arXiv subjects

R. Senthamizhan

Publications and source records attributed to R. Senthamizhan.

3 recordsLinked to original sources

arXiv2026

Effect of biharmonic coupling in frequency-weighted Kuramoto oscillators

We investigate the collective dynamics of globally coupled phase oscillators with frequency-weighted biharmonic coupling. Although frequency-weighted and biharmonic extensions of the Kuramoto model have each been studied independently, their combined effect has remained unexplored. By combining numerical branch continuation with analytical stability analysis, we construct the complete phase diagram in the two-parameter coupling plane. The competition between the first- and second-harmonic interactions gives rise to three distinct collective states: the incoherent state (IC), the antipodal multibranch state (APMS), and the symmetry-broken multibranch state (SBMS). These states are separated by three bistable regions and a narrow tristable region in which all three states coexist as stable attractors. The transitions from the incoherent state to both ordered states are discontinuous and hysteretic, reflecting the explosive synchronization induced by frequency weighting, while the transition between the APMS and SBMS is also abrupt. Analytically, we derive the linear instability thresholds of the incoherent state together with the existence and local stability conditions for the SBMS, and show that the theoretical predictions are in good agreement with extensive numerical simulations.

nlin.AO↗

arXiv2025

Swarmalators with frequency-weighted interactions

We investigate the role of frequency-weighted interactions in a solvable model of one-dimensional (1D) swarmalators confined to a ring, where both spatial and phase couplings are scaled by the heterogeneous natural frequencies of individual agents. Our analysis identifies three distinct collective states: the asynchronous state , the phase-wave state , and the bistrip mixed state characterized by antipodal clusters that are internally split into frequency-dependent sub-strips. We further establish that the onset of abrupt transitions are driven by heterogeneous coupling. Using a self-consistency analysis, we precisely determine the conditions for dynamical transitions among the identified states, thereby extending the theoretical understanding of swarmalator dynamics under heterogeneous interaction rules, which are in good agreement with the numerical simulation results.

nlin.AO↗

arXiv2025

Frustration Induced Chimeras and Motion in Two Dimensional Swarmalators

Swarmalators are phase oscillators capable of simultaneous swarming and synchronization, making them potential candidates for replicating complex dynamical states. In this work, we explore the effects of a frustration parameter in the phase interaction functions of a two-dimensional swarmalator model inspired by the solvable Sakaguchi-swarmalators that move in a one-dimensional ring. The impact of the frustration parameter in these models has been a topic of great interest. Real-world coupled systems with frustration exhibit remarkable collective dynamical states, underscoring the relevance of this study. The frustration parameter induces various states exhibiting non-stationarity, chimeric clustering, and global translational motion, where swarmalators move spontaneously in two-dimensional space. We investigate the characteristics of these states and their responses to changes in the frustration parameter. Notably, the emergence of chimeric states suggests the crucial role of non-stationarity in phase interactions for spontaneous population clustering. Additionally, we examine how phase non-stationarity influences the spatial positions of swarmalators and provide a classification of these states based on different order parameters.

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