2,596 research outputs found
Chimera states in networks of Van der Pol oscillators with hierarchical connectivities
This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Chaos 26, 094825 (2016) and may be found at https://doi.org/10.1063/1.4962913.Chimera states are complex spatio-temporal patterns that consist of coexisting domains of coherent and incoherent dynamics. We analyse chimera states in ring networks of Van der Pol oscillators with hierarchical coupling topology. We investigate the stepwise transition from a nonlocal to a hierarchical topology and propose the network clustering coefficient as a measure to establish a link between the existence of chimera states and the compactness of the initial base pattern of a hierarchical topology; we show that a large clustering coefficient promotes the occurrence of chimeras. Depending on the level of hierarchy and base pattern, we obtain chimera states with different numbers of incoherent domains. We investigate the chimera regimes as a function of coupling strength and nonlinearity parameter of the individual oscillators. The analysis of a network with larger base pattern resulting in larger clustering coefficient reveals two different types of chimera states and highlights the increasing role of amplitude dynamics.
Chimera states are an example of intriguing partial synchronization patterns appearing in networks of identical oscillators. They exhibit a hybrid structure combining coexisting spatial domains of coherent (synchronized) and incoherent (desynchronized) dynamics.1,2 Recent studies have demonstrated the emergence of chimera states in a variety of topologies and for different types of individual dynamics. In this paper, we analyze chimera states in networks with complex coupling topologies arising in neuroscience. We provide a systematic analysis of the transition from nonlocal to hierarchical (quasi-fractal) connectivities in ring networks of identical Van der Pol oscillators and use the clustering coefficient and the symmetry properties to classify different topologies with respect to the occurrence of chimera states. We show that symmetric connectivities with large clustering coefficients promote the emergence of chimera states, while they are suppressed by slight topological asymmetries or small clustering coefficient.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzept
Structure of Cell Networks Critically Determines Oscillation Regularity
Biological rhythms are generated by pacemaker organs, such as the heart
pacemaker organ (the sinoatrial node) and the master clock of the circadian
rhythms (the suprachiasmatic nucleus), which are composed of a network of
autonomously oscillatory cells. Such biological rhythms have notable
periodicity despite the internal and external noise present in each cell.
Previous experimental studies indicate that the regularity of oscillatory
dynamics is enhanced when noisy oscillators interact and become synchronized.
This effect, called the collective enhancement of temporal precision, has been
studied theoretically using particular assumptions. In this study, we propose a
general theoretical framework that enables us to understand the dependence of
temporal precision on network parameters including size, connectivity, and
coupling intensity; this effect has been poorly understood to date. Our
framework is based on a phase oscillator model that is applicable to general
oscillator networks with any coupling mechanism if coupling and noise are
sufficiently weak. In particular, we can manage general directed and weighted
networks. We quantify the precision of the activity of a single cell and the
mean activity of an arbitrary subset of cells. We find that, in general
undirected networks, the standard deviation of cycle-to-cycle periods scales
with the system size as , but only up to a certain system size
that depends on network parameters. Enhancement of temporal precision is
ineffective when . We also reveal the advantage of long-range
interactions among cells to temporal precision
Incremental embodied chaotic exploration of self-organized motor behaviors with proprioceptor adaptation
This paper presents a general and fully dynamic embodied artificial neural system, which incrementally explores and learns motor behaviors through an integrated combination of chaotic search and reflex learning. The former uses adaptive bifurcation to exploit the intrinsic chaotic dynamics arising from neuro-body-environment interactions, while the latter is based around proprioceptor adaptation. The overall iterative search process formed from this combination is shown to have a close relationship to evolutionary methods. The architecture developed here allows realtime goal-directed exploration and learning of the possible motor patterns (e.g., for locomotion) of embodied systems of arbitrary morphology. Examples of its successful application to a simple biomechanical model, a simulated swimming robot, and a simulated quadruped robot are given. The tractability of the biomechanical systems allows detailed analysis of the overall dynamics of the search process. This analysis sheds light on the strong parallels with evolutionary search
Mechanisms of Zero-Lag Synchronization in Cortical Motifs
Zero-lag synchronization between distant cortical areas has been observed in
a diversity of experimental data sets and between many different regions of the
brain. Several computational mechanisms have been proposed to account for such
isochronous synchronization in the presence of long conduction delays: Of
these, the phenomenon of "dynamical relaying" - a mechanism that relies on a
specific network motif - has proven to be the most robust with respect to
parameter mismatch and system noise. Surprisingly, despite a contrary belief in
the community, the common driving motif is an unreliable means of establishing
zero-lag synchrony. Although dynamical relaying has been validated in empirical
and computational studies, the deeper dynamical mechanisms and comparison to
dynamics on other motifs is lacking. By systematically comparing
synchronization on a variety of small motifs, we establish that the presence of
a single reciprocally connected pair - a "resonance pair" - plays a crucial
role in disambiguating those motifs that foster zero-lag synchrony in the
presence of conduction delays (such as dynamical relaying) from those that do
not (such as the common driving triad). Remarkably, minor structural changes to
the common driving motif that incorporate a reciprocal pair recover robust
zero-lag synchrony. The findings are observed in computational models of
spiking neurons, populations of spiking neurons and neural mass models, and
arise whether the oscillatory systems are periodic, chaotic, noise-free or
driven by stochastic inputs. The influence of the resonance pair is also robust
to parameter mismatch and asymmetrical time delays amongst the elements of the
motif. We call this manner of facilitating zero-lag synchrony resonance-induced
synchronization, outline the conditions for its occurrence, and propose that it
may be a general mechanism to promote zero-lag synchrony in the brain.Comment: 41 pages, 12 figures, and 11 supplementary figure
Form Follows Function: A Different Approach to Neuron Connectivity
It may be possible to discover much of the organization of synaptic
connections in nervous systems by designing simple logic circuits that can
perform a single, biologically advantageous function. This method has led to
neuronal networks that can generate neural correlates of phenomena central to
color vision, olfaction, short-term memory, and brain waves. One of the network
designs is a family of general information processors that exhibit major
features of cerebral cortex physiology and anatomy. A similar logic circuit
approach applied to two primitive ganglia that have been studied extensively
led to discoveries of how the ganglia can produce lobster peristaltic action
and lamprey locomotion.
For each network design, all neurons, connections, and types of connections
are shown explicitly. The neurons' operation depends only on explicitly stated,
minimal properties of excitement and inhibition. This operation is dynamic in
the sense that the level of neuron activity is the only cellular change, making
the networks' operation consistent with the speed of most brain functions.
Conclusions that the networks can generate neural correlates of known phenomena
are not claims; they are theorems that follow from the models' explicit
architectures and minimal neuron capabilities.
The logic circuit designs can be implemented with electronic components. A
few of the designs are apparently new to engineering, filling gaps and
providing improvements in well-known families of logic circuits. A novel
transformation can convert certain electronic logic circuit designs to neuronal
network designs, and vice versa
- …