Multiscroll in Bidirectionally Coupled Jerk Oscillators: Theoretical Analysis and PSpice Verification

Abstract

It is known that the unidirectional coupling between a double-scroll system (drive) in the oscillation regime with another system (response) in the steady-state, gives rise to more complex dynamics such as multiscroll attractors [Dana et al., 2008]. This paper shows the way to move from n-scroll to 2n-scroll in a bidirectional coupling scheme between two jerk oscillators. The coupling considered can be interpreted as a perturbation to each oscillator’s amplitude through a signal proportional to the amplitude of the other. Indeed, starting from a situation of two oscillators which can generate double-scroll dynamics individually, we perform a bidirectional coupling of both oscillators which results in more complex dynamics such as multistability and 4-scroll chaotic attractor in the coupled system (not observed in an isolated oscillator). The underlined coupling scheme provides an efficient method for generating higher-order multiscroll attractors. The route to the 4-scroll chaotic attractor is explained with the help of bifurcation diagrams, plots of several phase portraits, and basins of attractions. Indirect validation of the theoretical analysis is carried out by using the PSpice simulation software.