Chaotic discrete map of pulse oscillator dynamics with threshold nonlinear rate coding

Abstract

Abstract The study presents 1D discrete map (DM) to describe the dynamics of the oscillator with chaotic pulse position modulation (PPM). The model circuit has pulse voltage-controlled oscillator (PVCO) and feedback (FB) loop with a threshold of pulse rate coding, which performs non-retriggerable monostable multivibrator (MMV). DM is based on the analysis of this circuit using a simple approximation of the frequency modulation, which includes a threshold condition on the pulse period and sigmoid function of rate coding. The model circuit and DM demonstrate dynamic chaos in a wide range of control parameters. The transition to the chaos occurs by a jump either from a fixed point (tangent bifurcation), or from a limit cycle. An experimental (digital-analog) circuit of the chaotic pulse oscillator, in which the FB unit is MMV with a microcontroller (MC), is implemented. The relationship between the presented DM and the well-known sawtooth (Bernoulli) map (STM), widely used in engineering, is discussed.