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Exponential dichotomies of impulsive dynamic systems with applications on time scales
Author(s) -
Wang Chao,
Agarwal Ravi P.
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3325
Subject(s) - mathematics , dichotomy , exponential function , class (philosophy) , scale (ratio) , exponential growth , homogeneous , exponential dichotomy , impulse (physics) , differential equation , mathematical analysis , computer science , statistics , combinatorics , physics , quantum mechanics , artificial intelligence
In this paper, it is the first time that some important inequalities are obtained to estimate the exponential type of upper and lower bounds of solutions for the three representative classes of homogeneous impulsive dynamic systems on time scales. Based on these, some new criteria are established for admitting an exponential dichotomy of the impulsive dynamic systems. The obtained results are essentially new, even the time scale T = R or T = Z . In addition, in applications, we apply the obtained results to discuss the almost periodic problems of a class of integro‐differential systems, and the numerical simulations are given to illustrate that our timescale methods are feasible and effective. Finally, we present the conclusion and further discussion related to this topic. Copyright © 2014 John Wiley & Sons, Ltd.