We study nonlinear stochastic systems with time-delayed feedback using the concept of delay Fokker-Planck equations introduced by Guillouzic, L'Heureux, and Longtin. We derive an analytical expression for stationary distributions using first-order perturbation theory. We demonstrate how to determine drift functions and noise amplitudes of this kind of systems from experimental data. In addition...

The stability problem of impulsive discrete systems with multiple delays is studied. By means of the Lyapunov stability theory and discrete-time Halanay-type inequality technique, we develop sufficient conditions for the exponential stability for the impulsive discrete systems with multiple delays, which involves multiple delays not only at non-impulsive time instants but also at impulsive time...