Similar Master Stability Functions for Different Coupling Schemes in Basic Chaotic Systems

Zahra Dayani, Fatemeh Parastesh∗ and Sajad Jafari†,‡
Department of Biomedical Engineering,
Amirkabir University of Technology (Tehran Polytechnic), Iran
∗Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai, India
†Health Technology Research Institute,
Amirkabir University of Technology (Tehran Polytechnic), Iran
‡sajadjafari83@gmail.com

Eckehard Scholl
Institut f¨ur Theoretische Physik, Technische Universit¨at Berlin,
Hardenbergstrasse 36, 10623 Berlin, Germany
Bernstein Center for Computational Neuroscience Berlin,
Humboldt-Universit¨at, 10115 Berlin, Germany
Potsdam Institute for Climate Impact Research,
Telegrafenberg A 31, 14473 Potsdam, Germany

Jurgen Kurths
Potsdam Institute for Climate Impact Research,
Telegrafenberg A 31, 14473 Potsdam, Germany
Department of Physics, Humboldt University Berlin,
Berlin 12489, Germany

Julien Clinton Sprott
Department of Physics, University of Wisconsin–Madison,
Madison, WI 53706, USA

Received July 18, 2023

Synchronization is a prominent phenomenon in coupled chaotic systems. The master stability function (MSF) is an approach that offers the prerequisites for the stability of complete synchronization, which is dependent on the coupling configuration. In this paper, some basic chaotic systems with the general form of the Sprott-A, Sprott-B, Sprott-D, Sprott-F, Sprott-G, Sprott-O, and Jerk systems are considered. For each system, their parametric form is designed, and constraints required to have similar MSFs in different coupling schemes are determined. Then, the parameters of the designed chaotic systems are found through an exhaustive computer search seeking chaotic solutions. The simplest cases found in this way are introduced, and similar synchronization patterns are confirmed numerically.