Index

Z2 symmetry, 20 antiphase, 4, 215, 216, 220, 309, 313 α band, 174 antiphase point , 7 β band, 174, 176, 177 Aplysia, 187 β-desynchronization, 342 articulatory processes, 275 δ band, 174 associative learning, 191 γ band, 174, 176, 177 Asymmetric Bimanual Coordination, λ-hypothesis, 108 109 σ- small-world metric, 174 Attention, 190 θ band, 174 attention, 314 ∆ω,8 , 10, 49, 163–165 (In)stability, 209 dimension, 163–165 (REM) sleep, 253 attractor landscape, 101 “ecological” approach, 261 attractor strength, 7 “edge of criticality”, 162, 173, 177 attractors, 262 ‘maintenance’ tendencies, 297 auditory, 341 corticomuscular coherence, 142 autocorrelation, 164, 165 1:1 frequency locking, 3 autonomous nervous system (ANS), 231 Awareness, 191 absolute coordination, 286, 288 action understanding, 319 basal ganglia, 194, 342 adjacency matrix, 174, 175 basic laws, 327, 345 affordances, 70, 261 basin of entrainment, 281, 297, 299 air cusion, 341 BCI technology, 229 allocentric, 17 beamforming, 143 alpha, 315, 316 behavior amplitude dynamics, 22 adaptive, 162 analysis of variance (ANOVA), 166, 172 chaotic, 163, 164 anatomical connections, 185 collective, 163 anchoring, 334 emergent, 162 and syncopation, 214 nonlinear, 163, 164 animal-environment system, 265 unstable, 172 anterior cingulate cortex, 190 behavioral catalyst, 184 anti-phase, 327 behavioral dynamics, 45 348 Index bi-stability, 207 short-range synaptic, 169 bifurcation, 45 connectivity function, 344 bifurcation diagram, 23, 329 consciousness, 200, 253 bifurcations, 262 constant bearing strategy, 55 bimanual, 215 constraints, 218 bimanual co, 216 context-dependent, 218 bimanual coordination, 171, 205, 207, contingence, 247 214 control laws, 47 binding control parameter, 19, 21, 205, 207, 266, sensorimotor, 176 328 bistable, 329 convergence, 339 BOLD, 212, 215, 217 coordination, 4, 262 bottom-up, 328 coordination device, 269 brachial plexus, 172 Coordination Dynamics, 205, 207, 209, brain functional networks, 174, 176 211, 213, 215, 217, 219, 221, 223, brain maturation, 166 225, 227, 309 brain rhythms, 312, 313 coordination dynamics, 45, 205, 206, brain–machine interfaces, 230 221 Broca’s area, 171 copation, 210 Coriolis force that, 98 cancelation effect, 71 corollary discharge, 95 category learning, 101 correlation dimension, 162, 164, 166, Category-specificity, 188 169 caudal cingulate cortex, 125 correlations, 188 cerebellar patients, 115 cortex cerebellum, 125, 171, 218, 219, 342 heteromodal association, 166 chaos cortical inhibition, 141 deterministic, 164, 169 cortical surface, 343 chaotic systems coupled oscillator, 264 adaptability, 162 coupled oscillators, 331 unpredictability, 162, 164 coupled systems, 176, 177 children, 166 coupling, 206, 313, 318 cingulate, 171, 212, 218 coupling function, 329 clozapine, 169 covariances, 188 clustering coefficient, 174, 176, 177 critical fluctuations, 207 Cognitive, 183 critical rate, 327 cognitive strategies, 210 critical slowing down, 206 coherence, 165, 166, 169 critical value, 333, 341 collective variable, 311 cross-recurrence quantification analysis, competition, 72 269 complementary pair, 221 crowd behavior, 46 complex networks, 174 complex system, 328 damping, 48 complex systems, 163, 173 Daubechies, 174 complexity, 3 definitions of relative phase, 17 connectivity, 169, 176 degenerate, 184 altered, 161 degree cortical, 161 of a network, 174 global pattern, 162 degree distribution, 174 Index 349

Delayed auditory , 99 equilibrium, 170 detunes, 13 equilibrium point hypothesis, 124 detuning, 285–287, 301, 302 Euclidean norm, 164 development Event-related brain potentials (ERPs), neural, 162 232 normal, 166 event-related dynamics, 312 diagonal matrix, 175 evoked responses, 312 differential equation, 344 execution of syncopation, 219 differential stability, 220 Extended Curie Principle, 10, 12 Dijkstra, 174 eye movements, 292, 296 dimensional complexity, 163, 165, 169 dimensionless imperfections, 10 feedback discrete, 211 motor control, 171, 173 discrete movement, 82 Fitts’ law, 107 discrete movements, 105 fixed point, 79, 329 divergence, 339 fixed-point attractor, 108 dopaminergic neurons, 169 fluphenazine, 169 dorsal and ventral pathways, 190 fMRI, 125, 191, 209, 210, 218 dual-EEG, 309, 315 Fourier transform, 165 Duffing, 329 fractal, 163, 176 dynamical system, 46 frequency locking, 332 dynamical systems, 77, 211, 261 functional connectivity, 254 dynamical , 5 functional MRI, 340 dynamics functional or effective connectivity, 188 critical, 173 fundamental units, 105 neural, 162 Gaussian model potential, 35 ecological niche, 261 Gaussian white noise, 7 EEG, 209, 229, 309 genetic variation, 162 EEG frequency bands, 174, 176 graph theory, 162 EEG spectrum, 315 graphs EEG-BCI, 232 connectivity, 176 effective connectivity, 254 random, 174 egocentric, 17 regular lattices, 174 eigenfrequency, 332 undirected, 174 eigenvalue, 197 electroencephalography, 340 half-center oscillator, 116 electroencephalography (EEG), haloperidol, 169 162–167, 169 handedness, 16, 70 electromyographic analyses, 112 handheld pendulums, 7 elementary coordination law, 5, 7 heading, 46 embedding dimension, 165 hemoglobin, 342 embodied, 47 heterogeneous connections, 344 emergent behavior, 46 HKB dynamics, 5, 14 empathy, 319 HKB model, 27, 28, 33–35, 39–41, 207, Endpoint adaptation, 99 328 entrainment, 262, 310 homeokinetic theory, 107 epilepsy, 163, 177 homogeneous connections, 344 equation of motion, 176 homologous muscles, 18 350 Index

Hopf bifurcation, 22 language, 269 hybrid oscillator, 330 language use, 262 hysteresis, 268 Laplacian matrix, 175, 176 limit cycle, 79, 328 imagination, 218, 219 limit cycles, 22 imitation, 263 linear dynamics, 162, 169 imperfect pitchfork bifurcation, 20, 21 local minima, 55 imperfect symmetry, 17 locked-in patients, 229 imperfection parameter, 13 locomotion, 45 imperfection parameters, 5 Lyapunov exponents, 162, 164–166, 169 in-phase, 4, 7, 215, 220, 327 in-phase coordination, 8, 9 macroscopic, 328 information, 45 magnetic field, 341 information processing, 211 magnetic fields, 138 inhibitory coupling, 119 magnetoencephalography, 340 initial bias, 36, 37 Magnetoencephalography (MEG), 137 initiation, 107 magnetoencephalography (MEG), 162, inphase, 309, 313 174 Instability, 205, 207, 209, 211, 213, 215, magnetometer, 341 217, 219, 221, 223, 225, 227 maintenance tendency, 286, 302 integral equation, 344 maximum overlap discrete wavelet integrated information, 254 transform (MODWT), 174 integration, 199 maxline, 269 interaction torques, 121 MEG, 209 interactional synchrony, 288, 291, 301 MEG-BCI, 232 interception, 55 membranes interhemispheric inhibition, 150 neuronal, 170 intermittency, 288 mesoscopic, 328 intermittent contacts, 115 mesoscopic level, 199 internal level, a biomechanical level and metabolism, 340 a parameter dynamic, 119 metronome frequency, 341 internal model, 46 mind, 183 Internal Models, 93 minimality principle, 23 internal models, 109 mirror movements, 150 interpersonal coordination, 214 model-independent approach, 3 interpersonal rhythmic coordination, monostable, 329 265 motor control, 77 intrapersonal rhythmic coordination, motor cortex, 138 265 motor equivalence, 96 intrinsic dynamics, 30, 33, 39–41 motor field, 139 invariance, 78 motor imagery, 218 invariants, 4 motor primitive, 78 inverse solutions, 143 motor processes, 218 ipsilateral movements, 150 Movement, 77 movement joint actions, 262 anti-phase, 171 in-phase, 171 landscape, 31 instability, 170 landscapes, 32 mirror, 170, 172, 173 Index 351

parallel, 170, 172, 173 neurorehabilitation, 247 preparation, 171 neurostimulation, 229 selection, 171 newborns, 166 stable, 162 nodes, 174, 175 temporal control, 171 noise, 53 timing, 171 nonlinear dynamics, 162–167, 169, 172, unstable, 162 173, 205 movement-evoked fields, 138 norm, 197 mu, 316 normal forms, 77 multi-joint coordination, 105 NREM sleep, 253 multi-sensory, 212 multi-stability, 206 object, 189 multimodal, 215 object recognition, 71 multimodal neuroimaging, 162, 173 obstacle avoidance, 47 multiple time scales, 188 one-dimensional model, 345 multistability, 268 online control, 53 muscle spindles, 97 onset phase, 117 muscle torque, 122 order parameter, 169, 205, 207 music, 205 frequency, 170 mutual dimension, 165, 169 order-parameter, 328 mutually inhibit, 116 oscillator dynamics, 329 oscillators, 176, 177 net torque, 122 networks P300-BCI, 232 adaptive reconfiguration, 173, 177 paradigm connections, 175, 176 bimanual motor coordination, 162, critical dynamics, 176, 177 170 dynamics, 175–177 motion control, 162 long-range connections, 176 parameter dynamic level, 111 small-world, 162, 174, 176, 177 parameter dynamics, 49, 124 neural activity, 340 parietal, 218 Neural and Biomechanical Constraints, parietal cortex, 212 121 Parkinson patients, 127 neural assemblies, 169, 170, 176 path formation, 45 neural context, 183 path length, 174, 176, 177 neural dynamics, 197 path planning, 46 neural field, 343 pathology neural oscillations, 141 neuro-, 163 Neural plasticity, 185 neuropsychiatric, 161, 177 neuro-feedback, 230 psycho-, 162 neuroanatomy, 161 pathophysiology, 166 neurodegenerative disorders, 177 Pattern Formation, 214 neuroleptic drugs, 162, 167 pattern generators, 116 neuroleptics pattern-energy factorization, 17 atypical, 169 patterns, 210 typical, 169 percent recurrence, 269 neuromarkers, 315 perception and action, 45 neurophysiology, 161 perception-action cycle, 211 neuroplasticity, 247 perceptual calibration, 97 352 Index perceptual space, 101 qualitative change, 332 perfect symmetry, 17 personal space, 70 Reaction, 213, 214 perturbation, 254, 257 reaction, 212 pharmacology, 161 Reaction times, 118 phase dynamics, 22 readiness field, 139 Phase Flow, 77 readiness potential, 137 phase relation, 332 reconfiguration phase shift, 10 spatial, 176 phase space, 77, 164, 165, 328 reflectional symmetry, 4 phase transition, 206, 283–285, 328 relative cerebral blood flow (rCBF), phase transitions, 20, 162, 170, 173, 170–172 177, 283 relative coordination, 290 phase wrapping, 332 relative phase, 4, 205, 215, 328 phase-coupled, 107 relaxation time, 7 phase-locking, 313, 314 repeller, 47 phenomenological and aggregated representations, 188 description, 23 rest, 166, 167, 173, 174 phi, 316 rhythmic, 211, 218, 221 phonemic category, 101 rhythmic movement, 85 right posterior parietal cortex, 191 population coding, 186 robotics, 55 position sense, 97 robots, 46 positron emission tomography, 189 route selection, 46 positron emission tomography (PET), 162, 170, 172 scale-invariant, 176 postural coordination, 214 scaling regime, 176 posture, 217 schizophrenia, 161–163, 166, 167, 169, potential (V) landscape, 29 177 potential field method, 55 altered connectivity, 162 potential function, 4, 15, 329 diagnosis, 167 potential landscape, 29 electrophysiology, 162 potential landscapes, 39 first episode, 167 potential well landscapes, 30 overt behavior, 162 potential wells, 7 treated, 162, 167, 169 power spectrum, 163–165 untreated, 162, 167, 169 prefrontal and parietal cortices, 125 segregation, 199 prefrontal cortex, 190 of neural systems, 161 premotor area (PMA), 171, 172 self-calibration, 98 premotor cortex, 218 self-organization, 170, 173 primary somatosensory hand area (S1), self-organized system, 205 172 self-similar, 162 primitives, 105 semiconnected, 184 Primitives of Action, 124 sensitive dependence on initial principal component analysis, 341 conditions, 164, 170, 172, 173 propagation velocity, 343 sensorimotor, 171, 341 proprioceptive feedback, 99, 138 sensorimotor coordination, 206, 215, psychiatric neuroscience, 162 334 pursuit strategy, 57 sensorimotor cortex, 151, 209 Index 353 sensory feedback, 211 superior temporal gyrus, 218 separatrix, 80 supplementary motor area, 125, 209 shared coordination dynamics, 209 supplementary motor area (SMA), 171, shared dynamical, 209 172 shortest path, 174 supramarginal gyrus sigmoidal function, 343 left, 171 simultaneously, 185 surrogate data, 165, 169 situational context, 187 switch skill learning, 319 behavioral, 162, 170 Sleep, 253 Switching Behavior, 63 Slow cortical potentials, 232 symmetries, 4 SMA, 209, 212, 216–219 symmetry, 5 smoothness criterion, 127 symmetry breaking, 11, 16, 332 SMR (sensorimotor rhythm), 232 symmetry sharing, 11 social coordination, 309, 313 synaptic firing rate, 170 social facilitation, 319 synchronizability, 176, 177 social integration, 319 Synchronization, 206 social segregation, 319 synchronization, 207, 209–214, 216, 219, social variables, 301 220, 342 space-time plot, 345 synchronized state, 176 spatial imperfection, 14 synchronizing, 218 Spatial imperfections, 15 syncopating, 218 spatial scales, 188 Syncopation, 207, 211 spatial visual pathways, 189 syncopation, 207, 209, 212, 213, 216, spatio-temporal pattern, 345 220, 342 spatio-temporal signal, 345 syncopation-synchronization paradigm, spectral analysis, 163, 165, 169 340 spectral power, 166, 169 synergetics, 169, 328 speech rhythms, 292, 294, 295 synthetic aperture magnetometry, 144 speed control, 60 spline interpolation tangent bifurcation, 64 surface, 166 task split-brain individual, 115 mental arithmetic, 167, 169 spurious attractors, 71 shape perception, 167, 169 SQuID, 341 synchronized tapping, 170, 173, 174, stability, 47, 211, 215, 217, 220 176, 177 stable fixed point, 64 Taxonomy, 77 state space, 78 temporal imperfection parameter, 14 steady-state, 312 temporal imperfections, 15 steering, 46 temporal symmetry, 9 steering dynamics, 55 thalamocortical complex, 254 stiffness, 48 thalamocortical system, 253 stochastic resonance, 299 thalamus, 194, 212, 218 structural equation modeling, 192 The Medial Temporal Lobe, 193 subconsciously, 253 threshold subcritical, 20 synchronization, 176, 177 subcritical pitchfork bifurcation, 5, 17, wavelet correlation, 174, 175 20 time series, 165 supercritical, 20 time-delay embedding, 164, 165 354 Index time-phase delays, 163 tremor, 107 time-to-contact, 49 tuning curves, 186 time-translational symmetry, 4 timing, 81 unimodal, 215 timing-power factorization, 17 unweighted summation, 119 TMS, 218, 254 TMS-evoked response, 255 van-der-Pol, 329 verbal transformation effect, 95 TMS-locked activity, 255 Virtual Environment, 48 top-down, 328 visual cognition topological equivalence, 80 dorsal pathway, 169 topological structures, 79 vocal gestures, 275 topology, 77, 173–177 voluntary movements, 137 trajectory curvature, 99 Trajectory Formation, 77 wakefulness, 253 transcranial magnetic stimulation, 149, wavelet correlation, 174 254 wavelet decomposition, 162 transcranial magnetic stimulation wavelet scale, 162, 174, 176, 177 (TMS), 162, 172, 173 wavelets, 174 transition Working Memory, 191 order/disorder, 176, 177 transitions, 311, 319 zotepine, 169 Understanding Complex Systems

Jirsa, V.K.; Kelso, J.A.S. (Eds.) Baglio, S.; Bulsara, A. (Eds.) Coordination Dynamics: Issues and Trends Device Applications of Nonlinear Dynamics XIV, 272 p. 2004 [978-3-540-20323-0] XI, 259 p. 2006 [978-3-540-33877-2]

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