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Absorbing State 34, 36 Adaptive Boolean Networks 78 Adaptive Chemical Network 73 Adaptive Coupled Map Lattices 66 Adaptive Epide

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Absorbing State 34, 36 Adaptive Boolean Networks 78 Adaptive Chemical Network 73 Adaptive Coupled Map Lattices 66 Adaptive Epide 239 Index a b absorbing state 34, 36 b-value 107, 109, 112, 119 adaptive Boolean networks 78 Bak–Sneppen model 74, 75 adaptive chemical network 73 benchmark 216, 217, 234 adaptive coupled map lattices 66 Bethe–Peierls approach 225 adaptive epidemiological network betweenness of a node 68 95 bill-tracking website 6 adaptive network of coupled biodiversity 46 oscillators 83 biological evolution 73 adaptive networks 63–66, 70–72, bipartite networks 211 74, 83, 90, 98, 100, 102 bipartite structure 216 adaptive rewiring 91, 92 bipartition 218, 220 adaptive SIS model 96 bipartitioning problem 219 adjacency matrix 9, 66, 206, 207, birth-death processes 31, 37 209–211, 217, 223 bisection problem 232 aftershock 108, 113, 121, bistability 27 125–129, 131, 134, 135, 137 bivariate analysis 164 aftershock magnitudes 127 bivariate measures 162 aftershock sequence 121, 123 bivariate nonlinear approaches aftershock sequences 136 163 agent-based models 73 bivariate time-series analysis agent-based simulation 172, 173, 178 frameworks 3 block-structure 201, 203, 217, air transportation network 2, 10 222, 234, 235 anti-epileptic drugs 159, 163 Boolean networks 65, 76, 79 assortative 67 bounded rationality 25 attractor 164 box-counting technique 112, 113 autoregressive modeling 161, brain 161 172, 175 Brownian motion 6, 7 avalanche size 139 burst-firing 169, 170 average shortest path length 167 bursting 166, 167, 170 Reviews of Nonlinear Dynamics and Complexity. Edited by Heinz Georg Schuster Copyright c 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN: 978-3-527-40850-4 240 Index c conflicting opinions 98 cable theory 166 connection template 176 Cantor set 109, 112, 115–119, 123, connectivity 67 139, 140, 143, 144, 147–149, 152 cooperation 46, 47, 83 causal relationships 172 cooperative game theory 25 causality 175 coordination game 40, 42, 85 cavity fields 225, 227 core-periphery structure 206 cavity method 222, 224, 234 coupled oscillator networks 79 cell differentiation 100 creation of links 70 cellular nonlinear networks 176 creation of nodes 70 central limit theorem 219 critical continuum-state branching change of the topology 69 model 135 Chay–Keizer model 167 cross-correlation functions 160 cluster 203, 206, 217, 227, 228, 230, 232, 235 d cluster coefficient 167, 180 data collection 202 cluster structure 235 data-driven analysis 202 coevolutionary networks 64 data-mining on networks 236 coexistence 28 decay 93 coexistence games 35 deception of randomness 218 cohesive subgroups 201, 217 degree distribution 67, 201 coloring random graphs 224 degree of a node 67 combinatorial optimization degree–degree correlations 215 problem 203, 211 deletion of links 70 communication network 87 deletion of nodes 70 communities in networks 217 dimension 162 community detection 201, 233 dimensionality reduction 203, community structure 201, 222, 204, 208 234 direction of interaction 172 complete synchronization 173 disassortative 67 complex networks 63, 201 disease dynamics 13 complex systems 201–203 division of labor 66, 79, 81, 85, complexity 69 92, 99, 100, 102, 103 computational models 165 dominance 27 computational neuroscience 165 dynamic networks 64, 69 computer science 63 dynamic state 68 conditional fixation times 36 dynamical disease 184 conditional mutual information dynamical scenarios 28 175 e conductance-based models 166 earthquake 107, 108, 125, 126, configuration model 219 137 Index 241 earthquake dynamics 107, 108, first-order transitions 95 137 fitness 26 earthquake rupture 135 FitzHugh–Nagumo model 167 earthquake statistics 107 fixation probability 31, 40, 42 edge of chaos 76 fixation time 34, 37 edges 66 flux of dollar bills 9 EEG 160–166, 168, 170, 171, focal epilepsy 163, 182 176–179, 182, 183 focal onset seizures 164, 182 electrical circuits 100 focal seizures 159 embedding theorems 175 Fokker–Planck equation 20, 44, emerging topologies 88 45 entropy 162, 175 followers 81 epidemic network 90 food web evolution 74 epidemic spreading 64 fractals 108–116, 121, 123, 124, epidemic thresholds 90 140, 147 epidemiological models 88 fractional derivative 19 epidemiology 63 fractional diffusion equations 19 epilepsy 159, 160, 164–171, 178, fractional Laplacian 19 183, 184 frequency distribution 118 equal gains from switching 48 frequency–size distribution 112, Erd˝os–Rényi graphs 220 113 ergodicity assumption 4 frozen 69 error function 211, 213 functional magnetic resonance error matrix 210, 213 imaging 160 evolution 201 functional network topology 181 evolution of cooperation 73 functional neuroimaging 164 evolutionary game theory 26, 29 future challenges 103 evolutionary games in finite populations 50, 56 g evolving networks 68, 69 game theory 25, 84 games on adaptive networks 66 f Gaussian distribution 219 failure threshold 137 Gaussian orthogonal ensemble fault 112, 134, 140 182 fault networks 112 gene regulation 202 fault surfaces 108, 110–112 generalized synchronization 173, fault zone 110, 111, 129, 133, 135 174 Fermi process 41–43, 48 generalized-onset seizures 182 ferromagnetic spin system 227 GENESIS 166 fiber bundle model 108, 137, 138, genetic code 202 140 genetic networks 72, 78, 100 finite populations 29, 43 genetic programs 202 242 Index genetic variation 201 information networks 72 geodesic distance 205 information theory 172, 174 George Price 26 innovative game dynamics 29 global scale 180 integrate-and-fire-neurons 170 global self-organization 78 inter-cluster connections 92 GPS (global positioning via inter-species variation 204 satellite) 3 interacting swarms of robots 100 GR law (Gutenberg–Richter law) interaction networks 180 107–109, 112, 119, 120, 122, 125, interconnected faults 108 128, 139, 140, 147 intermittent clustering dynamics graph partitioning 217, 218, 234 81 graph theory 66 internet 63, 72 intra-species variation 204 h Iris data 203 hallmarks of adaptive networks Itô calculus 45 98 heteroclinic cycle 50 j hierarchical transition 82 John Maynard Smith 26 hierarchy of interactions 202 John von Neumann 25 Hilbert transform 174 joint recurrence plots 175 Hindmarsh–Rose model 167 jump downwards 93 Hodgkin–Huxley model 166 jump upwards 93 Hodgkin–Huxley-type formalisms 169 k Hopf bifurcation 96 k-sat problem 211 Hoshen–Kopelman algorithm Kauffman networks 78 152 kin selection 48 hubs 67, 168 Kramers–Moyal expansion 43 human mobility 1–6, 8, 10–12 Kullback–Leibler distance 175 hyperexcitability 171 l hypothesis-driven research 203 Lévy flight 7, 8 i lag synchronization 173 ictogenic 159, 160 Laplacian matrix 206 image graph 214 Laplacian of a network 179 imaging techniques 160 leaders 79, 81 imitation 26, 29 LiDAR profile 112 immune system 73 link structure 203 indirect reciprocity 48 links 66 infection dynamics 1, 3 links per node 168 infinite populations 43 local degrees of freedom 99 information 202 local rules 78 Index 243 local scale 180 multi-agent systems 29 Lotka–Voltera equations 28 multi-scale mobility networks 8 low-dimensional chaos in the multi-scale transportation epileptic brain 183 networks 10 Lyapunov exponents 162 multivariate data 203, 205, 210 multivariate time-series analysis m 172, 179 magnitude 123, 125, 129, 131, mutual information 175 134–137 magnitude–time sequences 127 n mail network 72 Nash equilibrium 55 mainshock 121, 122, 129, 131 neighborhood 208 Markov chain 53, 54, 56 network clustering 201, 203 Markov models 168 network components 68 Markov process 31 network creation games 73 mass-action principle 13 network Nash equilibrium 86 master equation 18, 43 network of blood vessels 72 mean degree 67 network of coupled logistic maps mean field approximation 97 80 mean-field continuum model network topology 71 171 networks 234 mean-square error 208 NEURON 166 message passing 225 neuronal networks 165 meta-information 87 neuroscience 63 metapopulation 1, 5, 15–17, 19 neutral evolution 78 microcracks 137 neutral selection 37, 40, 45 microscopic density 4 neutrality 28 microscopic time dependent nodes 66 density 4 noise-induced transition 163 minority game 86 non-cooperative games 25 mobile phone dynamics 8 nondeterministic 202 modeling approaches 166 nonlinear time-series analysis modeling brain dynamics 166 162 modular structures 206, 218 nonparticipating loners 52 modularity 217, 218, 222, 234 normal form games 27 modularity of bipartition 231 null model 214 modules 217 Molloy–Reed algorithm 220 o money circulation network 8, 10 Omori law 108, 109, 121, 122, Moran process 30, 31, 37, 41–43, 127, 139, 140 50, 56 on-demand therapy 163 Morris–Lecar model 167 online databases 202 244 Index opinion formation 64, 88, 97 punctuated equilibrium 78 optimal image graph 213 punishment 54 overlap magnitude 115, 141, 147 q p q-state Potts model 211 pair approximation 94 qualitative models 166 pairwise comparison processes quality function 210, 214 29 passenger flux matrix 5 r payoff matrix 27 random Bethe lattice 229, 230 PCA (Principal Component random Cantor set 148–150 Analysis) 209 random fractals 152 penalty function 214 random graph 67, 201, 222, 231 percolating clusters 152, 154, 155 random matrix theory 181, 183 phase dynamics 172 random networks 218, 222 phase synchronization 174 random null model 215 phase-modeling 175 random Sierpinski gaskets 152 phenomenological models 167 randomness 202 Plant model 167 rational decision making 25 plate–plate interactions 107 reaction diffusion models 3 ploidy 204 real-world social networks 100 population models 171 red noise 111 positron emission tomography regular Sierpinski gaskets 149 160 relational data 203, 205 Potts model 223, 224 renormalization group approach
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