Synchronization in Coupled Duffing Oscillators: Numerical Exploration using Exponential Time Differencing

Ramadian Ridho Illahi; I Wayan Sudiarta; Marzuki Marzuki; Nurul Qomariyah

doi:10.20414/konstan.v10i2.821

Ramadian Ridho Illahi PS Fisika, FMIPA, Universitas Mataram, Mataram, NTB, Indonesia
I Wayan Sudiarta PS Fisika, FMIPA, Universitas Mataram, Mataram, NTB, Indonesia
Marzuki Marzuki PS Fisika, FMIPA, Universitas Mataram, Mataram, NTB, Indonesia
Nurul Qomariyah PS Fisika, FMIPA, Universitas Mataram, Mataram, NTB, Indonesia

DOI: https://doi.org/10.20414/konstan.v10i2.821

Keywords: Coupled Duffing Oscillators, Exponential Time Differencing, Phase Synchronized Chaos, Coupling Strength, Forcing Amplitude

Abstract

The regularity that emerges from the interaction between irregular components is one of the fundamental questions in nonlinear physics. In this study, we examine how two externally driven, coupled Duffing oscillators can achieve synchronization. To analyze the dynamics of this system, we use the second-order Exponential Time Differencing (ETD2) numerical method, which allows us to comprehensively map the parameter space by varying the coupling strength () and the driving force amplitude (). The results show that the synchronization process does not occur simply. The process only appears in a certain synchronization window at weak coupling (). Within this region, the most prominent behavior is Phase Synchronized Chaos, where both oscillators achieve perfect phase locking (Synchronization Index ), but their amplitudes remain chaotic and uncorrelated. We also find that the system is multistable, capable of exhibiting several different final states simultaneously. The boundaries between these basins of attraction are highly complex and exhibit fractal patterns, indicating extreme sensitivity to initial conditions. In other words, even if the system parameters remain constant, the final outcome remains difficult to predict. Overall, these findings provide a comprehensive picture of the dynamics of two coupled Duffing oscillators. The results highlight the balance between external driving forces, coupling strength, and intrinsic chaos that forms the basis for directed synchronization.

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