International Research Journal of Engineering and Technology (IRJET)
e-ISSN: 2395-0056
Volume: 12 Issue: 05 | May 2025
p-ISSN: 2395-0072
www.irjet.net
Short Communication
Spreadsheet-Based Coupling for Synchronization of the Henon and Logistic Maps Aditya Krishan Goel The Shri Ram School Aravali, Haryana. India -------------------------------------------------------------------***-------------------------------------------------------------------Abstract - This paper presents a coupling design to give the targeted synchronization in parameter mismatched chaotic
discrete dynamical systems via spreadsheet software. We propose an open-plus-closed-loop (OPCL) type design for which a suitable stability criterion is derived. We demonstrate the proposed coupling design using the 1D logistic map and 2D Henon map. Detailed spreadsheet implementation with formulas and tables is provided to facilitate practical implementation of chaotic synchronization without requiring specialized hardware or software tools.
Keywords – Dynamical Systems Theory, Difference and Functional Equations, Numerical Analysis, Optimization, Mathematical Applications
Introduction
Coupled chaotic oscillators can often model many dynamical systems and help understand coherent behaviors associated with them. Depending upon the nature of the problem under consideration, either continuous or discrete dynamical systems are used as individual oscillators for investigation. In this paper, we focus on discrete maps as they are straightforward to implement in spreadsheet software. Research on synchronization in coupled chaotic dynamical systems has increased significantly in the last few years because of its significance in several fields such as encryption, information theory, signal processing, ecology, climatology, sociology, and power systems. Various types of synchronization are complete synchronization (CS), phase synchronization (PS), anti-phase synchronization (APS), lag synchronization (LS), generalized synchronization (GS), and anti-synchronization (AS). Designing coupling methods have been suggested for achieving a specific type of synchronization. The primary distinction of such coupling design is that it begins with no a priori information about the coupling function. The coupling is formulated on a general stability criterion to aim towards a desired coherent state in target dynamical systems. We use spreadsheet software here to implement synchronization among coupled chaotic maps based solely on the coupling theory. We adopt an open-plus-closed-loop (OPCL) type coupling strategy as an approach toward the target synchronization.
THEORY OF COUPLING We describe the theory using an n-dimensional map as given by (1) which drives another identical map, (2) to achieve a goal , where is a real matrix, stands for parameter(s), and denotes the iteration number. Note that there is mismatch in the parameters of the systems (1) and (2), which is denoted by the term . The response system with the coupling term is given by
© 2025, IRJET
|
Impact Factor value: 8.315
|
ISO 9001:2008 Certified Journal
|
Page 1196