On the Existence and Exponential Attractivity of a Unique Positive Almost Periodic Solution to an Impulsive Hematopoiesis Model with Delays

Abstract

Abstract. In this paper, a generalized model of hematopoiesis with delays and impulses is considered. By employing the contraction mapping principle and a novel type of impulsive delay inequality, we prove the existence of a unique positive almost periodic solution of the model. It is also proved that, under the proposed conditions in this paper, the unique positive almost periodic solution is globally exponentially attractive. A numerical example is given to illustrate the effectiveness of the obtained results.Hematopoiesis model; almost periodic solution; impulsive systems.

Exponential Stability of Non-Autonomous Neural Networks with Heterogeneous Time-Varying Delays and Destabilizing Impulses

“…As mentioned in Remark 2, and by similar approach proposed in [1], it can be verified that, for given φ, ψ ∈ C([−τ, 0], R n ), system (11) has a unique solutionẑ(t) on [−τ, ∞). Since M 1 = −D +ÂF is a Metzler matrix and M 2 = B + G ≥ 0, (11) is a positive system [34].…”

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