Autonomous three-dimensional oscillator with five terms: spiking oscillations generation mechanism, microcontroller implementation and controls

Abstract

This paper presents a report on the microcontroller implementation of an autonomous three-dimensional oscillator with five terms (ATDOFT) and performance analysis based on partial and total amplitude controls. ATDOFT displays periodic spiking behaviors, period-tripling bifurcation to chaos, chaotic spiking attractors, coexisting attractors and bistable attractors. ATDOFT is divided into two subsystems; namely the fast and slow subsystems to investigate the mechanism of the spiking dynamics. Relying on the stability analysis based on the fast subsystem with respect to the slow variable, it is shown that the spiking oscillations present in the ATDOFT arise from the system switching between the unstable state and the stable state of the lone equilibrium point of the fast subsystem. By inserting two controller parameters into the rate equations of the ATDOFT, total and partial amplitude controls are achieved. Finally, the dynamical behaviors found in ATDOFT are validated by the microcontroller implementation.