Chaotic Bursts in Nonlinear Dynamical Systems

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Science  16 Jan 1987:
Vol. 235, Issue 4786, pp. 342-345
DOI: 10.1126/science.235.4786.342


Several elementary nonlinear dynamical systems in the complex plane may provide models for abrupt transitions to chaotic dynamics. In particular, the complex trigonometric and exponential functions explode into chaos as a parameter is varied. Numerical evidence is presented that supports the contention that these explosions occur whenever an elementary bifurcation occurs. This numerical evidence, in the form of computer graphics, is an example of the increasing importance of experimentation in mathematics research.