Hyperchaotic multiscroll dynamics, complex behavior in a simple homogeneous dynamical network of jerk oscillators: bidirectional coupling scheme method, dynamical study, analog circuit and microcontroller-based implementation

• Published in: European physical journal plus Vol. 138; no. 10; p. 918
• Main Authors: Ramakrishnan, Balamurali, Mekak-Egong, Hermann-Dior, Rakhmatullaeva, M. F., Jacques, Kengne, Rajagopal, Karthikeyan
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 16.10.2023; Springer Nature B.V
• Subjects: Analog circuits; Applied and Technical Physics; Atomic; Behavior; Bifurcation theory; Complex Systems; Condensed Matter Physics; Coupling; Data acquisition; Dynamical systems; Dynamics; Equilibrium; Liapunov exponents; Mathematical and Computational Physics; Microcontrollers; Molecular; Optical and Plasma Physics; Oscillators; Physics; Physics and Astronomy; Regular Article; Subsystems; Theoretical
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/s13360-023-04558-1

Network dynamics is the subject of a great deal of scientific research these days. Its scope is not only restricted to the study of the collective dynamic behavior of the internal subunits of a network or the interaction of connected systems with their neighbors, but it is also applicable to some of today's cutting-edge technologies, and helps us to understand the complex phenomena that define the world around us. In this study, a new simple dynamical network is constructed from a special bidirectional coupling between three jerk oscillators. The jerk oscillator has been widely studied in the literature, but little is known about the collective dynamics described by networks of jerk systems linked by a special bidirectional coupling scheme. The used coupling scheme is special in the sense that it favors the creation of twenty-seven additional equilibrium points in each subunit of the network. This extra point induces new complex behaviors in each subsystem of the network, in particular multiscroll behaviors, which have an extraordinary dynamic richness and are applicable to chaos-based technologies. However, as the methods used in the literature to generate multiscroll dynamics are not very explanatory, the special coupling scheme highlighted in this work constitutes a new method for generating multiscroll behavior in a system. New complex phenomena are understood through theoretical and numerical study, including symmetry, stability of equilibrium points, bifurcation diagrams, phase portraits, multistability, basins of attraction, coexisting bifurcation branches, one- and two-parameter diagrams, maximum Lyapunov exponent diagram and Lyapunov exponent spectrum to show the hyperchaotic aspect. Furthermore, as in most chaos-based applications, digital or analog implementation is an unavoidable exercise, we explored a practical realization of the new dynamical network using two different techniques: an analog circuit-based implementation with PSpice simulations and a microcontroller-based implementation, followed by a data acquisition module. These implementations validate the different results obtained numerically.