93.

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		2.4.7— Biological Implications of Bifurcations

		1— Small Changes in Parameters Can Make Large Changes in Behavior

		We are used to thinking that small changes in parameters must produce similarly small changes in the behavior of a system. This intuition is based on our experience with linear systems. This behavior is not necessarily true for nonlinear systems.

		The behavior of a nonlinear system can change dramatically when there is only a small change in the value of a parameter. Such an abrupt change is called a bifurcation.

		Biological experiments with similar experimental parameters can sometimes produce markedly different results. Biological effects do not always depend smoothly on the values of the experimental parameters. For example, the biological effects of electromagnetic radiation occur within a set of distinct "windows" in the amplitude and frequency parameters of the radiation applied.

		Perhaps some of these results arise from the sudden change of behavior when there are small changes in the values of the parameters that characterize bifurcations in nonlinear systems.

		2— Bifurcation Sequence to Evaluate Determinism

		A biological system can be confirmed to be deterministic if the bifurcation sequence predicted by a deterministic mathematical model of the system matches the bifurcation sequence that is experimentally observed.

		3— Bifurcation Sequence Versus Phase Space Set

		The bifurcation sequence is a qualitative set of behavior changes that may be easier to identify in an experimental system than determining the fractal dimension of the phase space set. Moreover, varying one parameter in an experiment means that the system can serve as its own control.

		However, determining the bifurcation sequence requires a good mathematical model of a system that is not needed to use the phase space set analysis.

 

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