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2 ð8Þ Case 2: Safety Application Packet Uses Distributed Coordination Function For analyze transmission of safety application packet, we use Markov chain of safety application packet in case 1 because the transmission of safety application packets are independent of transmission of WSA/RES packets. Now, we analyze transmission of WSA/RES packets. Let bs(t) and ss(t) be the stochastic process representing the backoff window size and backoff state for a given node at slot time Performance Analysis of a Hybrid Efficient and Reliable MAC … 47 t, respectively.

Later, in the 1950s–1960s, the study of the well-known Aizerman’s and Kalman’s conjectures on absolute stability led to the discovery of the possible coexistence of a hidden periodic oscillation and a unique stable stationary point in automatic control systems. In 1957 Kalman stated the following [26]: “If f ðeÞ in Fig. 1 [see Fig. , all transient solutions will r + e Σ f f(e) G(s c − Fig. 4 Nonlinear control system. GðsÞ is a linear transfer function, f ðeÞ is a single-valued, continuous, and differentiable [26] Hidden Attractors in Fundamental Problems and Engineering … 17 Fig.

Bragin VO, Vagaitsev VI, Kuznetsov NV, Leonov GA (2011) Algorithms for finding hidden oscillations in nonlinear systems. The Aizerman and Kalman conjectures and Chua’s circuits. J Comput Syst Sci Int 50(4):511–543 34. Leonov GA, Kuznetsov NV (2011) Algorithms for searching for hidden oscillations in the Aizerman and Kalman problems. Dokl Math 84(1):475–481 35. Kuznetsov NV, Leonov GA, Seledzhi SM (2011) Hidden oscillations in nonlinear control systems. IFAC Proc Vol (IFAC-PapersOnline) 18(1):2506–2510 Hidden Attractors in Fundamental Problems and Engineering … 21 36.

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