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Abstract

Our universe is a complex system. It is made up of many moving parts as a dynamic, multifaceted machine that works in perfect harmony to create the natural world that allows us life. The modeling of dynamical systems is the key to understanding the complex workings of our universe. One such complexity is chaos: a condition exhibited by an irregular or aperiodic nonlinear deterministic system. Data that is generated by a chaotic mechanism will appear scattered and random, yet can be defined by a system of nonlinear equations. These mathematical equations are characterized by their sensitivity to input values (initial conditions), so that small differences in the starting value will lead to large differences in the outcome. With deterministic chaos, it is nearly impossible to make long-term predictions of results.

A system must have at least three dimensions, and nonlinear characteristics, in order to generate deterministic chaos. When nonlinearity is introduced as a term in a deterministic model, chaos becomes possible. These nonlinear dynamical systems are seen in many aspects of nature and human physiology. This paper will discuss how the distribution of blood throughout the human body, including factors affecting the heart and blood vessels, demonstrate chaotic behavior.

The physiological studies presented in this paper represent some of the investigations into the chaotic systems that can be found in the human body. With modern computing technologies, we are able to identify patterns that were previously thought to be random variations of regular systems, such as the heartbeat. By understanding these systems on a mathematical level, scientists can produce mathematical models of irregular oscillations within the body. Currently, research is being conducted to develop chaos control techniques to treat patients with heart rhythm irregularities. This paper will first introduce chaos theory in a historical context, and then present some of its modern scientific applications.

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