Amplitude death induced by fractional derivatives in nonlinear coupled oscillators

作者：Liu, Q X; Liu, J K; Chen, Y M^*

来源：Communications in Nonlinear Science & Numerical Simulation, 2017, 48: 414-424.

DOI：10.1016/j.cnsns.2017.01.007

• Coupled oscillators
• Fractional derivative
• Amplitude death
• Eigenvalue analysis

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.

• 出版日期2017-7
• 单位中山大学