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		2.1.5— Definition of Chaos

		Chaos: Complex output that mimics random behavior that is generated by a simple, deterministic system.

		1— A Chaotic System Is Deterministic

		The present values of the variables depend entirely on their recent, previous values. There is no element of chance. This is called a dynamical system. Some dynamical systems are chaotic and some are not chaotic.

		Mathematically, dynamical systems are represented by difference or differential equations. These equations consist of a set of variables. The new values of the variables are computed from the previous values of the variables. In difference equations, time advances in discrete steps. The new values of the variables are computed from the values of the variables at earlier time steps. In differential equations, time advances continuously. The new values of the variables are computed from the values of the variables and their rate of change at earlier moments in time.

		2— A Chaotic System Has Only a Small Number of Independent Variables

		The equations that describe how the present values of the variables are computed from their previous values have only a small number of independent variables.

		3— The Output of a Chaotic System Is Very Complex

		The data that are generated by a chaotic system are so complex that they mimic the data generated by a system based on chance.

 

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