154.

[Cover] [Abbreviated Contents] [Contents] [Index]

Page 248

		3.1.2— Some Other Nonlinear Tools

		Fractals and chaos are only two tools from a wider class of nonlinear tools now being developed to help us understand systems that have many pieces that interact strongly with each other. Examples of some additional tools are:

		1— Self-Organizing Critical Systems

		These systems are deterministic systems with a large number of independent variables, unlike chaos, which has a small number of independent variables. These systems live just at the border of stability. If pushed over the edge, they relax back to just over the stable border. Thus these systems self-organize to live at the stable-unstable transition. A system poised at such a phase transition is called a critical system. These systems can generate fractals in space and time.

		2— Neural Networks

		These systems consist of nodes that have values and connections between them. At each computational step, the new value of a node depends on the values of the other nodes and on the strengths of the connections between them. Patterns of the values of the nodes are called memories. A set of starting values of the nodes evolve to that of the closest memory. Using rules to change the values of the connection strengths, these systems can learn new memories.

		3— Cellular Automata

		These systems consist of a set of boxes, each of which is in one of a small number of different possible states. At each computational step, a rule determines the new states of the boxes from the states of the surrounding boxes.

		4— Coupled Maps

		In these systems each point of an array is a chaotic system. Each chaotic system evolves in time and interacts with the surrounding chaotic systems.

 

[Cover] [Abbreviated Contents] [Contents] [Index]