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Modeling hybrid network dynamics under random perturbations. (English) Zbl 1166.93028

Summary: We define stochastic network models based on internal structural dynamics of individual nodes which undergo Markovian switching subject to noise and external shocks. Steady-state stability and reliability criteria are established in closed form and show explicit dependence on system parameters.

MSC:

93E15 Stochastic stability in control theory
93C73 Perturbations in control/observation systems
90B15 Stochastic network models in operations research
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
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[1] Luo, J., Stability of invariant sets of ito stochastic differential equations with Markovian switching, J. Appl. Stoch. Anal., 1-6 (2006) · Zbl 1109.60043
[2] Chandra, J.; Ladde, G. S., Stability analysis of stochastic hybrid systems, Int. J. Hybrid Syst., 4, 179-198 (2004)
[3] Korzeniowski, A., Mean reversal for stochastic hybrid systems, Nonlinear Anal.: Hybrid Syst., 2, 613-625 (2008) · Zbl 1161.60022
[4] Korzeniowski, A., Stability of stochastic differential equations under discretization, Stoch. Anal. Appl., 26, 1267-1273 (2008) · Zbl 1155.65009
[5] Ladde, G. S., Hybrid systems: Convergence and stability analysis of large-scale approximation schemes, Int. J. Hybrid Syst., 2, 237-262 (2002)
[6] Ladde, G. S., Hybrid systems: Convergence and stability analysis of stochastic large-scale approximation schemes, Dynam. Systems Appl., 13, 487-512 (2004) · Zbl 1139.93301
[7] Ross, S. M., Stochastic Processes (1996), Wiley & Sons: Wiley & Sons New York · Zbl 0888.60002
[8] Ross, S. M., Introduction to Probability Models (2007), Academic Press
[9] Ladde, G. S.; Lakshmikantham, V.; Leela, Asymptotically conditionally invariant sets and perturbed systems, Annali. di Mate Pura ed Appl., XCIV, 9, 33-40 (1972) · Zbl 0281.34051
[10] Ladde, G. S.; Leela, S., Analysis of invariant sets, Ann. Mat. Pura Appl., XCIV, 283-289 (1972) · Zbl 0288.34050
[11] Lakshmikantham, V.; Leela, S., Differential and Integral Inequalities: Theory and Applications, vol. 1 (1969), Academic Press: Academic Press NY · Zbl 0177.12403
[12] Ladde, G. S.; Lakshmikantham, V., Random Differential Inequalities (1980), Academic Press: Academic Press New York · Zbl 0466.60002
[13] Ladde, G. S.; Siljak, D. D., Connective stability of large-scale stochastic systems, Int. J. Syst. Sci., 6, 713-721 (1975) · Zbl 0313.93063
[14] Siljak, D. D., Large-scale Dynamic Systems — Stability and Structure (1978), North-Holland: North-Holland NY · Zbl 0384.93002
[15] Anabtawi, M. J.; Ladde, G. S., Dynamics of fluids flows under Markovian perturbations, Math. Comput. Modeling, 966-976 (2005) · Zbl 1121.76019
[16] Ladde, G. S., Stability of stochastic distributed parameter large-scale control under random structural perturbations, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 11, 233-254 (2004) · Zbl 1067.93060
[17] Griffin, B. L.; Ladde, G. S., Qualitative properties of stochastic iterative processes under random structural perturbations, Math. Comput. Simul., 67, 181-200 (2004) · Zbl 1067.65011
[18] Ladde, G. S.; Siljak, D. D., Multiplex control systems: Stochastic stability and dynamic reliability, Internat. J. Control, 28, 515-524 (1983) · Zbl 0524.93067
[19] Bremaud, Pierre, Markov Chains (2001), Springer · Zbl 0949.60009
[20] Ladde, G. S., Qualitative analysis of discrete iterative and automata networks, Proc. Neural, Parallel, Scientific Comput., 2, 151-256 (2002)
[21] Ladde, G. S.; Sambandhan, M., Stochastic Versus Deterministic Systems of Differential Equations (2004), Marcel Dekker: Marcel Dekker New York · Zbl 1056.60053
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