LEADER 05395nam 2200625Ia 450 001 9910830681203321 005 20230725023847.0 010 $a1-282-71239-X 010 $a9786612712395 010 $a3-527-63096-1 010 $a3-527-63097-X 035 $a(CKB)2670000000033528 035 $a(EBL)557611 035 $a(OCoLC)654029561 035 $a(SSID)ssj0000441800 035 $a(PQKBManifestationID)11328730 035 $a(PQKBTitleCode)TC0000441800 035 $a(PQKBWorkID)10406772 035 $a(PQKB)10150967 035 $a(MiAaPQ)EBC557611 035 $a(EXLCZ)992670000000033528 100 $a20100928d2010 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 00$aReviews of nonlinear dynamics and complexity$hVolume 3$b[electronic resource] /$fedited by Heinz Georg Schuster 210 $aWeinheim $cWiley-VCH ;$a[Chichester $cJohn Wiley, distributor]$dc2010 215 $a1 online resource (261 p.) 225 1 $aAnnual Reviews of Nonlinear Dynamics and Complexity (VCH) ;$vv.3 300 $aDescription based upon print version of record. 311 $a3-527-40945-9 320 $aIncludes bibliographical references and index. 327 $aReviews of Nonlinear Dynamics and Complexity; Contents; Preface; List of Contributors; 1 The Chaos Computing Paradigm; 1.1 Brief History of Computers; 1.2 The Conceptualization, Foundations, Design and Implementation of Current Computer Architectures; 1.3 Limits of Binary Computers and Alternative Approaches to Computation: What Lies Beyond Moore's Law?; 1.4 Exploiting Nonlinear Dynamics for Computations; 1.5 General Concept; 1.6 Continuous-Time Nonlinear System; 1.7 Proof-of-Principle Experiments; 1.7.1 Discrete-Time Nonlinear System; 1.7.2 Continuous-Time Nonlinear System 327 $a1.8 Logic from Nonlinear Evolution: Dynamical Logic Outputs1.8.1 Implementation of Half- and Full-Adder Operations; 1.9 Exploiting Nonlinear Dynamics to Store and Process Information; 1.9.1 Encoding Information; 1.9.2 Processing Information; 1.9.3 Representative Example; 1.9.4 Implementation of the Search Method with Josephson Junctions; 1.9.5 Discussions; 1.10 VLSI Implementation of Chaotic Computing Architectures: Proof of Concept; 1.11 Conclusions; References; 2 How Does God Play Dice?; 2.1 Introduction; 2.2 Model; 2.2.1 Bounce Map with Dissipation 327 $a2.3 Phase Space Structure: Poincare? Section2.4 Orientation Flip Diagrams; 2.5 Bounce Diagrams; 2.6 Summary and Conclusions; 2.7 Acknowledgments; References; 3 Phase Reduction of Stochastic Limit-Cycle Oscillators; 3.1 Introduction; 3.2 Phase Description of Oscillator; 3.3 Oscillator with White Gaussian Noise; 3.3.1 Stochastic Phase Equation; 3.3.2 Derivation; 3.3.3 Steady Phase Distribution and Frequency; 3.3.4 Numerical Examples; 3.4 Oscillator with Ornstein-Uhlenbeck Noise; 3.4.1 Generalized Stochastic Phase Equation; 3.4.2 Derivation; 3.4.3 Steady Phase Distribution and Frequency 327 $a3.4.4 Numerical Examples3.4.5 Phase Equation in Some Limits; 3.5 Noise effect on entrainment; 3.5.1 Periodically Driven Oscillator with White Gaussian Noise; 3.5.2 Periodically Driven Oscillator with Ornstein-Uhlenbeck Noise; 3.5.3 Conjecture; 3.6 Summary; References; 4 Complex Systems, numbers and Number Theory; 4.1 A Statistical Pattern in the Prime Number Sequence; 4.1.1 Benford's Law and Generalized Benford's Law; 4.1.2 Are the First-Digit Frequencies of Prime Numbers Benford Distributed?; 4.1.3 Prime Number Theorem Versus Size-Dependent Generalized Benford's Law 327 $a4.1.4 The Primes Counting Function L(N)4.1.5 Remarks; 4.2 Phase Transition in Numbers: the Stochastic Prime Number Generator; 4.2.1 Phase Transition; 4.2.1.1 Network Image and Order Parameter; 4.2.1.2 Annealed Approximation; 4.2.1.3 Data Collapse; 4.2.2 Computational Complexity; 4.2.2.1 Worst-Case Classification; 4.2.2.2 Easy-Hard-Easy Pattern; 4.2.2.3 Average-Case Classification; 4.3 Self-Organized Criticality in Number Systems: Topology Induces Criticality; 4.3.1 The Division Model; 4.3.2 Division Dynamics and SOC; 4.3.3 Analytical Developments: Statistical Physics Versus Number Theory 327 $a4.3.4 A More General Class of Models 330 $aWritten in a style that breaks the barriers between the disciplines, this monograph enables researchers from life science, physics, engineering, or chemistry to access the most recent results in a common language. The resulting review character of this project sets it apart from specialized journals, and allows each volume to respond quickly to new developments.This third volume contains new topics ranging from chaotic computing, via random dice tossing and stochastic limit-cycle oscillators, to a number theoretic example of self-organized criticality, wave localization in complex networks 410 0$aAnnual Reviews of Nonlinear Dynamics and Complexity (VCH) 606 $aNonlinear theories 606 $aComputational complexity 615 0$aNonlinear theories. 615 0$aComputational complexity. 676 $a003.75 701 $aSchuster$b Heinz Georg$f1943-$048625 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910830681203321 996 $aReviews of nonlinear dynamics and complexity$93929135 997 $aUNINA