000 03155nam a22004695i 4500
001 978-1-4419-6581-3
003 DE-He213
005 20140220084510.0
007 cr nn 008mamaa
008 100907s2010 xxu| s |||| 0|eng d
020 _a9781441965813
_9978-1-4419-6581-3
024 7 _a10.1007/978-1-4419-6581-3
_2doi
050 4 _aQA313
072 7 _aPBWR
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515.39
_223
082 0 4 _a515.48
_223
100 1 _aAkhmet, Marat.
_eauthor.
245 1 0 _aPrinciples of Discontinuous Dynamical Systems
_h[electronic resource] /
_cby Marat Akhmet.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2010.
300 _aXII, 180p. 40 illus., 20 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
505 0 _aDescription of the System with Fixed Moments of Impulses and Its Solutions -- Stability and Periodic Solutions of Systems with Fixed Moments of Impulses -- Basics of Linear Systems -- Nonautonomous Systems with Variable Moments of Impulses -- Differentiability Properties of Nonautonomous Systems -- Periodic Solutions of Nonlinear Systems -- Discontinuous Dynamical Systems -- Perturbations and Hopf Bifurcation of a Discontinuous Limit Cycle -- Chaos and Shadowing.
520 _aDiscontinuous dynamical systems have played an important role in both theory and applications during the last several decades. This is still an area of active research and techniques to make the applications more effective are an ongoing topic of interest. Principles of Discontinuous Dynamical Systems is devoted to the theory of differential equations with variable moments of impulses. It introduces a new strategy of implementing an equivalence to systems whose solutions have prescribed moments of impulses and utilizing special topologies in spaces of piecewise continuous functions. The achievements obtained on the basis of this approach are described in this book. The text progresses systematically, by covering preliminaries in the first four chapters. This is followed by more complex material and special topics such as Hopf bifurcation, Devaney's chaos, and the shadowing property are discussed in the last two chapters. This book is suitable for researchers and graduate students in mathematics and also in diverse areas such as biology, computer science, and engineering who deal with real world problems.
650 0 _aMathematics.
650 0 _aDifferentiable dynamical systems.
650 0 _aDifferential Equations.
650 0 _aDifferential equations, partial.
650 1 4 _aMathematics.
650 2 4 _aDynamical Systems and Ergodic Theory.
650 2 4 _aOrdinary Differential Equations.
650 2 4 _aPartial Differential Equations.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781441965806
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4419-6581-3
912 _aZDB-2-SMA
999 _c110660
_d110660