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    Asymptotic stability and instability of large-scale systems (1973)
    In:  Other Sources
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    Publication Date: 2019-06-27
    Description: The purpose of this paper is to develop new methods for constructing vector Lyapunov functions and broaden the application of Lyapunov's theory to stability analysis of large-scale dynamic systems. The application, so far limited by the assumption that the large-scale systems are composed of exponentially stable subsystems, is extended via the general concept of comparison functions to systems which can be decomposed into asymptotically stable subsystems. Asymptotic stability of the composite system is tested by a simple algebraic criterion. By redefining interconnection functions among the subsystems according to interconnection matrices, the same mathematical machinery can be used to determine connective asymptotic stability of large-scale systems under arbitrary structural perturbations.
    Keywords: NAVIGATION
    Type: IEEE Transactions on Automatic Control; AC-18; Dec. 197
    Format: text
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  • 2
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    Stochastic stability and instability of model ecosystems (1975)
    In:  Other Sources
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    Publication Date: 2019-07-13
    Description: In this work, we initiate a stability study of multispecies communities in stochastic environment by using Ito's differential equations as community models. By applying the direct method of Liapunov, we obtain sufficient conditions for stability and instability in the mean of the equilibrium populations. The conditions are expressed in terms of the dominant diagonal property of community matrices, which is a suitable mechanism for resolving the central problem of 'complexity vs stability' in model ecosystems. As a by-product of this analysis we exhibit important structural properties of the stochastic density-dependent models, and establish tolerance of community stability to a broad class of nonlinear time-varying perturbations.
    Keywords: LIFE SCIENCES (GENERAL)
    Type: International Federation of Automatic Control, Triennial World Congress; Aug 24, 1975 - Aug 30, 1975; oston; US
    Format: text
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