000 03254nam a22004935i 4500
001 978-94-91216-03-9
003 DE-He213
005 20140220083838.0
007 cr nn 008mamaa
008 110503s2011 fr | s |||| 0|eng d
020 _a9789491216039
_9978-94-91216-03-9
024 7 _a10.2991/978-94-91216-03-9
_2doi
050 4 _aQA372
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
082 0 4 _a515.352
_223
100 1 _aAkhmet, Marat.
_eauthor.
245 1 0 _aNonlinear Hybrid Continuous/Discrete-Time Models
_h[electronic resource] /
_cby Marat Akhmet.
264 1 _aParis :
_bAtlantis Press,
_c2011.
300 _aXIV, 218 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aAtlantis Studies in Mathematics for Engineering and Science,
_x1875-7642 ;
_v8
505 0 _a1. Introduction -- 2. Linear and quasi-linear systems with piecewise constant argument -- 3. The reduction principle for systems with piecewise constant argument -- 4. The small parameter and differential equations with piecewise constant argument -- 5. Stability -- 6. The state-dependent piecewise constant argument -- 7. Almost periodic solutions -- 8. Stability of neural networks -- 9. The blood pressure distribution -- 10. Integrate-and-fire biological oscillators.
520 _aThe book is mainly about hybrid systems with continuous/discrete-time dynamics. The major part of the book consists of the theory of equations with piece-wise constant argument of generalized type. The systems as well as technique of investigation were introduced by the author very recently. They both generalized known theory about differential equations with piece-wise constant argument, introduced by K. Cook and J. Wiener in the 1980s. Moreover, differential equations with fixed and variable moments of impulses are used to model real world problems. We consider models of neural networks, blood pressure distribution and a generalized model of the cardiac pacemaker. All the results of the manuscript have not been published in any book, yet. They are very recent and united with the presence of the continuous/discrete dynamics of time. It is of big interest for specialists in biology, medicine, engineering sciences, electronics. Theoretical aspects of the book meet very strong expectations of mathematicians who investigate differential equations with discontinuities of any type.
650 0 _aMathematics.
650 0 _aMedicine.
650 0 _aDifferential Equations.
650 0 _aPhysiology
_xMathematics.
650 1 4 _aMathematics.
650 2 4 _aOrdinary Differential Equations.
650 2 4 _aApplications of Mathematics.
650 2 4 _aPhysiological, Cellular and Medical Topics.
650 2 4 _aMedicine/Public Health, general.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9789491216022
830 0 _aAtlantis Studies in Mathematics for Engineering and Science,
_x1875-7642 ;
_v8
856 4 0 _uhttp://dx.doi.org/10.2991/978-94-91216-03-9
912 _aZDB-2-SMA
999 _c109729
_d109729