A physically intuitive, highly symmetric coupling of two van der Pol oscillators is considered here. The structure of the equilibrium points and the discrete symmetries of the model equations are discussed. For some combinations of the parameters, infinitely many equilibrium points appear and evidence is presented pointing to the existence of infinite periodic trajectories. A complete characterization of the dynamics is done on three specific cases, as a function of the coupling parameters. It is found that several attractors coexist in phase space, either having the symmetry of the model equations or appearing in pairs that restore such symmetry. The possibility that the asymptotic dynamics is different in the coexisting symmetric and asymmetric attractors is investigated, along with their creation or destruction, splitting, and merging, when a control parameter is varied. The presence of several attractors allows the points in phase space to change Rom one basin to another when a control parameter is changed. The route to chaos is through period doubling when only one attractor is explored. When oscillators lock onto an ordered behavior, the period and amplitude surfaces are computed as a function of the (two) coupling parameters and compared with those periods and amplitudes for the corresponding unperturbed oscillators. PACS number(s): 05.45.+b, 42.65.Vh

The classical modeling approach for laser study relies on the differential equations. In this paper, a cellular automaton model is proposed as an alternative for the simulation of population dynamics. Even though the model is simplified it captures the essence of laser phenomenology: (i) there is a threshold pumping rate that depends inversely on the decaying lifetime of the atoms and the photons; and (ii) depending on these lifetimes and on the pumping rate, a constant or an oscillatory behavior can be observed. More complex behaviors such as spiking and pattern formation can also be studied with the cellular automaton model.

Irregular and nonrepetitive transverse intensity distributions were measured in the near field during the gain-switch pulse (60-ns width) of a transversely excited atmospheric CO(2) laser. Transverse patterns are regular and repetitive in the long-pulse (1-micros width) mode and in ensemble average in the short-pulse mode, and in both cases symmetry is imposed by the boundary conditions. Short-pulse transverse patterns formed by lasing domains appear with a mean size of 0.8 mm. The prediction of domain size based on a model of population inversion filamentation agrees with the experimental result.

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