Complex dynamics is abolished in delayed recurrent systems with distributed feedback times

Thiel, Andreas; Schwegler, Helmut; Eurich, Christian W.

doi:10.1002/cplx.10087

Cited by 29 publications

(21 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Eurich et al showed that dynamical systems converge to a stabilizing state and a simpler dynamical pattern with more uniformly distributed delay [10]. Several other studies showed similar results that distributed delay yields stabilizing state and simpler dynamical pattern [20,19,14]. Furthermore, networks with random delay were shown to have steady-state synchronization in coupled chaotic maps whereas those with fixed delay were shown to have chaotic synchronization [15].…”

Section: Research On Delaymentioning

confidence: 89%

See 1 more Smart Citation

Effects of varying the delay distribution in random, scale-free, and small-world networks

Jang

Mann

Choe

2008

2008 IEEE International Conference on Granular Computing

View full text Add to dashboard Cite

Graph-theory-based approaches have been used with great success when analyzing abstract properties of natural and artificial networks. However, these approaches have not factored in delay, which plays an important role in real-world networks. In this paper, we (1) developed a simple yet powerful method to include delay in graphbased analysis of networks, and (2) evaluated how different classes of networks (random, scale-free, and small-world) behave under different forms of delay (peaked, unimodal, or uniform delay distribution). We compared results from synthetically generated networks using two different sets of algorithms for network construction. In the first approach (naive), we generated directed graphs following the literal definition of the three types of networks. In the second approach (modified conventional), we adapted methods by Erdös-Rényi (random), Barabasi (scale-free), and WattsStrogatz (small-world). With these networks, we investigated the effect of adding and varying the delay distribution. As a measure of robustness to added delay, we calculated the ratio between the sum of shortest path length between every node. Our main findings show that different types of network show different levels of robustness, but the shape of the delay distribution has more influence on the overall result, where uniformly randomly distributed delay showed the most robust result. Other network parameters such as neighborhood size in small-world networks were also found to play a key role in delay tolerance. These results are expected to extend our understanding of the relationship between network structure and delay.

show abstract

Section: Research On Delaymentioning

confidence: 89%

“…Networks must deal with delay which may vary for each connection. So far, only few studies have included time delay in dynamic network analysis [20,1,10,15,19,17]. These studies typically use delay differential equations.…”

Section: Introductionmentioning

confidence: 99%

Effects of varying the delay distribution in random, scale-free, and small-world networks

Jang

Mann

Choe

2008

2008 IEEE International Conference on Granular Computing

View full text Add to dashboard Cite

show abstract

“…Simply calculating the delay distribution can already provide great insights into brain function. For example, [51] showed that the complexity of network dynamics critically depends on the delay distribution. Also see [52] on the relationship between neuroanatomy and brain dynamics.…”

Section: Graph Theoretical Analysismentioning

confidence: 99%

Knife-edge scanning microscopy for connectomics research

Choe

Mayerich

Kwon

et al. 2011

The 2011 International Joint Conference on Neural Networks

View full text Add to dashboard Cite

In this paper, we will review a novel microscopy modality called Knife-Edge Scanning Microscopy (KESM) that we have developed over the past twelve years (since 1999) and discuss its relevance to connectomics and neural networks research. The operational principle of KESM is to simultaneously section and image small animal brains embedded in hard polymer resin so that a near-isotropic, sub-micrometer voxel size of 0.6 µm × 0.7 µm × 1.0 µm can be achieved over ∼1 cm 3 volume of tissue which is enough to hold an entire mouse brain. At this resolution, morphological details such as dendrites, dendritic spines, and axons are visible (for sparse stains like Golgi). KESM has been successfully used to scan whole mouse brains stained in Golgi (neuronal morphology), Nissl (somata), and India ink (vasculature), providing unprecedented insights into the system-level architectural layout of microstructures within the mouse brain. In this paper, we will present whole-brain-scale data sets from KESM and discuss challenges and opportunities posed to connectomics and neural networks research by such detailed yet system-level data.

show abstract

“…Models with distributed delay have been developed mostly in applications to population biology and epidemiology. Examples include the work of Thiel et al [43] on how distributed delays may abolish complex dynamics present with fixed delays, work on blood cell population models [1,2,5], chemostat models [27,38,45,46], epidemic models [3], ecological models [4,11,19,36], and enzyme kinetics [20]. More examples can be found in the references within these papers.…”

Section: Introductionmentioning

confidence: 99%

Approximating the stability region of a neural network with a general distribution of delays

Jessop

Campbell

2010

Neural Networks

View full text Add to dashboard Cite

We investigate the linear stability of a neural network with distributed delay, where the neurons are identical. We examine the stability of a symmetrical equilibrium point via the analysis of the characteristic equation both when the connection matrix is symmetric and when it is not. We determine a mean delay and distribution independent stability region. We then illustrate a way of improving on this conservative result by approximating the true region of stability when the actual distribution is not known, but some moments or cumulants of the distribution are. Finally, we compare the approximate stability regions with the stability regions in the case of the uniform and gamma distributions. We show that the approximations improve as more moments or cumulants are used, and that the approximations using cumulants give better results than the ones using moments.

show abstract

Complex dynamics is abolished in delayed recurrent systems with distributed feedback times

Abstract: Feedback systems with a single delay time-as described by delay-differential equations

Cited by 29 publications

References 15 publications

Effects of varying the delay distribution in random, scale-free, and small-world networks

Effects of varying the delay distribution in random, scale-free, and small-world networks

Knife-edge scanning microscopy for connectomics research

Approximating the stability region of a neural network with a general distribution of delays

Contact Info

Product

Resources

About