Dynamics of FitzHugh-Nagumo excitable systems with delayed coupling

Small lattices of $N$ nearest neighbor coupled excitable FitzHugh-Nagumo systems, with time-delayed coupling are studied, and compared with systems of FitzHugh-Nagumo oscillators with the same delayed coupling. Bifurcations of equilibria in N=2 case are studied analytically, and it is then numerically confirmed that the same bifurcations are relevant for the dynamics in the case $N>2$. Bifurcations found include inverse and direct Hopf and fold limit cycle bifurcations. Typical dynamics for different small time-lags and coupling intensities could be excitable with a single globally stable equilibrium, asymptotic oscillatory with symmetric limit cycle, bi-stable with stable equilibrium and a symmetric limit cycle, and again coherent oscillatory but non-symmetric and phase-shifted. For an intermediate range of time-lags inverse sub-critical Hopf and fold limit cycle bifurcations lead to the phenomenon of oscillator death. The phenomenon does not occur in the case of FitzHugh-Nagumo oscillators with the same type of coupling.Comment: accepted by Phys.Rev.

Synchronization in a System of Globally Coupled Oscillators with Time Delay

We study the synchronization phenomena in a system of globally coupled oscillators with time delay in the coupling. The self-consistency equations for the order parameter are derived, which depend explicitly on the amount of delay. Analysis of these equations reveals that the system in general exhibits discontinuous transitions in addition to the usual continuous transition, between the incoherent state and a multitude of coherent states with different synchronization frequencies. In particular, the phase diagram is obtained on the plane of the coupling strength and the delay time, and ubiquity of multistability as well as suppression of the synchronization frequency is manifested. Numerical simulations are also performed to give consistent results

On Phase Transitions in Learning Sparse Networks

In this paper [1] we study the identification of sparse interaction networks, from a given set of observations, as a machine learning problem. An example of such a network is a sparse gene-protein interaction network, for more details see [2]. Sparsity means that we are provided with a small data set and a high number of unknown components of the system, most of which are zero. Under these circumstances, a model needs to be learned that fits the underlying system, capable of generalization. This corresponds to the student-teacher setting in machine learning. In some engineering applications, the number of measurements M available for system identification and model validation is much smaller than the system order N, which represents the number of components. This substantial lack of data can give rise to an identifiability problem, in which case a larger subset of the model class is entirely consistent with the observed data so that no unique model can be proposed. Since conventional techniques for system identification are not well suited to deal with such situations, it thus becomes important to work around this by exploiting as much additional information as possible about the underlying system. In particular, we are interested i

Optimizing topology and parameters of gene regulatory network models from time-series experiments

Abstract. In this paper we address the problem of finding gene regulatory networks from experimental DNA microarray data. Different approaches to infer the dependencies of gene regulatory networks by identifying parameters of mathematical models like complex S-systems or simple Random Boolean Networks can be found in literature. Due to the complexity of the inference problem some researchers suggested Evolutionary Algorithms for this purpose. We introduce enhancements to the Evolutionary Algorithm optimization process to infer the parameters of the non-linear system given by the observed data more reliably and precisely. Due to the limited number of available data the inferring problem is under-determined and ambiguous. Further on, the problem often is multi-modal and therefore appropriate optimization strategies become necessary. We propose a new method, which evolves the topology as well as the parameters of the mathematical model to find the correct network.

Numbers and age standardized rates of in situ cervix uteri by year of diagnosis, and histologic type, Korea, 1993–2009.

1<p>ASR: Age-standardized rates.</p>2<p>EAPC: Estimated annual percent change.</p

Hub Gene Selection Methods for the Reconstruction of Transcription Networks

Contains fulltext : 84448.pdf (publisher's version ) (Closed access

Jamming and correlation patterns in traffic of information on sparse modular networks

89.75.Hc Networks and genealogical trees, 05.40.Ca Noise, 02.70.-c Computational techniques; simulations,

Lifetime of the incoherent state of coupled phase oscillators

In this paper we have studied the relaxation of the incoherent state to the coherent state of coupled phase oscillators with time delay in terms of lifetime of the incoherent state both in the presence and absence of noise. To make the present study general we have considered both Gaussian and non Gaussian noises. Our investigation shows that the mean lifetime (MLT) decreases exponentially as the coupling strength among the oscillators grows. It also shows that MLT changes non monotonically with an increase in time delay. Another observation is that the mean lifetime increases exponentially as a function of noise strength for white noise. However, for colour noise, it grows linearly with an increase in noise strength. Enhancement of the correlation time of the coloured noise suppresses MLT. The rate of suppression is faster for non-Gaussian noise compared to the Gaussian case. Finally, we have observed that the mean lifetime increases exponentially as the noise behaviour deviates more from the Gaussian characteristics