Images of nonlinearity

INTRODUCTION Recent research has shown that many simple nonlinear deterministic systems can behave in an apparently unpredictable and chaotic manner [ I-5 ]. For some value of a system parameter, only a nonchaotic attracting orbit (set of points) occurs, whereas, at some other value of the parameter, a chaotic attractor (strange attractor) occurs. Linear interconnection between the nonlinearities usually changes the nature of the attractors. Graphical representations o f this fact are illustrated in Figs. I and 2. REFERENCES 1. J. P. Crutchfield, J. D. Farmer, N. H. Packard and R. Shaw, Chaos. Scientific American 255 ( 6 ), 46-57 ( 1986 ). 2. A. K. Dcwdney, Computer recreations: Probing the strange attractions of chaos. Scientific American 257 ( l ), 108-111 (1987). 3. C. Grebogi, E. ot t and J. A. York¢, Chaos, strange attractors, and fractal basin boundaries in nonlinear dynamics. Science 238, 632-638 (1987). 4. Hao Bai-Lin, Chaos, World Scientific Publishing ( 1984 ). 5. R. May, Simple mathematical models with very complicated dynamics. Nature 261, 459--467 (1976).