On the general problem of stability for impulsive differential equations
By Marat U. Akhmet. 2003
84 citations recorded by the source corpus.
Criteria for stability, asymptotical stability and instability of the nontrivial solutions of the impulsive system dx dt = f( t,x ), t� θi (x), ∆x|t =θi (x) = Ii (x), i ∈ N ={ 1, 2 ,... }, where ∆x|t =θ := x(θ+) − x(θ), x(θ+) = limt →θ + x(t) are obtained by Lyapunov’s second method. The construction of a reduced system in the neighbourhood of a nontrivial solution is a central auxiliary result of the paper.
Subfields: Applied Mathematics, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/a39422720fc817ab51f1522957b4999882d6b759
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In Applied Mathematics
In Control and Systems Engineering
Citations in the corpus
- Li-Yorke chaos in the system with impacts (2009, methodology): “We attempt to shape the Li–Yorke chaos for system (1) by implementing a special initial value problem, where the moments of impulsive action are functionally dependent on the initial moment, and by using the results of the theory of impulsive differential equations [1–3,11,17,25].”