| Abstract: |
| Coupled oscillator systems have been studied in various fields of physical and biological phenomena. Among them, systems of nonlocally coupled oscillators can exhibit chimera states, which consist of spatially coherent and incoherent states. Chimera states have relations to neurological diseases such as epileptic seizures. Recently, several studies of chimera states based on numerical simulation have been reported by Omelchenko et al. However, as far as we know, the stability and bifurcation origin of chimera states have not been understood. Stuart-Landau type nonlinearity enables us to formulate the stability problem of traveling waves precisely through Floquet theory. We analyzed Floquet multiplier and confirmed the transition of stability of traveling wave by changing the parameters of nonlocal coupling. In this study, we will discuss the relationship between the stability of traveling waves and chimera states. |
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