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Random Noninstantaneous Impulsive Models for Studying Periodic Evolution Processes in Pharmacotherapy

  • JinRong Wang
  • Michal FečkanEmail author
  • Yong Zhou
Chapter
Part of the Nonlinear Systems and Complexity book series (NSCH, volume 14)

Abstract

In this chapter we offer a new class of impulsive models for studying the dynamics of periodic evolution processes in pharmacotherapy, which is given by random, noninstantaneous, impulsive, nonautonomous periodic evolution equations. This type of impulsive equation can describe the injection of drugs in the bloodstream, and the consequent absorption of them in the body is a random, periodic, gradual, and continuous process. Sufficient conditions on the existence of periodic and subharmonic solutions are established, as are other related results such as their globally asymptotic stability. The dynamical properties are also derived for the whole system, leading to the theory of fractals. Finally, examples are given to illustrate our theoretical results.

Notes

Acknowledgements

The first author acknowledges the support of the National Natural Science Foundation of China (11201091) and the Outstanding Scientific and Technological Innovation Talent Award of the Education Department of Guizhou Province [2014]240. The second author acknowledges the support of grants VEGA-MS 1/0071/14 and VEGA-SAV 2/0029/13. The third author acknowledges the support of the National Natural Science Foundation of China (11271309), the Specialized Research Fund for the Doctoral Program of Higher Education (20114301110001), and Key Projects of Hunan Provincial Natural Science Foundation of China (12JJ2001).

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of MathematicsGuizhou UniversityGuizhouPeople’s Republic of China
  2. 2.Department of Mathematical Analysis and Numerical MathematicsComenius University in BratislavaBratislavaSlovakia
  3. 3.Mathematical Institute of Slovak Academy of SciencesBratislavaSlovakia
  4. 4.Department of MathematicsXiangtan UniversityXiangtanPeople’s Republic of China

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