000 03978nam a22005295i 4500
001 978-1-4471-2918-9
003 DE-He213
005 20140220083236.0
007 cr nn 008mamaa
008 120419s2012 xxk| s |||| 0|eng d
020 _a9781447129189
_9978-1-4471-2918-9
024 7 _a10.1007/978-1-4471-2918-9
_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 _aHan, Maoan.
_eauthor.
245 1 0 _aNormal Forms, Melnikov Functions and Bifurcations of Limit Cycles
_h[electronic resource] /
_cby Maoan Han, Pei Yu.
264 1 _aLondon :
_bSpringer London,
_c2012.
300 _aXI, 401p. 77 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aApplied Mathematical Sciences,
_x0066-5452 ;
_v181
505 0 _aHopf Bifurcation and Normal Form Computation -- Comparison of Methods for Computing Focus Values -- Application (I)—Hilbert’s 16th Problem -- Application (II)—Practical Problems -- Fundamental Theory of the Melnikov Function Method -- Limit Cycle Bifurcations Near a Center -- Limit Cycles Near a Homoclinic or Heteroclinic Loop -- Finding More Limit Cycles Using Melnikov Functions -- Limit Cycle Bifurcations in Equivariant Systems.
520 _aDynamical system theory has developed rapidly over the past fifty years. It is a subject upon which the theory of limit cycles has a significant impact for both theoretical advances and practical solutions to problems. Hopf bifurcation from a center or a focus  is integral to the theory of bifurcation of limit cycles, for which normal form theory is a central tool. Although Hopf bifurcation has been studied for more than half a century, and normal form theory for over 100 years, efficient computation in this area is still a challenge with implications for Hilbert’s 16th problem. This book introduces the most recent developments in this field and provides major advances in fundamental theory of limit cycles. Split into two parts, the first focuses on  the study of limit cycles bifurcating from Hopf singularity using normal form theory with later application to Hilbert’s 16th problem, while the second considers near Hamiltonian systems using Melnikov function as the main mathematical tool. Classic topics with new results are presented in a clear and concise manner and are accompanied by the liberal use of illustrations throughout. Containing a wealth of examples and structured algorithms that are treated in detail, a good balance between theoretical and applied topics is demonstrated. By including complete Maple programs within the text, this book also enables the reader to reconstruct the majority of formulas provided, facilitating the use of concrete models for study. Through the adoption of an elementary and practical approach, this book will be of use to graduate mathematics students wishing to study the theory of limit cycles as well as scientists, across a number of disciplines, with an interest in the applications of periodic behavior.
650 0 _aMathematics.
650 0 _aDifferentiable dynamical systems.
650 0 _aDifferential Equations.
650 0 _aComputer software.
650 1 4 _aMathematics.
650 2 4 _aDynamical Systems and Ergodic Theory.
650 2 4 _aApproximations and Expansions.
650 2 4 _aOrdinary Differential Equations.
650 2 4 _aMathematical Software.
650 2 4 _aNonlinear Dynamics.
700 1 _aYu, Pei.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781447129172
830 0 _aApplied Mathematical Sciences,
_x0066-5452 ;
_v181
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4471-2918-9
912 _aZDB-2-SMA
999 _c100730
_d100730