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We study the collective behaviors in a ring of coupled nonidentical nonlinearoscillators with unidirectional coupling, of which natural frequencies aredistributed in a random way. We find the amplitude death phenomena in the caseof unidirectional couplings and discuss the differences between the cases ofbidirectional and unidirectional couplings. There are three main differences;there exists neither partial amplitude death nor local clustering behavior butoblique line structure which represents directional signal flow on thespatio-temporal patterns in the unidirectional coupling case. Theunidirectional coupling has the advantage of easily obtaining global amplitudedeath in a ring of coupled oscillators with randomly distributed naturalfrequency. Finally, we explain the results using the eigenvalue analysis ofJacobian matrix at the origin and also discuss the transition of dynamicalbehavior coming from connection structure as coupling strength increases.

Amplitude death in a ring of nonidentical nonlinear oscillators with unidirectional coupling