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SIMPLE BUT NONLINEAR. “But despite the irregularity in the values of successive points, the relationship between one point and the next is always very simple, though nonlinear.” https://lnkd.in/d9T6yEgv View in LinkedIn

THE FORMULA. “When the data in Fig. 1 are plotted in this manner, known as a Poincare plot, a very simple relationship becomes apparent (Fig.2). In this example, the relationship is simply the curve described by the equation for a parabola: " "Xn = aXnI (1 -Xn-l) (Equation 1).” https://lnkd.in/d9T6yEgv View in LinkedIn

PHYSIOLOGIC CHAOS. “Any clinical state in which a key physiological parameter, e.g., blood pressure, hormone levels, immunological responses, etc., is shown to be chaotic is potentially amenable to control by introducing small, critically timed perturbations based on this technique.” https://lnkd.in/d9T6yEgv View in LinkedIn

FAILURE OF REDUCTIONISM. “The approach, however, has remarkable success of this reductionist approach, however, has limitations when one tries to reassemble the whole from the individual components to predict behavior in a system as complex as a biological organ. This s especially true when the interactions between the components are nonlinear and the potential for chaos exists.” https://lnkd.in/d9T6yEgv View in LinkedIn

STANDARD APPROACH. “Biomedical research has traditionally focused on analyzing the behavior of an organ system by breaking it down into individual components and studying these in increasing detail.” https://lnkd.in/d9T6yEgv View in LinkedIn

ARRHYTHMIA EXAMPLE. “We adapted chaos control theory for its first biological application, the chaotic cardiac arrhythmia described below.” https://lnkd.in/d9T6yEgv View in LinkedIn

BIOLOGICAL APPLICATIONS. “The method has now been applied successfully to several physical and chemical systems. It also has been speculated that chaos control may be a physiologic mechanism of information processing by the brain.” https://lnkd.in/d9T6yEgv View in LinkedIn

HEURISTIC MODEL. “Recently, however, a new technique has been developed that focuses on controlling, rather than eliminating, chaos. This method does not require detained knowledge of the system, but only the ability to observe the chaotic behavior in real time and to apply brief small perturbations to the system.” https://lnkd.in/d9T6yEgv View in LinkedIn