Displaying similar documents to “Estimates of solutions of impulsive parabolic equations and applications to the population dynamics.”

On Semicontinuity in Impulsive Dynamical Systems

Krzysztof Ciesielski (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

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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...

The dynamic behaviors of a new impulsive predator prey model with impulsive control at different fixed moments

Lin Jun Wang, You Xiang Xie, Qi Cheng Deng (2018)

Kybernetika

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In this paper, we propose a new impulsive predator prey model with impulsive control at different fixed moments and analyze its interesting dynamic behaviors. Sufficient conditions for the globally asymptotical stability of the semi-trivial periodic solution and the permanence of the present model are obtained by Floquet theory of impulsive differential equation and small amplitude perturbation skills. Existences of the "infection-free" periodic solution and the "predator-free" solution...

On time reparametrizations and isomorphisms of impulsive dynamical systems

Krzysztof Ciesielski (2004)

Annales Polonici Mathematici

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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 initial value problems for a class of first order impulsive differential inclusions

Mouffak Benchohra, Abdelkader Boucherif, Juan J. Nieto (2001)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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We investigate the existence of solutions to first order initial value problems for differential inclusions subject to impulsive effects. We shall rely on a fixed point theorem for condensing maps to prove our results.

A new continuous dependence result for impulsive retarded functional differential equations

Márcia Federson, Jaqueline Godoy Mesquita (2016)

Czechoslovak Mathematical Journal

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We consider a large class of impulsive retarded functional differential equations (IRFDEs) and prove a result concerning uniqueness of solutions of impulsive FDEs. Also, we present a new result on continuous dependence of solutions on parameters for this class of equations. More precisely, we consider a sequence of initial value problems for impulsive RFDEs in the above setting, with convergent right-hand sides, convergent impulse operators and uniformly convergent initial data. We assume...