By Ivanka Stamova, Gani Stamov

Using the speculation of impulsive differential equations, this ebook makes a speciality of mathematical types which replicate present examine in biology, inhabitants dynamics, neural networks and economics. The authors give you the simple history from the basic concept and provides a scientific exposition of modern effects with regards to the qualitative research of impulsive mathematical types. inclusive of six chapters, the e-book provides many appropriate innovations, making them on hand in one resource simply available to researchers attracted to mathematical types and their functions. Serving as a helpful reference, this article is addressed to a large viewers of execs, together with mathematicians, utilized researchers and practitioners.

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1. t/ are almost periodic. 2. 3 are met. 10). Proof. 1. 1. The results in this section show that by means of appropriate impulsive perturbations we can control the almost periodic dynamics of these equations. 2 An Impulsive Model of Hematopoiesis In this section the existence and asymptotic stability of a positive almost periodic solution for a nonlinear impulsive delay model of hematopoiesis is investigated. 11) where ˛ > 0; ˇ > 0; ! > 0, n 2 N, has been proposed by Mackey and Glass [216] as an appropriate model of hematopoiesis, which describes the process of production of all types of blood cells generated by a remarkable self-regulated system that is responsive to the demands put upon it.

16) implies that the unique positive almost periodic solution of Eq. 12) is exponentially stable. 3 A More General n-Dimensional Impulsive Biological Model In this section we shall consider a generalization of the models investigated in Sects. 2. t; x/ are continuous real functions, includes many mathematical ecological models. 21) are often affected by possible exterior or interior impulsive effects. Most notably this takes place due to certain infectious diseases, drug therapies, resource availability, food supplies, mating habits, etc.

6. The set of sequences ftk g; tk D tkCj tk ; k; j D ˙1; ˙2; : : :, is uniformly almost periodic if and only if for every sequence of real numbers fs0m g there exists a subsequence fsn g; sn D s0mn , such that T sn D ftk sn g is uniformly convergent for n ! 1 on B. Proof. The proof follows directly from Theorem 1 in [257]. In the investigation of the existence of almost periodic solutions of impulsive models, the question of the separation from the origin of the sequences ftk g 2 B is very important.