CMOS circuits generating arbitrary chaos by using pulsewidth modulation techniques

This paper describes CMOS circuits generating arbitrary chaotic signals. The proposed circuits implement discrete-time continuous-state dynamics by means of analog processing in a time domain. Arbitrary nonlinear transformation functions can be generated by using the conversion from an analog voltage to a pulsewidth modulation (PWM) signal; for the transformation, time-domain nonlinear voltage waveforms having the same shape as the inverse function of the desired transformation function are used. The circuit simultaneously 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 real time. Common waveform generators can be shared by many independent chaos generator circuits. Because the proposed circuits mainly consist of capacitors, switches, and CMOS logic gates, they are suitable for scaled VLSI implementation. CMOS circuits generating arbitrary chaos with up to third-order nonlinearity and two variables have been designed and fabricated using a 0.4 μm CMOS process. Chaos has been successfully generated by using tent, logistic, and Henon maps, and a chaotic neuron model