This paper give the algebraic criteria for all delay stability of two dimensional degenerate differential systems with delays and give two examples to illustrate the use of them.
According to the three-dimensional geometry of the engagement,the explicit algebraic expression of differential geometric guidance command(DGGC)is proposed.Compared with the existing solutions,the algebraic solution i...According to the three-dimensional geometry of the engagement,the explicit algebraic expression of differential geometric guidance command(DGGC)is proposed.Compared with the existing solutions,the algebraic solution is much simpler and better for the further research of the characteristics of DGGC.Time delay control(TDC)is a useful method to tackle the uncertainty problem of a control system.Based on TDC,taking the target maneuvering acceleration as a disturbance,the estimation algorithm of the target maneuvering acceleration is presented,which can be introduced in DGGC to improve its performance.Then,the augmented DGGC(ADGGC)is obtained.The numerical simulation of intercepting a high maneuvering target is conducted to demonstrate the effectiveness of ADGGC.展开更多
A differential-algebraic prey--predator model with time delay and Allee effect on the growth of the prey population is investigated. Using differential-algebraic system theory, we transform the prey predator model int...A differential-algebraic prey--predator model with time delay and Allee effect on the growth of the prey population is investigated. Using differential-algebraic system theory, we transform the prey predator model into its normal form and study its dynamics in terms of local analysis and Hopf bifurcation. By analyzing the associated characteristic equation, it is observed that the model undergoes a Hopf bifurcation at some critical value of time delay. In particular, we study the direction of Hopf bifurcation and the stability of bifurcated periodic solutions, and an explicit algorithm is given by applying the normal form theory and the center manifold reduction for functional differential equations. Finally, numerical simulations supporting the theoretical analysis are also included.展开更多
文摘This paper give the algebraic criteria for all delay stability of two dimensional degenerate differential systems with delays and give two examples to illustrate the use of them.
基金supported by the National Natural Science Foundation of China(Grant Nos.11272346)the National Basic Research Program of China("973"Project)(Grant No.2013CB733100)
文摘According to the three-dimensional geometry of the engagement,the explicit algebraic expression of differential geometric guidance command(DGGC)is proposed.Compared with the existing solutions,the algebraic solution is much simpler and better for the further research of the characteristics of DGGC.Time delay control(TDC)is a useful method to tackle the uncertainty problem of a control system.Based on TDC,taking the target maneuvering acceleration as a disturbance,the estimation algorithm of the target maneuvering acceleration is presented,which can be introduced in DGGC to improve its performance.Then,the augmented DGGC(ADGGC)is obtained.The numerical simulation of intercepting a high maneuvering target is conducted to demonstrate the effectiveness of ADGGC.
基金This work was supported by National Science Foundation of China 61273008 and 61203001, Doctor Startup Fund of Liaoning Province （20131026）, Fundamental Research Funds for the Central University （N140504005） and China Scholarship Council. The authors gratefully thank referees for their valuable suggestions.
文摘A differential-algebraic prey--predator model with time delay and Allee effect on the growth of the prey population is investigated. Using differential-algebraic system theory, we transform the prey predator model into its normal form and study its dynamics in terms of local analysis and Hopf bifurcation. By analyzing the associated characteristic equation, it is observed that the model undergoes a Hopf bifurcation at some critical value of time delay. In particular, we study the direction of Hopf bifurcation and the stability of bifurcated periodic solutions, and an explicit algorithm is given by applying the normal form theory and the center manifold reduction for functional differential equations. Finally, numerical simulations supporting the theoretical analysis are also included.
