NOISE-INDUCED FIRST-ORDER PHASE TRANSITIONS IN CHAOTIC BRAIN ACTIVITY

1999 ◽  
Vol 09 (11) ◽  
pp. 2215-2218 ◽  
Author(s):  
WALTER J. FREEMAN
Keyword(s):  
Degrees Of Freedom ◽  
Brain Activity ◽  
Reaction Diffusion ◽  
Normative Values ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Wave Forms ◽  
Sensory Cortices ◽  
Low Dimensional ◽  
First Order Phase

Brain electrical activity in animals during normal behaviors has aperiodic wave forms suggesting its origin in chaotic dynamics. Attempts at finding experimental proofs using low-dimensional, deterministic chaotic models have not succeeded. The assumptions of autonomy, stationarity,and noise-free operation that are needed to define these at tractors and their embedding dimensions have been shown not to hold for brains, because numerical estimates of correlation dimensions and Lyapunov exponents have failed to converge to normative values. Analysis of EEGs from sensory cortices show that a very different model applies to brains, which is more closely related to lasers than models of twist–flip maps and reaction–diffusion systems. Neurons interact with each other through channels with nonlinear, amplitude-dependent gains, by which they form fields of white noise. When the strengths of interaction are increased by input from receptors, the neurons interact more strongly and lose their high degrees of freedom. The macroscopic constraint on their activity appears as an order parameter in the form of spatially coherent, indeterministic chaos.

scholarly journals Exact Solutions of Low-Dimensional Reaction-Diffusion Systems

1997 ◽  
Vol 11 (01n02) ◽  
pp. 109-114 ◽  
Author(s):  
António M. R. Cadilhe ◽  
M. Lawrence Glasser ◽  
Vladimir Privman
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Reaction Diffusion ◽  
Single Species ◽  
Exact Results ◽  
Reaction Diffusion Systems ◽  
Diffusion Limited ◽  
Diffusion Systems ◽  
Novel Method ◽  
Low Dimensional

We briefly review some common diffusion-limited reactions with emphasis on results for two-species reactions with anisotropic hopping. Our review also covers single-species reactions. The scope is that of providing reference and general discussion rather than details of methods and results. Recent exact results for a two-species model with anisotropic hopping and with 'sticky' interaction of like particles, obtained by a novel method which allows exact solution of certain single-species and two-species reactions, are discussed.

MULTIPARTICLE LATTICE GAS AUTOMATA FOR REACTION DIFFUSION SYSTEMS

1994 ◽  
Vol 05 (01) ◽  
pp. 47-63 ◽  
Author(s):  
BASTIEN CHOPARD ◽  
LAURENT FRACHEBOURG ◽  
MICHEL DROZ
Keyword(s):  
Degrees Of Freedom ◽  
Lattice Gas ◽  
Diffusion Processes ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Lattice Gas Automata ◽  
Diffusion Systems ◽  
Diffusion Phenomena ◽  
New Algorithms ◽  
Number Of Particles

Lattice gas automata are a powerful tool to model reaction-diffusion processes. However, the evolution rules limit the number of particles that can be present at each lattice site. This restriction is often a strong limitation to modelling several reaction-diffusion phenomena and, also, lead to very noisy numerical simulations. We propose and study new algorithms which allow for an arbitrary number of particle, while keeping the benefits of the cellular automata approach (close to a microscopic level of description, deal correctly with all degrees of freedom, and is numerically exact).

A review and guidance for pattern selection in spatiotemporal system

2018 ◽  
Vol 32 (06) ◽  
pp. 1830003 ◽  
Author(s):  
Chunni Wang ◽  
Jun Ma
Keyword(s):  
Pattern Formation ◽  
Reaction Diffusion ◽  
Stability Control ◽  
External Stimulus ◽  
Multi Agent Systems ◽  
Reaction Diffusion Systems ◽  
Collective Response ◽  
Diffusion Systems ◽  
Multi Agent ◽  
Low Dimensional

Pattern estimation and selection in media can give important clues to understand the collective response to external stimulus by detecting the observable variables. Both reaction–diffusion systems (RDs) and neuronal networks can be treated as multi-agent systems from molecular level, intrinsic cooperation, competition. An external stimulus or attack can cause collapse of spatial order and distribution, while appropriate noise can enhance the consensus in the spatiotemporal systems. Pattern formation and synchronization stability can bridge isolated oscillators and the network by coupling these nodes with appropriate connection types. As a result, the dynamical behaviors can be detected and discussed by developing different spatial patterns and realizing network synchronization. Indeed, the collective response of network and multi-agent system depends on the local kinetics of nodes and cells. It is better to know the standard bifurcation analysis and stability control schemes before dealing with network problems. In this review, dynamics discussion and synchronization control on low-dimensional systems, pattern formation and synchronization stability on network, wave stability in RDs and neuronal network are summarized. Finally, possible guidance is presented when some physical effects such as polarization field and electromagnetic induction are considered.

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