Perfect adaptation of general nonlinear systems
Su Wei
AbstractPerfect adaptation describes the ability of a biological system to restore its biological function precisely to the pre-perturbation level after being affected by the environmental disturbances. Mathematically, a biological system with perfect adaptation can be modelled as an input-output nonlinear system whose output, usually determining the biological function, is asymptotically stable under all input disturbances concerned. In this paper, a quite general input-output mathematical model is employed and the 'functional' of biological function (FBF) - output Lyapunov function - is explored to investigate its perfect adaptation ability. Sufficient condition is established for the systems with FBF to achieve perfect adaptation. Then a sufficient and necessary condition is obtained for the linear systems to possess an output Lyapunov function. Furthermore, it is shown that the 'functional' of receptors activity exists in the perfect adaptation model of E. coli chemotaxis. Different with the existing mathematical surveys on perfect adaptation, most of which are based on the standpoint of control theory, we first investigate this problem using ways of nonlinear systems analysis.
KeywordOutput Lyapunov function perfect adaptation perturbed nonlinear systems
WOS Research AreaMathematics
WOS SubjectMathematics, Interdisciplinary Applications
WOS IDWOS:000370162300004
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Document Type期刊论文
Corresponding AuthorSu Wei
AffiliationChinese Acad Sci, Acad Math & Syst Sci, Key Lab Syst & Control, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Su Wei. Perfect adaptation of general nonlinear systems[J]. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,2016,29(1):61-73.
APA Su Wei.(2016).Perfect adaptation of general nonlinear systems.JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,29(1),61-73.
MLA Su Wei."Perfect adaptation of general nonlinear systems".JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY 29.1(2016):61-73.
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