Displaying similar documents to “Multi-type synchronization of impulsive coupled oscillators via topology degree”

On time reparametrizations and isomorphisms of impulsive dynamical systems

Krzysztof Ciesielski (2004)

Annales Polonici Mathematici

Similarity:

We prove that for a given impulsive dynamical system there exists an isomorphism of the basic dynamical system such that in the new system equipped with the same impulse function each impulsive trajectory is global, i.e. the resulting dynamics is defined for all positive times. We also prove that for a given impulsive system it is possible to change the topology in the phase space so that we may consider the system as a semidynamical system (without impulses).

On Semicontinuity in Impulsive Dynamical Systems

Krzysztof Ciesielski (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

In the important paper on impulsive systems [K1] several notions are introduced and several properties of these systems are shown. In particular, the function ϕ which describes "the time of reaching impulse points" is considered; this function has many important applications. In [K1] the continuity of this function is investigated. However, contrary to the theorem stated there, the function ϕ need not be continuous under the assumptions given in the theorem. Suitable examples are shown...