The complex dynamics of the cardiovascular system

Date

2009-12-15

Author

Akhmet, Marat

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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.

Subject Keywords

Blood pressure, The differential equation with impulses, Devaney's ingredients of chaos 6

URI

https://hdl.handle.net/11511/39170

Collections

Department of Mathematics, Article