计算机代数比较了平均SPDE和原始慢-快SPDE的随机超low流形
Computer algebra compares the stochastic superslow manifold of an averaged SPDE with that of the original slow-fast SPDE
摘要：
这里记录的计算机代数例程使您能够复制和检查一篇关于慢-快随机系统的大偏差的文章中描述的许多细节[abs：1001.4826]。我们考虑一个“小”空间域与两个耦合的浓度场，一个由“慢”反应扩散方程和一个随机的“快”线性方程。在随机分岔的制度，我们得到两个超慢模型的动态：第一个是通过大偏差原则推导出的慢动态的平均模型;第二个是原来的快-慢动态。比较两个超低速模型验证了在该参数范围内的大偏差原则中的平均。
英文摘要：
The computer algebra routines documented here empower you to reproduce and check many of the details described by an article on large deviations for slow-fast stochastic systems [abs:1001.4826]. We consider a 'small' spatial domain with two coupled concentration fields, one governed by a 'slow' reaction-diffusion equation and one governed by a stochastic 'fast' linear equation. In the regime of a stochastic bifurcation, we derive two superslow models of the dynamics: the first is of the averaged model of the slow dynamics derived via large deviation principles; and the second is of the original fast-slow dynamics. Comparing the two superslow models validates the averaging in the large deviation principle in this parameter regime.
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