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Global stability of a class of delay differential systems. (English) Zbl 1189.34145
The author establishes new criteria for global stability of a positive equilibrium of a class of systems of delay differential equations, without considering the derivative of the Lyapunov functional employed in the investigation. The results obtained are applicable to some practical problems in population dynamics and ecology. Examples are given to illustrate the usefulness and effectiveness of the new results.

MSC:
34K20 Stability theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations
34K21 Stationary solutions of functional-differential equations
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[1] Smith, H.L., Monotone dynamical systems, () · Zbl 1162.39009
[2] Wright, E.M., A non-linear difference-differential equation, J. reine angew. math., 194, 66-87, (1955) · Zbl 0064.34203
[3] Yorke, J.A., Asymptotic stability for one dimensional delay-differential equations, J. differential equations, 7, 189-202, (1970) · Zbl 0184.12401
[4] So, J.W.-H.; Yu, J.S., Global stability for a general population model with time delays, (), 447-457 · Zbl 0921.34068
[5] Faria, T.; Liz, E.; Oliveira, J.J.; Trofimchuk, S., On a generalized Yorke condition for scalar delayed population models, Discrete contin. dyn. syst., 12, 3, 481-500, (2005) · Zbl 1074.34069
[6] Gyori, I., A new approach to the global stability problem in a delay lotka – volterra differential equation, Math. comput. modelling, 31, 9-28, (2000) · Zbl 1042.34571
[7] Takeuchia, Yasuhiro; Wangb, Wendi; Saitoa, Yasuhisa, Global stability of population models with patch structure, Nonlinear anal.: real world appl., 7, 235-247, (2006) · Zbl 1085.92053
[8] Gyori, I.; Trofimchuk, S., Global attractivity in \(x^\prime(t) = - \delta x(t) + p f(x(t - \tau))\), Dynam. systems appl., 8, 197-210, (1999) · Zbl 0965.34064
[9] Faria, T., Asymptotic stability for delayed logistic type equations, Math. comput. modelling, 43, 433-445, (2006) · Zbl 1145.34043
[10] Smith, H.L., Monotone semiflows generated by functional differential equations, J. differential equations, 66, 420-442, (1987) · Zbl 0612.34067
[11] Gopalsamy, K., Stability and oscillation in delay differential equations of population dynamics, (1992), Kluwer Academic Publishers Dordrecht · Zbl 0752.34039
[12] Yi, T.S.; Huang, L.H., Convergence for pseudo monotone semiflows on product ordered topological spaces, J. differential equations, 214, 429-456, (2005) · Zbl 1066.37016
[13] Wu, J., ()
[14] Saker, S.H., Oscillation of continuous and discrete diffusive delay nicholson’s blowflies models, Appl. math. comput., 167, 179-197, (2005) · Zbl 1075.92051
[15] Lia, J.; Du, C., Existence of positive periodic solutions for a generalized nicholson’s blowflies model, J. comput. appl. math., 221, 226-233, (2008) · Zbl 1147.92031
[16] Yi, T.S.; Zou, X., Global attractivity of the diffusive Nicholson blowflies equation with Neumann boundary condition: A non-monotone case, J. differential equations, 245, 11, 3376-3388, (2008) · Zbl 1152.35511
[17] Hale, J.K.; Verduyn Lunel, S.M., Introduction to functional differential equations, (1993), Springer-Verlag New York · Zbl 0787.34002
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