Synchronization of networked harmonic oscillators subject to Markovian jumping coupling strengths

Exponential stabilization of stochastic complex networks with Markovian switching topologies via intermittent discrete-time state observations control

“…From (19), we know that Assumptions 1-3 are satisfied. Therefore, we can infer that all conditions in Theorem 1 are satisfied, which implies that system (17) achieve the exponential stability.…”

“…For example, transportation networks are connected by means of railway, highway, airline and other transportation methods. Moreover, some interesting results on multi-links complex networks have been reported [15][16][17][18][19][20].…”

Practical stochastic synchronisation of coupled harmonic oscillators subjected to heterogeneous noises and its applications to electrical systems

“…For example, Sun et al [5] investigated the stochastic synchronisation of coupled harmonic oscillators with the current and delayed information. Wang et al [6] studied the stochastic synchronisation for coupled harmonic oscillators with dissipative coupling and Markovian jumping restorative coupling.…”

“…However, from the view of statistical mechanics or ergodicity [11], the differences of two coupled stochastic harmonic oscillators can reach the stochastic synchronisation in the sense of probability distribution, i.e. two coupled stochastic harmonic oscillators can realise the practical stochastic synchronisation [12] in the sense of probability distribution, which has different probabilistic sense with the works of [5, 6], and can show more random properties of coupled harmonic oscillator.…”