Chaotic itinerancy

Chaotic itinerancy is universal dynamics in high-dimensional dynamical systems, showing itinerant motion among varieties of low-dimensional ordered states through high-dimensional chaos. Discovery, basic features, characterization, examples, and significance of chaotic itinerancy are surveyed.

[1]  J. L. Hudson,et al.  Experiments on arrays of globally coupled chaotic electrochemical oscillators: Synchronization and clustering. , 2000, Chaos.

[2]  K. Ikeda,et al.  Isothermal dynamics simulations of spontaneous alloying in a microcluster , 2002 .

[3]  C. Furusawa,et al.  Theory of robustness of irreversible differentiation in a stem cell system: chaos hypothesis. , 2000, Journal of theoretical biology.

[4]  H. Nozawa,et al.  Solution of the optimization problem using the neural network model as a globally coupled map , 1994 .

[5]  Hideki Tanaka,et al.  Potential energy surfaces for water dynamics. II. Vibrational mode excitations, mixing, and relaxations , 1990 .

[6]  Kunihiko Kaneko,et al.  Globally coupled circle maps , 1991 .

[7]  Martin Ackermann,et al.  Evolution of cooperation: Two for One? , 2004, Current Biology.

[8]  Kazuyuki Aihara,et al.  Associative Dynamics in a Chaotic Neural Network , 1997, Neural Networks.

[9]  Ichiro Tsuda,et al.  Memory Dynamics in Asynchronous Neural Networks , 1987 .

[10]  Fischer,et al.  Fast pulsing and chaotic itinerancy with a drift in the coherence collapse of semiconductor lasers. , 1996, Physical review letters.

[11]  W. Singer,et al.  Synchronization of oscillatory neuronal responses in cat striate cortex: Temporal properties , 1992, Visual Neuroscience.

[12]  Edward Ott,et al.  A physical system with qualitatively uncertain dynamics , 1993, Nature.

[13]  W. Freeman,et al.  How brains make chaos in order to make sense of the world , 1987, Behavioral and Brain Sciences.

[14]  W. Freeman.  Simulation of chaotic EEG patterns with a dynamic model of the olfactory system , 1987, Biological Cybernetics.

[15]  Kunihiko Kaneko,et al.  On the strength of attractors in a high-dimensional system: Milnor attractor network, robust global attraction, and noise-induced selection , 1998, chao-dyn/9802016.

[16]  I. Tsuda,et al.  Extended information in one-dimensional maps , 1987 .

[17]  Shinjo.  Formation of a glassy solid by computer simulation. , 1989, Physical review. B, Condensed matter.

[18]  Giacomelli,et al.  Experimental evidence of chaotic itinerancy and spatiotemporal chaos in optics. , 1990, Physical review letters.

[19]  P. Grassberger,et al.  Symmetry breaking bifurcation for coupled chaotic attractors , 1991 .

[20]  K. Kaneko.  Dominance of Milnor attractors in globally coupled dynamical systems with more than 7+/-2 degrees of freedom. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Masahide Kimoto,et al.  Weather Regimes, Low-Frequency Oscillations, and Principal Patterns of Variability: A Perspective of Extratropical Low-Frequency Variability , 1999 .

[22]  T. Ikegami,et al.  Homeochaos: dynamic stability of a symbiotic network with population dynamics and evolving mutation rates , 1992 .

[23]  Kunihiko Kaneko,et al.  Clustered motion in symplectic coupled map systems , 1992 .

[24]  P. Holmes,et al.  Structurally stable heteroclinic cycles , 1988, Mathematical Proceedings of the Cambridge Philosophical Society.

[25]  I. Stewart,et al.  Bubbling of attractors and synchronisation of chaotic oscillators , 1994 .

[26]  Otsuka.  Self-induced phase turbulence and chaotic itinerancy in coupled laser systems. , 1990, Physical review letters.

[27]  J. Milnor.  On the concept of attractor , 1985 .

[28]  Kaneko.  Global traveling wave triggered by local phase slips. , 1992, Physical review letters.

[29]  K. Kaneko.  Dominance of Milnor Attractors and Noise-Induced Selection in a Multiattractor System , 1997 .

[30]  Ichiro Tsuda,et al.  Mathematical description of brain dynamics in perception and action , 1999 .

[31]  Eizo Akiyama,et al.  Evolution of cooperation, differentiation, complexity, and diversity in an iterated three-person game , 1995 .

[32]  Kunihiko Kaneko,et al.  Complex Systems: Chaos and Beyond: A Constructive Approach with Applications in Life Sciences , 2000 .

[33]  Kunihiko Kaneko,et al.  Information cascade with marginal stability in a network of chaotic elements , 1994 .

[34]  C Grebogi,et al.  Preference of attractors in noisy multistable systems. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[35]  B. Baars,et al.  Toward an interpretation of dynamic neural activity in terms of chaotic dynamical systems , 2005 .

[36]  K. Ikeda,et al.  Maxwell-Bloch Turbulence , 1989 .

[37]  Kunihiko Kaneko,et al.  Rayleigh-Be´nard convection: pattern, chaos, spatiotemporal chaos and turbulence , 1995 .

[38]  Ichiro Tsuda,et al.  Neocortical gap junction-coupled interneuron systems may induce chaotic behavior itinerant among quasi-attractors exhibiting transient synchrony , 2004, Neurocomputing.

[39]  Josef Hofbauer,et al.  Evolutionary Games and Population Dynamics: Asymmetric games , 1998 .

[40]  K. Kaneko.  Clustering, coding, switching, hierarchical ordering, and control in a network of chaotic elements , 1990 .

[41]  Tsuyoshi Chawanya,et al.  Coexistence of infinitely many attractors in a simple flow , 1997 .

[42]  W. Freeman.  Societies of Brains: A Study in the Neuroscience of Love and Hate. By W. J. Freeman. Erlbaum: Hillsdale, NJ. 1994. , 1997, Psychological Medicine.

[43]  Ichiro Tsuda,et al.  Information theoretical approach to noisy dynamics , 1985 .

[44]  Masaki Sano,et al.  Phase Wave in a Cellular Structure , 1993 .

[45]  R Huerta,et al.  Dynamical encoding by networks of competing neuron groups: winnerless competition. , 2001, Physical review letters.

[46]  István Z Kiss,et al.  Collective dynamics of chaotic chemical oscillators and the law of large numbers. , 2002, Physical review letters.

[47]  Kunihiko Kaneko,et al.  Recursiveness, switching, and fluctuations in a replicating catalytic network. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[48]  Naoteru Gouda,et al.  Chaotic Itinerancy and Thermalization in a One-Dimensional Self-Gravitating System , 1997 .

[49]  Masahide Kimoto,et al.  Chaotic itinerancy with preferred transition routes appearing in an atmospheric model , 1997 .

[50]  Ichiro Tsuda,et al.  Dynamic link of memory--Chaotic memory map in nonequilibrium neural networks , 1992, Neural Networks.

[51]  Walter J. Freeman,et al.  Reafference and Attractors in the Olfactory System During Odor Recognition , 1996, Int. J. Neural Syst..

[52]  I. Tsuda,et al.  Calculation of information flow rate from mutual information , 1988 .