Large-Scale Systems: Complexity, Stability, Reliability

After showing that a complex dynamic system with a competitive structure has highly reliable stability, a class of noncompetitive dynamic systems for which competitive models can be constructed is defined. It is shown that such a construction is possible in the context of the hierarchic stability analysis. The scheme is based on the comparison principle and vector Liapunov functions.

[1]  E. Kamke Zur Theorie der Systeme gewöhnlicher Differentialgleichungen. , 1929 .

[2]  E. Kamke Zur Theorie der Systeme gewöhnlicher Differentialgleichungen. II. , 1932 .

[3]  Kenneth J. Arrow,et al.  PRICE-QUANTITY ADJUSTMENTS IN MULTIPLE MARKETS WITH RISING DEMANDS , 1958 .

[4]  P. K. Newman Some Notes on Stability Conditions , 1959 .

[5]  N. Rashevsky,et al.  Arms and insecurity , 1960 .

[6]  M. Fiedler,et al.  On matrices with non-positive off-diagonal elements and positive principal minors , 1962 .

[7]  H. H. Rosenbrock A lyapunov function for some naturally-occurring linear homogeneous time-dependent equations , 1963, Autom..

[8]  Norman,et al.  Structural Models: An Introduction to the Theory of Directed Graphs. , 1966 .

[9]  B. A. Farbey,et al.  Structural Models: An Introduction to the Theory of Directed Graphs , 1966 .

[10]  H. Antosiewicz,et al.  Differential Equations: Stability, Oscillations, Time Lags , 1967 .

[11]  Peter Lancaster,et al.  The theory of matrices , 1969 .

[12]  Richard Bellman Topics in pharmacokinetics I: Concentration-dependent rates , 1970 .

[13]  W. Walter Differential and Integral Inequalities , 1970 .

[14]  James P. Quirk,et al.  Introduction to general equilibrium theory and welfare economics , 1971 .

[15]  K. Arrow,et al.  General Competitive Analysis , 1971 .

[16]  Dragoslav D. Siljak,et al.  Stability of Large-Scale Systems under Structural Perturbations , 1972, IEEE Trans. Syst. Man Cybern..

[17]  D. Siljak,et al.  Asymptotic stability and instability of large-scale systems , 1973 .

[18]  Dragoslav D. Šiljak,et al.  Competitive economic systems: Stability, decomposition, and aggregation , 1973, CDC 1973.

[19]  Dragoslav D. Šiljak,et al.  Exponential stability of large-scale discrete systems , 1974 .

[20]  Connective stability of nonlinear matrix systems , 1974 .

[21]  Dragoslav D. Šiljak,et al.  On connective stability and instability of competitive equilibrium , 1974 .

[22]  D. Siljak,et al.  Decomposition-aggregation stability analysis of the spinning Skylab , 1974 .

[23]  D. Siljak,et al.  Connective stability of complex ecosystems , 1974, Nature.

[24]  D. Siljak When is a complex ecosystem stable , 1975 .