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In this paper, we study the attracting and invariant sets for a class of nonlinear neutral differential equations with delays. By using the properties of M-matrix, a new delay differential-difference inequality is established. Based on the new inequality, we get the global attracting and invariant sets and the sufficient condition ensuring the exponential stability in Lyapunov sense of nonlinear neutral differential equations with delays. Our results are independent of time delays and do not require the differentiability, boundedness of the derivative of delay functions and the boundedness of activation functions. Two examples are presented to illustrate the effectiveness of our conclusion. © 2012 Long.

Attracting and invariant sets of nonlinear neutral differential equations with delays