Eigenvalue-matching renormalization-group analysis of tricritical behavior in unidirectionally coupled maps

초록

We study the scaling behavior in two unidirectionally coupled one-dimensional maps near tricritical points which lie at ends of Feigenbaum critical lines and near edges of the complicated parts of the boundary of chaos. Note that both period-doubling cascades to chaos and multistability (associated with saddle-node bifurcations) occur in any neighborhood of the tricritical point. For this tricritical case, the response subsystem exhibits a type of non-Feigenbaum codimension-2 scaling behavior, while the drive subsystem is in a periodic state. To analyze the tricritical behavior, we develop an eigenvalue-matching renormalization-group (RG) method and obtain the scaling factors. These RG results agree well with those of previous work.

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