Type-I intermittency route to chaos in a saturable ring-cavity-retarded differential difference system

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Abstract
The saturable ring cavity driven by a retarded feedback is studied as an example of a retarded differential-difference device. A method is proposed to find the relevant Floquet multipliers. A first-return map is also analyzed. Both studies lead us to claim that the system exhibits a type-I intermittency route to chaos in a case of strong absorption. The numerical calculation of the correlation functions of the intermittent signal shows that the laminar-regime mean duration (T) behaves as |1n ε|, where e is the small increment of the control parameter above the threshold value. This unexpected law for type-I intermittency is explained by a special spiraling injection process into the laminar regime, which arises from the joint action of several Floquet multipliers.