CC.11 Chaos

ESSENTIAL TO KNOW

• Some interactions in natural systems are linear (or almost linear over the range of values present in the environment), but many are nonlinear because the components do not vary in direct proportion to each other. For example, doubling the food supply may cause the population of an animal species to double if food is scarce, but it may result in little change in population if food is already abundant.
• Linear systems are predictable. If we increase one parameter (e.g., the available food supply), the system will adjust to equilibrium (the population will rise to a new stable value that is related in direct proportion to the new food supply).
• Nonlinear systems behave unpredictably. Changing one parameter may lead to a new equilibrium (which may be drastically different from the original system) or may cause the system to oscillate in a chaotic way.
• Complex nonlinear systems with many interactions are chaotic and unpredictable, but they tend to oscillate irregularly within an identifiable range of conditions. For example, weather is inherently unpredictable, but climate (range and average conditions) does not generally change from year to year.
• Complex nonlinear systems may respond to unusual changes in one or more parameters by “jumping” to oscillate around a different set of average conditions.
• Natural systems include many interactions, at least some of which are nonlinear. The Earth, atmosphere, and ocean processes are therefore chaotic.
• Because natural systems are chaotic, their exact state cannot ever be forecast (predicted) accurately. These systems are inherently variable, and they may undergo sudden changes to new average conditions.