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首页> 外文期刊>Physical review, E. Statistical physics, plasmas, fluids, and related interdisciplinary topics >Coupled map lattices as models of deterministic and stochastic differential delay equations
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Coupled map lattices as models of deterministic and stochastic differential delay equations

机译：耦合图格作为确定性和随机微分延迟方程的模型

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摘要

We discuss the probabilistic properties of a class of differential delay equations (DDE's) by first reducing the equations to coupled map lattices, and then considering the spectral properties of the associated transfer operators. The analysis is carried out for the deterministic case and a stochastic case perturbed by additive or multiplicative white noise. This scheme provides an explicit description of the evolution of phase space densities in DDE's, and yields an evolution equation that approximates the analog for delay equations of the generalized Liouville and Fokker-Planck equations. It is shown that in many cases of interest, for both stochastic and deterministic delay equations, the phase space densities reach a limit cycle in the asymptotic regime. This statistical cycling is observed numerically in continuous time systems with delay and discussed in light of our analytical description of the transfer operators.
机译：我们通过首先将方程简化为耦合图格，然后考虑相关传递算符的频谱特性，来讨论一类微分延迟方程（DDE）的概率性质。对确定性情况和随机性情况进行分析，该情况受到加性或乘性白噪声的干扰。该方案提供了DDE相空间密度演化的明确描述，并生成了一个演化方程，该方程近似于广义Liouville和Fokker-Planck方程的延迟方程的模拟。结果表明，在许多感兴趣的情况下，对于随机和确定性延迟方程，在渐近状态下，相空间密度均达到极限环。这种统计循环在连续时间系统中被数字地观察到有延迟，并根据我们对转移算子的分析描述进行了讨论。

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