The paper examines in depth two approaches, namely the describing function and Tsypkin methods, for predicting the autonomous behaviour of simple nonlinear feedback systems. Both procedures are supported by software which, in the case of the describing function method, allows iteration to the exact limit cycle solution and, for both methods, enables display of resulting limit cycle waveforms. One advantage of the Tsypkin method, which is applicable primarily to relay systems, is that the exact stability of the limit cycle solution can be found. It is shown how this may be helpful in indicating the possibility of chaotic motion. Several examples are given to show the advantages and limitations of the software implementations of the methods.

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