Pub. date: 2008 | Online Pub. Date: April 25, 2008 | DOI: 10.4135/9781412963893 | Print ISBN: 9781412958783 | Online ISBN: 9781412963893| Publisher:SAGE Publications, Inc.About this encyclopedia
NONLINEAR DYNAMICAL SYSTEMS that have sensitive dependence on initial conditions may exhibit chaotic behavior. In other words, if initial conditions are available only with some finite precision, two solutions starting from undistinguishable initial conditions (i.e., whose difference is smaller than the precision) can exhibit completely different future evolutions after time. Thus, the system behavior is unpredictable. Sensitive dependence on initial conditions can occur even in deterministic systems whose solutions are not influenced by any stochastic effects. Chaos theory attempts to find an underlying order in such chaotic behavior In the early 1900s, H. Poincaré noticed that simple nonlinear deterministic systems can behave in a chaotic fashion. While studying the three-body problem in celestial mechanics, he found that the evolution of three planets could be complex and sensitive to their relative initial positions. Other early pioneers in chaotic dynamics from a mathematical viewpoint include G. Birkhoff, M.T. Cartright, J.E. Littlewood, S. ...