Instability in reaction-superdiffusion systems
Instability in reaction-superdiffusion systems
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DOI：
10.1103/physreve.94.052202
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发表时间：
2016-11-01
影响因子：
2.4
通讯作者：
Rezaei, Zahra
中科院分区：
文献类型：
--
作者：
Torabi, Reza;Rezaei, Zahra
研究了超扩散对反应扩散系统不稳定性的影响。结果表明，反应超扩散系统的图灵不稳定性是等价的时间依赖的Ginzburg-Landau模型和相应的自由能的介绍。这种依赖于超扩散指数的广义自由能决定了反应-超扩散系统在图灵分岔附近的稳定性、动力学和涨落。此外，我们表明，对于一般的n-组分反应-超扩散系统，分数复Ginzburg-Landau方程出现的Hopf不稳定性附近的振幅方程。通过对该方程的数值模拟，说明了超扩散对时空模式的影响。最后，研究了反应扩散系统的一种特殊情形---扩散子模型中超扩散对不稳定性的影响。一般来说，超扩散引入了一个新的参数，它改变了系统在不稳定性附近的行为。
We study the effect of superdiffusion on the instability in reaction-diffusion systems. It is shown that reaction-superdiffusion systems close to a Turing instability are equivalent to a time-dependent Ginzburg-Landau model and the corresponding free energy is introduced. This generalized free energy which depends on the superdiffusion exponent governs the stability, dynamics, and the fluctuations of reaction-superdiffusion systems near the Turing bifurcation. In addition, we show that for a general n-component reaction-superdiffusion system, a fractional complex Ginzburg-Landau equation emerges as the amplitude equation near a Hopf instability. Numerical simulations of this equation are carried out to illustrate the effect of superdiffusion on spatiotemporal patterns. Finally, the effect of superdiffusion on the instability in the Brusselator model, as a special case of reaction-diffusion systems, is studied. In general, superdiffusion introduces a new parameter that changes the behavior of the system near the instability.