Research paperAmplitude death induced by fractional derivatives in nonlinear coupled oscillators

- Amplitude death is studied for coupled nonlinear oscillators with fractional derivatives.
- The AD region will enlarge due to fractional derivatives.
- AD can arise for much weaker coupling strength, when there is no AD in integer-order systems.
- Similar phenomena happen to the systems with lower frequency.
- The feature is found to be universal for a variety of coupled oscillators.

This paper presents a study on amplitude death in nonlinear coupled oscillators containing fractional derivatives. Analytical criterion for amplitude death region is obtained by eigenvalue analysis and verified by numerical results. It is found that amplitude death regions can be enlarged to a large extent by fractional derivatives. For this reason, amplitude death can be detected in fractional Stuart-Landau systems with weak coupling strength and low frequency, whereas it never appears in integer-order systems. Interestingly, the widening of amplitude death region induced by fractional derivative is shared by a variety of oscillators with different types of coupling mechanisms. An interpretation for the underlying mechanism of this phenomenon is briefly addressed, based on which we further suggest a coupling organization leading to amplitude death only in fractional oscillators.