03501nam 2200757 450 991045377550332120200903223051.03-11-026828-010.1515/9783110268287(CKB)2550000001169782(EBL)1130390(OCoLC)865329972(SSID)ssj0001060764(PQKBManifestationID)11985606(PQKBTitleCode)TC0001060764(PQKBWorkID)11087638(PQKB)10627849(MiAaPQ)EBC1130390(DE-B1597)173647(OCoLC)955604655(OCoLC)979906368(DE-B1597)9783110268287(Au-PeEL)EBL1130390(CaPaEBR)ebr10819967(CaONFJC)MIL551767(EXLCZ)99255000000116978220130612h20142014 uy| 0engur|n|---|||||txtccrComplexity and evolution of dissipative systems an analytical approach /Sergey VakulenkoBerlin ;Boston :Walter de Gruyter GmbH & Co., KG,[2014]©20141 online resource (316 p.)De Gruyter Series in Mathematics and Life Sciences ;4De Gruyter series in mathematics and life sciences,2195-5530 ;4Description based upon print version of record.3-11-026648-2 1-306-20516-6 Includes bibliographical references and index. Frontmatter -- Preface -- Contents -- 1. Introduction -- 2. Complex dynamics in neural and genetic networks -- 3. Complex patterns and attractors for reaction-diffusion systems -- 4. Random perturbations, evolution and complexity -- Bibliography -- Index -- BackmatterThis book focuses on the dynamic complexity of neural, genetic networks, and reaction diffusion systems. The author shows that all robust attractors can be realized in dynamics of such systems. In particular, a positive solution of the Ruelle-Takens hypothesis for on chaos existence for large class of reaction-diffusion systems is given. The book considers viability problems for such systems - viability under extreme random perturbations - and discusses an interesting hypothesis of M. Gromov and A. Carbone on biological evolution. There appears a connection with the Kolmogorov complexity theory. As applications, transcription-factors-microRNA networks are considered, patterning in biology, a new approach to estimate the computational power of neural and genetic networks, social and economical networks, and a connection with the hard combinatorial problems. De Gruyter Series in Mathematics and Life SciencesMathematical physicsEnergy dissipationBiophysicsAttractors (Mathematics)Chaotic behavior in systemsElectronic books.Mathematical physics.Energy dissipation.Biophysics.Attractors (Mathematics)Chaotic behavior in systems.003SK 560rvkVakulenko Sergey1036379MiAaPQMiAaPQMiAaPQBOOK9910453775503321Complexity and evolution of dissipative systems2456679UNINA