center of pressure(Co P) were calculated for the AP and ML directions.Four 3 × 5(group × condition) repeated measures ANOVAs were used to determine significant effects of group and condition on variables of interest.Results:USA exhibited smaller Ap En values than SSA in the AP signals while no significant differences were observed in the ML Co P signals.Generally,the negative feedback conditions were associated with significantly greater RMS values than the positive feedback conditions.Conclusion:USA exhibit unique postural strategies compared to SSA.These unique strategies seemingly exhibit a direction-specific attribute and may be associated with divergent motor control strategies.
