What is "nonlinear science"?

Nonlinear science is one of a number of emerging methodological and theoretical constructs that make up what is often called the "science of complexity." The popular name for this new science is "chaos theory." The chaos referred to in the theory is not a lack of organization or order but is, instead, a complex state in which apparant randomness of a system is really constrained by a type of order that is nonlinear.

What is the aim of nonlinear science?

The aim of nonlinear science is a richer description of the complexity of phenomena, not prediction and control in the usual sense. It lends itself to the exploration of multidimensional interactions within and among individuals, families and communities.

What are the critical principles of nonlinear science?

The critical principles of this new science are as follows:
 

    * Nonlinear systems can, under certain conditions, display highly chaotic behavior.
    * The behavior of a chaotic system can change drastically in response to small changes in the system's initial conditions.
    * A chaotic system is deterministic.
    * System output is not proportionate to system input.

What is meant by "iteration?"

Iteration is the terminology used to describe how a nonlinear system moves through time. It refers to a process of continuously feeding the results from a system of equations back into the system itself.

What is an "attractor?"

Roughly speaking, an attractor is what the behavior of a system settles down to or that to which it is attracted. The attractor forms the limits of the pattern of the system. Imagine that you are taking the pulse, blood pressure and temperature of a person every hour, and you want to graph the relationships among all three vital signs as they change over time. You would construct a graph that was marked at the center by the intersection of three axes, one for each of the vital signs. Connecting these points in temporal sequence forms a trajectory. In nonlinear science, this trajectory is referred to as an attractor.

What is the "butterfly effect?"

The butterfly effect is a term used to describe the principles of nonlinearity and sensitivity to initial conditions, which hold that a nonlinear equation can have solutions that are irregular. The irregularity results in small changes being amplified by the nonlinear nature of the system. This means that if the initial state of the nonlinear system is changed only slightly, one cannot predict the difference in how each system will evolve over time. One often-cited example of the effects of nonlinearity and sensitivity to initial conditions was given by the meterologist, Ed Lorenz. He explained, mathematically, why predicting the weather with precision is impossible. Lorenz demonstrated that two virtually identical weather systems will behave differently over time due to their complex, nonlinear nature and due to inputs from the environment that are infinitely small. He suggested, somewhat tongue-in-cheek, that even the flapping wings of a butterfly could result in a tornado because of nonlinear processes at work even with the smallest factors causing the weather.

What is a "fractal?"

Fractals are structural, geometric concepts that apply to a wide class of complex shapes that are irregular but have an underlying pattern. A key feature of a fractal pattern is self-similarity.

What is "self-similarity?"

Features of a structure or process are self-similar when they look alike at different scales of magnification or length of time.

Why is nonlinear science important to nursing and other disciplines?

Few systems with which researchers work could truly be called linear. If a system is linear, outputs of that system will be in proportion to inputs. Second, if a system is linear, two trajectories at nearby points in phase space would evolve in close proximity. Whether studying physiologic responses of individuals or health problems of entire communities, researchers are faced with understanding apparently nonlinear systems in which very small inputs can result in disproportionately large outputs. In addition, research challenges scientists to describe and explain phenomena that seem to evolve very differently in apparently similar systems. In other words, we ask, "Why would a health care intervention for two essentially equivalent clients result in such different outcomes?" or "Why is a particular type of service effective in one community and ineffective in another when the two seem to be demographically indistinguishable?"