https://doi.org/10.1140/epjp/s13360-023-04558-1
Regular Article
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
1
Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai, India
2
Department of Physics, Faculty of sciences, University of Dschang, Dschang, Cameroon
3
Tashkent University of Information Technology, Tashkent, Uzbekistan
4
Unité de Recherche d’Automatique et Informatique Appliquée (UR-AIA), Department of Electrical Engineering, IUT-FV Bandjoun, P.O. Box 134, Bandjoun, Cameroon
5
Department of Electronics and Communication Engineering, Venu Institute of Technology, Chittoor, India
6
Center for Nonlinear Systems, Chennai Institute of Technology, Chennai, India
7
Department of Electronics and Communications Engineering and University Center for Research and Development, Chandigarh University, 140 413, Mohali, Punjab, India
Received:
25
July
2023
Accepted:
4
October
2023
Published online:
16
October
2023
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.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
