9 research outputs found
Chaos Synchronization with Dynamic Filters: Two Way is Better Than One Way
Two chaotic systems which interact by mutually exchanging a signal built from
their delayed internal variables, can synchronize. A third unit may be able to
record and to manipulate the exchanged signal. Can the third unit synchronize
to the common chaotic trajectory, as well? If all parameters of the system are
public, a proof is given that the recording system can synchronize as well.
However, if the two interacting systems use private commutative filters to
generate the exchanged signal, a driven system cannot synchronize. It is shown
that with dynamic private filters the chaotic trajectory even cannot be
calculated. Hence two way (interaction) is more than one way (drive). The
implication of this general result to secret communication with chaos
synchronization is discussed
Synthetic reverberating activity patterns embedded in networks of cortical neurons
Synthetic reverberating activity patterns are experimentally generated by
stimulation of a subset of neurons embedded in a spontaneously active network
of cortical cells in-vitro. The neurons are artificially connected by means of
conditional stimulation matrix, forming a synthetic local circuit with a
predefined programmable connectivity and time-delays. Possible uses of this
experimental design are demonstrated, analyzing the sensitivity of these
deterministic activity patterns to transmission delays and to the nature of
ongoing network dynamics.Comment: 8 pages, 5 figure
Spiking Optical Patterns and Synchronization
We analyze the time resolved spike statistics of a solitary and two mutually
interacting chaotic semiconductor lasers whose chaos is characterized by
apparently random, short intensity spikes. Repulsion between two successive
spikes is observed, resulting in a refractory period which is largest at laser
threshold. For time intervals between spikes greater than the refractory
period, the distribution of the intervals follows a Poisson distribution. The
spiking pattern is highly periodic over time windows corresponding to the
optical length of the external cavity, with a slow change of the spiking
pattern as time increases. When zero-lag synchronization between the two lasers
is established, the statistics of the nearly perfectly matched spikes are not
altered. The similarity of these features to those found in complex interacting
neural networks, suggests the use of laser systems as simpler physical models
for neural networks
Public Channel Cryptography: Chaos Synchronization and Hilbert's Tenth Problem
The synchronization process of two mutually delayed coupled deterministic
chaotic maps is demonstrated both analytically and numerically. The
synchronization is preserved when the mutually transmitted signal is concealed
by two commutative private filters that are placed on each end of the
communication channel. We demonstrate that when the transmitted signal is a
convolution of the truncated time delayed output signals or some powers of the
delayed output signals synchronization is still maintained. The task of a
passive attacker is mapped onto Hilbert's tenth problem, solving a set of
nonlinear Diophantine equations, which was proven to be in the class of
NP-Complete problems. This bridge between two different disciplines,
synchronization in nonlinear dynamical processes and the realm of the NPC
problems, opens a horizon for a new type of secure public-channel protocols
Patterns of Chaos Synchronization
Small networks of chaotic units which are coupled by their time-delayed
variables, are investigated. In spite of the time delay, the units can
synchronize isochronally, i.e. without time shift. Moreover, networks can not
only synchronize completely, but can also split into different synchronized
sublattices. These synchronization patterns are stable attractors of the
network dynamics. Different networks with their associated behaviors and
synchronization patterns are presented. In particular, we investigate
sublattice synchronization, symmetry breaking, spreading chaotic motifs,
synchronization by restoring symmetry and cooperative pairwise synchronization
of a bipartite tree
Public-channel cryptography based on mutual chaos pass filters
We study the mutual coupling of chaotic lasers and observe both
experimentally and in numeric simulations, that there exists a regime of
parameters for which two mutually coupled chaotic lasers establish isochronal
synchronization, while a third laser coupled unidirectionally to one of the
pair, does not synchronize. We then propose a cryptographic scheme, based on
the advantage of mutual-coupling over unidirectional coupling, where all the
parameters of the system are public knowledge. We numerically demonstrate that
in such a scheme the two communicating lasers can add a message signal
(compressed binary message) to the transmitted coupling signal, and recover the
message in both directions with high fidelity by using a mutual chaos pass
filter procedure. An attacker however, fails to recover an errorless message
even if he amplifies the coupling signal
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Automated long-term recording and analysis of neural activity in behaving animals
Addressing how neural circuits underlie behavior is routinely done by measuring electrical activity from single neurons in experimental sessions. While such recordings yield snapshots of neural dynamics during specified tasks, they are ill-suited for tracking single-unit activity over longer timescales relevant for most developmental and learning processes, or for capturing neural dynamics across different behavioral states. Here we describe an automated platform for continuous long-term recordings of neural activity and behavior in freely moving rodents. An unsupervised algorithm identifies and tracks the activity of single units over weeks of recording, dramatically simplifying the analysis of large datasets. Months-long recordings from motor cortex and striatum made and analyzed with our system revealed remarkable stability in basic neuronal properties, such as firing rates and inter-spike interval distributions. Interneuronal correlations and the representation of different movements and behaviors were similarly stable. This establishes the feasibility of high-throughput long-term extracellular recordings in behaving animals