412 research outputs found
Experiments with a Malkus-Lorenz water wheel: Chaos and Synchronization
We describe a simple experimental implementation of the Malkus-Lorenz water
wheel. We demonstrate that both chaotic and periodic behavior is found as wheel
parameters are changed in agreement with predictions from the Lorenz model. We
furthermore show that when the measured angular velocity of our water wheel is
used as an input signal to a computer model implementing the Lorenz equations,
high quality chaos synchronization of the model and the water wheel is
achieved. This indicates that the Lorenz equations provide a good description
of the water wheel dynamics.Comment: 12 pages, 7 figures. The following article has been accepted by the
American Journal of Physics. After it is published, it will be found at
http://scitation.aip.org/ajp
Quantifying Spatiotemporal Chaos in Rayleigh-B\'enard Convection
Using large-scale parallel numerical simulations we explore spatiotemporal
chaos in Rayleigh-B\'enard convection in a cylindrical domain with
experimentally relevant boundary conditions. We use the variation of the
spectrum of Lyapunov exponents and the leading order Lyapunov vector with
system parameters to quantify states of high-dimensional chaos in fluid
convection. We explore the relationship between the time dynamics of the
spectrum of Lyapunov exponents and the pattern dynamics. For chaotic dynamics
we find that all of the Lyapunov exponents are positively correlated with the
leading order Lyapunov exponent and we quantify the details of their response
to the dynamics of defects. The leading order Lyapunov vector is used to
identify topological features of the fluid patterns that contribute
significantly to the chaotic dynamics. Our results show a transition from
boundary dominated dynamics to bulk dominated dynamics as the system size is
increased. The spectrum of Lyapunov exponents is used to compute the variation
of the fractal dimension with system parameters to quantify how the underlying
high-dimensional strange attractor accommodates a range of different chaotic
dynamics
Synchronous Behavior of Two Coupled Electronic Neurons
We report on experimental studies of synchronization phenomena in a pair of
analog electronic neurons (ENs). The ENs were designed to reproduce the
observed membrane voltage oscillations of isolated biological neurons from the
stomatogastric ganglion of the California spiny lobster Panulirus interruptus.
The ENs are simple analog circuits which integrate four dimensional
differential equations representing fast and slow subcellular mechanisms that
produce the characteristic regular/chaotic spiking-bursting behavior of these
cells. In this paper we study their dynamical behavior as we couple them in the
same configurations as we have done for their counterpart biological neurons.
The interconnections we use for these neural oscillators are both direct
electrical connections and excitatory and inhibitory chemical connections: each
realized by analog circuitry and suggested by biological examples. We provide
here quantitative evidence that the ENs and the biological neurons behave
similarly when coupled in the same manner. They each display well defined
bifurcations in their mutual synchronization and regularization. We report
briefly on an experiment on coupled biological neurons and four dimensional ENs
which provides further ground for testing the validity of our numerical and
electronic models of individual neural behavior. Our experiments as a whole
present interesting new examples of regularization and synchronization in
coupled nonlinear oscillators.Comment: 26 pages, 10 figure
Dynamical Encoding by Networks of Competing Neuron Groups: Winnerless Competition
Following studies of olfactory processing in insects and fish, we investigate neural networks whose dynamics in phase space is represented by orbits near the heteroclinic connections between saddle regions (fixed points or limit cycles). These networks encode input information as trajectories along the heteroclinic connections. If there are N neurons in the network, the capacity is approximately e(N-1)!, i.e., much larger than that of most traditional network structures. We show that a small winnerless competition network composed of FitzHugh-Nagumo spiking neurons efficiently transforms input information into a spatiotemporal output
Modeling of Spiking-Bursting Neural Behavior Using Two-Dimensional Map
A simple model that replicates the dynamics of spiking and spiking-bursting
activity of real biological neurons is proposed. The model is a two-dimensional
map which contains one fast and one slow variable. The mechanisms behind
generation of spikes, bursts of spikes, and restructuring of the map behavior
are explained using phase portrait analysis. The dynamics of two coupled maps
which model the behavior of two electrically coupled neurons is discussed.
Synchronization regimes for spiking and bursting activity of these maps are
studied as a function of coupling strength. It is demonstrated that the results
of this model are in agreement with the synchronization of chaotic
spiking-bursting behavior experimentally found in real biological neurons.Comment: 9 pages, 12 figure
Self-consistent Pomeranchon coupling ratios in the multiperipheral model
Given the two leading eigenvalues and eigenfunctions of the resonance (low-subenergy) component of a multiperipheral kernel and assuming lower eigenvalues to be unimportant, it is shown how the mixture corresponding to the Pomeranchon eigenfunction may be calculated from considerations of self-consistency. The method is illustrated in a multiperipheral model with pseudoscalar-meson links by associating the two leading unperturbed eigenstates with the 2+ particles f(1260) and f′(1514)
- …