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Maximal hysteretic range for explosive synchronization

Author

Listed:
  • Xu, Tianle
  • Guan, Shuguang
  • Liu, Zonghua
  • Zou, Yong

Abstract

Traditionally, phase oscillators on a frequency-degree correlated star network provides a building motif for understanding explosive transitions to synchronization and the associated hysteresis behavior. Here we show that a transition from explosive to continuous synchronization is resulted from the frustration term when implementing αc=π/4 in the Kuramoto-Sakaguchi models on a star. Interestingly, the existence condition for phase locking manifold does not coincide with the backward critical threshold for desynchronization. In addition, the nonlinear effects of the phase shifts are derived analytically, showing a maximal hysteresis range when the frequency-degree correlation is strong enough, i.e., β>βc. On the other hand, the hysteresis range decreases monotonically when β<βc. The maximal hysteresis ranges are not found in other models. Furthermore, numerical results precisely confirm the theoretical predictions. Therefore, the phase shift provides a natural way to control explosive synchronization.

Suggested Citation

  • Xu, Tianle & Guan, Shuguang & Liu, Zonghua & Zou, Yong, 2024. "Maximal hysteretic range for explosive synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:chsofr:v:180:y:2024:i:c:s0960077924000067
    DOI: 10.1016/j.chaos.2024.114455
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