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

The study presents 1D discrete map (DM) to describe the dynamics of the oscillator with chaotic pulse position modulation. The model circuit has pulse voltage-controlled oscillator and feedback loop with a threshold of pulse rate coding, which performs nonretriggerable monostable multivibrator. 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 feedback unit is a monostable multivibrator with a microcontroller, is implemented. The maximum Lyapunov exponent and the maximum entropy of DM are on the edge of chaos and are close to the well-known Bernoulli shift map, the analogy with which is discussed.