Classes of stochastically switched (blinking) systems

—It is investigated to what extent the trajectories of a stochastically switched (blinking) system follow the corresponding trajectories of the averaged system. Four cases have to be distinguished, depending on whether or not the averaged system has a unique attractor and whether or not the attractor(s) is (are) invariant under the dynamics of the blinking system. The corresponding asymptotic behavior of the trajectories of the blinking system is described and illustrative examples are given. I. BLINKING AND AVERAGED SYSTEM Consider a system described by time-dependent ordinary differential equations of the form ( ) ( )( ) ( ) { }MN N+M M , , : , 0,1 d t t dt t = ∈ → ∈ x F x s x F s (1) where the function s(t) is piecewise constant, taking the constant binary vector value ( )1 M, ,k k k s s=s in the time interval [(k-1)τ, kτ] (Figure 1). We call system (1) a blinking system. Of primary interest is the asymptotic behavior of solutions of (1) starting at t = 0. We call the sequ...

• Type: Conference
• Year: 2007
• Where: ISCAS
• Authors: Martin Hasler, Igor Belykh, Vladimir N. Belykh
• Keywords: Averaged System, Blinking, Blinking System, ISCAS 2007