Stability analysis of one-dimensional dynamical systems applied to an isolated beating heart

Fruchter, Gila E.; Ben‐Haim, Shlomo A.

doi:10.1016/s0022-5193(05)80340-6

Cited by 8 publications

(3 citation statements)

References 16 publications

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“…In this figure the region showed that it contains the attractive fixed point of the function f 2 (z,α) and these points are non-zero, belonged to in the region is specified as M={α∈C and β∈N: and the O(Z 0 ) is bounded under f(z,α,β)} and the Set M contains all complex number α in which |α|≤(β+1)((1/β+1))/β. Now, let's compare our results of the works in [27,29] and let's find that easy and direct since it depends on visualization technique and gives a quick judge on the function whiteout need to go the derivative direction.…”

Section: Discussion Of the Research Results Of Logistic Function Analysis And Its Behaviormentioning

confidence: 99%

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Development of mandelbrot set for the logistic map with two parameters in the complex plane

Ahmed

Abbas

Khamees

et al. 2021

EEJET

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In this paper, the study of the dynamical behavior of logistic map has been disused with representing fractals graphics of map, the logistic map depends on two parameters and works in the complex plane, the map defined by f(z,α,β)=αz(1–z)β. where and are complex numbers, and β is a positive integers number, the visualization method used in this work to generate fractals of the map and to inspect the relation between the value of β and the shape of the map, this visualization analysis showed also that, as the value of β increasing, as the number of humps in the function also increasing, and it demonstrate that is true also for the function’s first iteration , f2(x0)=f(f(x0)) and the second iteration , f3(x0)=f(f2(x0)), beside that , the visualization technique showed that the number of humps in that fractal is less than the ones in the second iteration of the original function ,the study of the critical points and their properties of the logistic map also discussed it, whereas finding the fixed point led to find the critical point of the function f, in addition , it haven proven for the set of all pointsα∈C and β∈N, the iteration function f(f(z) has an attractive fixed points, and belongs to the region specified by the disc |1–β(α–1)|<1. Also, The discussion of the Mandelbrot set of the function defined by the f(f(z)) examined in complex plans using the path principle, such that the path of the critical point z=z0 is restricted, finally, it has proven that the Mandelbrot set f(z,α,β) contains all the attractive fixed points and all the complex numbers in which α≤(1/β+1) (1/β+1) and the region containing the attractive fixed points for f2(z,α,β) was identified

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Section: Discussion Of the Research Results Of Logistic Function Analysis And Its Behaviormentioning

confidence: 99%

“…Definition 1 [29]. A one-dimensional dynamical system is a pair (I, f) where f is a function f: I→I, and I is a subset of R nearly permanently, the interval I will be a subinterval of R, that contains the probability I=R.…”

Section: Methodsmentioning

confidence: 99%

Development of mandelbrot set for the logistic map with two parameters in the complex plane

Ahmed

Abbas

Khamees

et al. 2021

EEJET

View full text Add to dashboard Cite

show abstract

“…In this model, the heart is reduced, as in [6], to the left ventricle (LV) pump, with the mitral and aortic valves; the vascular system is represented by an elastic chamber (reservoir) with a constant compliance C and a rigid tube of a constant resistance R. (See Table 1. ) Let un' Xn, and Yn be the venous return volume, the end-diastolic volume, and the stroke volume at the nth beat, respectively.…”

Section: Model Developmentmentioning

confidence: 99%