The complex dynamics of the cardiovascular system


NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, vol.71, no.12, 2009 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 71 Issue: 12
  • Publication Date: 2009
  • Doi Number: 10.1016/


In our paper, we consider the dynamics of blood pressure, initiated in [M.U. Akhmet, G.A. Bekmukhambetova, A prototype compartmental model of blood pressure distribution, Nonlinear Anal. RWA (in press)], concentrating on the interaction between systemic arterial pressure and periphery blood pressure. A system of impulsive differential equations is applied as a model. The main result of the present paper is the existence of Devaney's chaos ingredients: sensitivity of solutions, transitivity, and existence of infinitely many periodic solutions, in the case, when the moments of discontinuity are defined as a special initial value problem. The method of creating a chaos [M.U. Akhmet, Dynamical synthesis of the quasi-minimal set, Internat. J. Bifur. Chaos (in press); M.U. Akhmet, Devaney's chaos in a relay system, Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 1486-1493; M.U. Akhmet, Li-Yorke chaos in the system with impacts, J. Math. Anal. Appl. 351 (2009) 804-810] is applied. Appropriate examples are provided, including a simulation of the chaotic attractor. (C) 2009 Elsevier Ltd. All rights reserved.