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Collective behavior of multi-agent network dynamic systems under internal and external random perturbations. (English) Zbl 1193.37068
The authors investigate a broad class of collective behavior in a multi-agent interacting dynamical system. Their principal interests are in the qualitative and quantitative properties such as cohesion, robustness, convergence and stability. Utilizing energy-like functions and the theory of differential inequalities, they derive explicit conditions that are sufficient, algebraically simple and computable. The methods do not require the explicit knowledge of solution processes. The qualitative results such as cohesion, convergence and stability are readily applicable to a broad class of social networks.

37H10Generation, random and stochastic difference and differential equations
Full Text: DOI
[1] Chandra, J.; Ladde, G. S.: Stability analysis of stochastic hybrid systems, Abstracts: joint mathematics meeting (San antonio, TX, 2006) 27 (2006)
[2] A.G. Ladde, G.S. Ladde, An introduction to differential equations II: Stochastic modeling and analysis, Unknown, 2009, (in press) · Zbl 1166.93028
[3] Chandra, J.; Landon, J.: Towards a reliable and resilient mobile wireless architecture, Stochast. anal. Appl. 24, 827-841 (2006) · Zbl 1136.60352 · doi:10.1080/07362990600753569
[4] Arnold, L.: Stochastic differential equations, (1971) · Zbl 0219.60047
[5] Chandra, J.; Ladde, G. S.: Stability analysis of stochastic hybrid systems, Internat. J. Hybrid syst. 4, 179-198 (2004)
[6] Ladde, G. S.; Lakshmikantham, V.: Random differential inequalities, (1980) · Zbl 0488.60069
[7] Gazi, V.; Passino, K. M.: Stability analysis of swarms, IEEE trans. Automat. control. 48, 692-697 (2003)
[8] Branicky, M. S.: Multiple Lyapunov functions and analysis tools for switched and hybrid systems, IEEE trans. Automat. control. 43, 475-482 (1998) · Zbl 0904.93036 · doi:10.1109/9.664150
[9] Ladde, G. S.; Sambandham, M.: Stochastic versus deterministic systems of differential equations, (2004) · Zbl 1056.60053