Chaotic Grid-Scroll Attractors and Multistability in a Pair of Mutually Coupled Third-Order Systems

Abstract

This research delves into simple Jerk-type dynamical networks, constructed using a specific bidirectional coupling scheme that influences the sub-oscillators and compound nonlinearity gradient functions that perturb each sub-unit of the network. The novelty of this work is to demonstrate a new pedagogical method able to stimulate the formation of higher-order multiscroll dynamics in the Jerk sub-oscillator. This is done by modeling a simple dynamic network built by applying a special bidirectional coupling between the Jerk sub-systems. Another novelty of this approach is that it allows us to study the collective dynamics of Jerk system networks, which has not yet been done in the literature. Multiscroll systems are exceedingly complex dynamically, making them valuable in chaos-based applications. The pedagogical approach used in this study is exceptional because it produces many additional equilibrium points (from 5 to 25 in dynamical network 1, and from 3 to 15 in dynamical network 2) in each Jerk sub-unit of the network. These equilibria elevate the complexity of Jerk systems by emulating higher-order multiscroll dynamics. The methodology used in this study is efficient and differs from those used in the literature, which mainly uses nonlinear multizero functions in dissipative systems. This research further explores the dynamic system characterization tools and conducts an experimental investigation on a microcontroller (ATMEGA2560) to confirm the predictions.