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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

WIDESPREAD PHENOMENON. “The appreciation that a simple equation, such as eq. 1, can produce extremely irregular behavior has profound implications: it suggests that despite the very complex behavior that is typical of most physical and biological phenomena, they may yet be governed by a simple set of rules.” https://lnkd.in/d9T6yEgv View in LinkedIn

MINUTIAE AMPLIFIED. “The "butterfly effect" is so-named because one can imagine that even a butterfly flapping its wings could create enough of a disturbance in the initial conditions of a chaotic weather system to cause a completely (different weather pattern to evolve over time, perhaps generating a hurricane that would not have occurred otherwise.” https://lnkd.in/d9T6yEgv View in LinkedIn

CONSEQUENCES. “When the initial value of xO was changed from 0.2000000 (solid line) to 0.2000001 (dashed line), the curves remained virtually superimposed for the first 20 iterations of eq 1, but then rapidly diverged and evolved completely different behavior. This extreme sensitivity to initial conditions, in which small differences diverge exponentially, is a feature that characterizes all chaotic systems.” https://lnkd.in/d9T6yEgv View in LinkedIn

TINY VARIANCE. “The system evolved over time in an irregular chaotic pattern. If he used a slightly different value for the initial conditions of the same equations, by changing one part in a million, the system initially behaved in a similar manner; however, after time, it started to diverge and evolved a completely different pattern.” https://lnkd.in/d9T6yEgv View in LinkedIn

LORENZ’S MODEL. “Using a relatively simple set of nonlinear differential equations to simulate atmospheric weather changes, he assigned a set of initial conditions and computed the subsequent behavior of the system.” https://lnkd.in/d9T6yEgv View in LinkedIn

500 year old history intact underfoot in the 2,000 year old city of Girona. View in LinkedIn