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A simple chaotic system with a single nonquadratic term is developed to be a switchable chaotic signal generator in this paper. Additional nonlinearity of the absolute value function is introduced for reforming the structure without damaging the basic dynamics but yielding a new independent amplitude–frequency controller. A switchable chaotic experimental oscillator is designed afterwards, where two coefficients corresponding to two independent rheostats rescale the amplitude and frequency of the chaotic signals smoothly. To our knowledge, this has never been found in other chaotic oscillators.