期刊
出版社
ROYAL SOC
DOI: 10.1098/rspa.2015.0874
关键词
linear systems; non-normal matrices; external perturbations; internal perturbations; stability radius; white-noise perturbations
资金
- TULIP Laboratory of Excellence [ANR-10-LABX-41]
- AnaEE France project [ANR-11-INBS-0001]
- BIOSTASES advanced grant - European Research Council under the European Union [666971]
- European Research Council (ERC) [666971] Funding Source: European Research Council (ERC)
We exhibit a fundamental relationship between measures of dynamical and structural stability of linear dynamical systems-e.g. linearized models in the vicinity of equilibria. We show that dynamical stability, quantified via the response to external perturbations (i.e. perturbation of dynamical variables), coincides with the minimal internal perturbation (i.e. perturbations of interactions between variables) able to render the system unstable. First, by reformulating a result of control theory, we explain that harmonic external perturbations reflect the spectral sensitivity of the Jacobian matrix at the equilibrium, with respect to constant changes of its coefficients. However, for this equivalence to hold, imaginary changes of the Jacobian's coefficients have to be allowed. The connection with dynamical stability is thus lost for real dynamical systems. We show that this issue can be avoided, thus recovering the fundamental link between dynamical and structural stability, by considering stochastic noise as external and internal perturbations. More precisely, we demonstrate that a linear system's response to white-noise perturbations directly reflects the intensity of internal white-noise disturbance that it can accommodate before becoming stochastically unstable.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据