# gst: twisted state stability under local order parameter adaptation.

<< ️Twisted states commonly arise in nonlocally coupled ring networks. (AA) study the stability of twisted states in networks with higher-order interactions under the adaptive mechanism based on the local order parameter. >>

<< ️The adaptive feedback dynamically regulates the coupling strength and thus reshapes the collective dynamics of the system. Analytical and numerical results show that higher-order adaptivity reduces the linear stability of twisted states, whereas pairwise adaptivity enhances it. Numerical simulations further demonstrate that increasing the exponent of higher-order adaptation drives the system toward more ordered states and correspondingly enlarges the basin of twisted states. >>

<< Moreover, a larger coupling range reduces twisted-state stability, while in random hypergraphs, higher-order adaptivity enlarges the synchronization basin without significantly changing the linear stability. These findings reveal a nonequilibrium relationship between linear stability and basin stability and highlight the important role of adaptive regulation in higher-order network dynamics. >>

Xueqin Wang, Hong He, Wende Tang, et al. Twisted state stability under local order parameter adaptation. Phys. Rev. E 114, 014209. Jul 13, 2026. 

https://journals.aps.org/pre/abstract/10.1103/p2wd-nfbr

Also: network, stability, chimera, order, disorder, fluctuations, random, twist, in https://www.inkgmr.net/kwrds.html 

Keywords: gst, networks, stability, chimera, order, disorder, fluctuations, randomness, synchronization, coupled oscillators, adaptive feedbacks, twisted states, basin stability.