RESUMEN

We study the phase reduction of two coupled van der Pol oscillators with asymmetric repulsive coupling under an external harmonic force. We show that the system of two phase oscillators undergoes a Hopf bifurcation and possesses multistability on a 2π-periodic phase plane. We describe the bifurcation mechanisms of formation of multistability in the phase-reduced system and show that the Andronov-Hopf bifurcation in the phase-reduced system is not an artifact of the reduction approach but, indeed, has its prototype in the nonreduced system. The bifurcational mechanisms presented in the paper enable one to describe synchronization effects in a wide class of interacting systems with repulsive coupling e.g., genetic oscillators.

RESUMEN

Although the fugu Takifugu rubripes has attracted attention as a model organism for genomic studies because of its compact genome, it is not generally appreciated that there are approximately 25 closely related species with limited distributions in the waters of East Asia. We performed molecular phylogenetic analyses and constructed a time tree using whole mitochondrial genome sequences from 15 Takifugu species together with 10 outgroups to examine patterns of diversification. The resultant time tree showed that the modern Takifugu species underwent explosive speciation during the Pliocene 1.8-5.3 Ma, which is comparable with that of the Malawi cichlids and tropheine cichlids in Lake Tanganyika. Considering their limited distributions and remarkable variations in coloration, morphology, and behavior, the results of the present study strongly suggest that Takifugu species are strong candidates as a model system for evolutionary studies of speciation mechanisms in marine environments where few such organisms are available.

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RESUMEN

The statistics of a subcritical spatially homogeneous XY spin system driven by dichotomous Markov noise as an external field is investigated, particularly focusing on the switching process of the sign of the order parameter parallel to the external field. The switching process is classified in two types, which are called the Bloch-type switching and the Ising-type switching, according to whether or not the order parameter perpendicular to the external field takes finite value at the switching. The phase diagram for the onset of the switching process with respect to the amplitude of the external field and the anisotropy parameter of the system is constructed. It is revealed that the power spectral density I(omega) for the time series of the order parameter in the case of the Bloch-type switching is proportional to omega(-32) in an intermediate region of omega. Furthermore, the scaling function of I(omega) near the onset point of the Bloch-type switching is derived.

RESUMEN

The domain dynamics of magnetization obeying the time-dependent Ginzburg-Landau equation driven by a dichotomous Markov noise is discussed. The system with various domain sizes in the early stage temporally evolves following an annihilation of neighboring domain walls, where each domain wall moves diffusively. Three statistics on the domain size, i.e., average domain size, the ensemble average of the domain size distribution function, and the spatial power spectrum of the magnetization, are evaluated to characterize the domain wall annihilation process. A phenomenological evolution equation for the domain-size distribution function is constructed by simplifying the annihilation process of the domain wall appropriately, and the underlying mechanism of those statistics is investigated.

RESUMEN

Based on the complex Ginzburg-Landau equation (CGLE), a new mapping model of oscillatory media is proposed. The present dynamics is fully determined by an effective phase field renormalized by amplitude. The model exhibits phase turbulence, amplitude turbulence, and a frozen state reported in the CGLE. In addition, we find a state in which the phase and amplitude have spiral structures with opposite rotational directions. This state is found to be observed also in the CGLE. Thus, one concludes that the behaviors observed in the CGLE can be described by only the phase dynamics appropriately constructed.