CMOS circuits generating arbitrary chaos by using pulsewidth modulation techniques

This paper describes CMOS circuits generating arbitrary chaotic signals. Th e proposed circuits implement discrete-time continuous-state dynamics by me ans of analog processing in a time domain, Arbitrary nonlinear transformati on functions can be generated by using the conversion from an analog voltag e to a pulsewidth modulation (PWM) signal; for the transformation, time-dom ain nonlinear voltage waveforms having the same shape as the inverse functi on of the desired transformation function are used. The circuit simultaneou sly outputs both voltage and PWM signals following the desired dynamics. If the nonlinear voltage waveforms are generated by digital circuits and D/A converters with low-pass filters, high flexibility and controllability are obtained, Moreover, the nonlinear dynamics can be changed in realtime, Comm on waveform generators can be shared by many independent chaos generator ci rcuits, Because the proposed circuits mainly consist of capacitors, switche s, and CMOS logic gates, they are suitable for scaled VLSI implementation. CMOS circuits generating arbitrary chaos with up to third-order nonlinearit y and two variables have been designed and fabricated using a 0.4 mum CMOS process. Chaos has been successfully generated by using tent, logistic, and Henon maps, and a chaotic neuron model.