论文信息 - Stability Analysis of Differential Equations with Time-Dependent Delay

Stability Analysis of Differential Equations with Time-Dependent Delay

In this Letter, we study the stability of differential equations with time-dependent delay. Several theorems are established for stability on a finite time interval, called "interval stability" for simplicity, and Liapunov stability. These theorems are applied to the generalized Gauss-type predator–prey models, and satisfactory results are obtained.

[1] Carmen Chicone,et al. Inertial and slow manifolds for delay equations with small delays , 2003 .

[2] Bai Xiao-xuan. Application of the Method of Small Sample in EW Simulation Test , 2005 .

[3] Denis Blackmore,et al. On the exponentially self-regulating population model , 2002 .

[4] Analysis of thermostat models , 1997, European Journal of Applied Mathematics.

[5] Generic oscillations for delay differential equations , 1998 .

[6] Anatoly Swishchuk,et al. Predator-Prey Models , 2003 .

[7] Robert M. May,et al. Time‐Delay Versus Stability in Population Models with Two and Three Trophic Levels , 1973 .

[8] Xianhua Tang,et al. Oscillation of first order delay differential equations with distributed delay , 2004 .

[9] C. Hua. TIME-DEPENDENT BIFURCATION AND DYNAMICAL BEHAVIORS OF THE ABSORPTIVE OPTICAL BISTABILITY EQUATION , 2000 .

[10] S. Ruan,et al. Predator-prey models with delay and prey harvesting , 2001, Journal of mathematical biology.

[11] A. Favini,et al. Degenerate non-stationary differential equations with delay in Banach spaces , 2003 .

[12] K. Gopalsamy. Stability and Oscillations in Delay Differential Equations of Population Dynamics , 1992 .

[13] Qishao Lu,et al. Time-Dependent bifurcation: a New Method and Applications , 2001, Int. J. Bifurc. Chaos.

[14] Delay equations and radiation damping , 2001, gr-qc/0101122.