Abstract
A merging of two coe;'isting phase·locked chaotic attractorsinto one phase·unlocked chaotic attractor occurs in the region where two Arnold tongues overlap each other. This merging is studied in terms of a weighted average A(q), (00 q > qp is dominated by the normal orbits with A equal to a positive Liapunov exponent A k , (k=l, 2). A theory of the q·phase transitions is proposed. Just after the merging, the phase·unlocked attract or has a singular local structure,and A(q) exhibits a new discontinuous transition from Al to A2 at q=q,=l.O due to the intermittent hopping motions between two repellers with A' Al and A' A z. These features of the attractors just before and after the merging are quite universal and can be summarized in terms of linear parts of the expansion-rate spectrum h(il).
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