Descalzi Orazio, Cartes Carlos, Cisternas Jaime, Brand Helmut R
Complex Systems Group, Facultad de Ingeniería y Ciencias Aplicadas, Universidad de los Andes, Av. San Carlos de Apoquindo 2200, Santiago, Chile.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 May;83(5 Pt 2):056214. doi: 10.1103/PhysRevE.83.056214. Epub 2011 May 25.
We investigate the route to exploding dissipative solitons in the complex cubic-quintic Ginzburg-Landau equation, as the bifurcation parameter, the distance from linear onset, is increased. We find for a large class of initial conditions the sequence: stationary localized solutions, oscillatory localized solutions with one frequency, oscillatory localized solutions with two frequencies, and exploding localized solutions. The transition between localized solutions with one and with two frequencies, respectively, is analyzed in detail. It is found to correspond to a forward Hopf bifurcation for these localized solutions as the bifurcation parameter is increased. In addition, we make use of power spectra to characterize all time-dependent states. On the basis of all information available, we conclude that the sequence oscillatory localized solutions with one frequency, oscillatory localized solutions with two frequencies, and exploding dissipative solitons can be interpreted as the analog of the Ruelle-Takens-Newhouse route to chaos for spatially localized solutions.
我们研究了在复立方 - 五次金兹堡 - 朗道方程中，作为分岔参数（即与线性起始点的距离）增加时，通向爆炸耗散孤子的路径。我们发现，对于一大类初始条件，存在这样的序列：静态局域解、单频振荡局域解、双频振荡局域解以及爆炸局域解。我们详细分析了单频局域解和双频局域解之间的转变。结果发现，随着分岔参数的增加，这些局域解的转变对应于正向霍普夫分岔。此外，我们利用功率谱来表征所有随时间变化的状态。基于所有可得信息，我们得出结论：单频振荡局域解、双频振荡局域解以及爆炸耗散孤子的序列可以被解释为空间局域解通向混沌的鲁埃勒 - 塔肯斯 - 纽豪斯路径的类似物。
