Observation of chaotic and strange nonchaotic attractors in a simple multi-scroll system

Abstract

The dynamics of third-order chaotic circuit with threshold controller as a nonlinear element is reported. The circuit and the preliminary result reported by Chithra et al. (J Comput Electron 16:883---889, 2017), are considered as a prototype by adding quasiperiodic force in the original circuit. This present work focuses attention on exhibiting all possible nonlinear dynamical phenomena (i.e., periodic motion, chaotic, strange nonchaotic and multi-scroll attractor) for a different set of circuit parametric values. The approach helps in proof-of-experimental concept to implement all possible complex dynamical behaviors from a single circuit. Further, we also place emphasis on numerical simulation and physical circuit realization on the breadboard. The existence of strange nonchaotic attractor is quantitatively confirmed by calculating $${ 0}{-}{} { 1}$$0-1 test and singular-continuous spectrum analysis. We then find this circuit has potential to produce multi-scroll strange nonchaotic attractor by increasing threshold values. The experimental results are identical to numerical simulations.