Bifurcation Analysis of Wilson-Cowan Model with Singular Impulses

2021-01-01
Çağ, Sabahattin
Akhmet, Marat
The paper concerns with Wilson-Cowan neural model. The main novelty of the study is that besides the traditional singularity of the model, we consider singular impulses. A new technique of analysis of the phenomenon is suggested. This allows to consider the existence of solutions of the model and bifurcation in ultimate neural behavior observed through numerical simulations. The bifurcations are reasoned by impulses and singularity in the model and they concern the structure of attractors, which consist of newly introduced sets in the phase space such that medusas and rings.
Discontinuity, Nonlinearity, and Complexity

Suggestions

A low-order nonlinear amplifier model with distributed delay terms
YÜZER, AHMET HAYRETTİN; Demir, Şimşek (The Scientific and Technological Research Council of Turkey, 2014-01-01)
In this paper, a novel behavioral modeling technique for the characterization of memory effects of amplifiers is proposed. This characterization utilizes asymmetric intermodulation distortion (IMD)components, which are the result of a 2-tone excitation of a nonlinear amplifier. These asymmetric IMD components are represented basically by a power series, where each term in the series has its own time delay term. These time delay terms successfully justify the presence of asymmetry in the intermodulation comp...
Discrete parameter Nonlinear Constrained Optimization of a Gear Train by Genetic Algorithms
Dölen, Melik; Seıreg, Alı (2005-01-01)
This paper investigates the optimal design of a four-stage gear train using genetic algorithms. Five different genetic encoding schemes, which incorporate various heuristic search techniques, are proposed to deal with the most critical constraints of the problem. The fitness criterion used by all genetic algorithms includes a merit function for minimising the size of the gearbox. The results show improvement in the design merit over previous approaches without reliance on the designer's interaction to avoid...
A generative model for multi class object recognition and detection
Ulusoy, İlkay (2006-01-01)
In this study, a generative type probabilistic model is proposed for object recognition. This model is trained by weakly labelled images and performs classification and detection at the same time. When test on highly challenging data sets, the model performs good for both tasks (classification and detection).
Constraints on a noncommutative physics scale with neutrino-electron scattering
Bilmiş, Selçuk; Li, H. B.; Li, J.; Liao, H. Y.; Lin, S. T.; Singh, V.; Wong, H. T.; Yildirim, I. O.; Yue, Q.; Zeyrek, Mehmet Tevfik (2012-04-19)
Neutrino-electron scatterings (nu - e) are purely leptonic processes with robust standard model predictions. Their measurements can therefore provide constraints to physics beyond the standard model. Noncommutative (NC) field theories modify space-time commutation relations, and allow neutrino electromagnetic couplings at the tree level. Their contribution to the neutrino-electron scattering cross section was derived. Constraints were placed on the NC scale parameter Lambda(NC) from nu - e experiments with ...
A Multi-Box Behavioural Mixer Model and its Validation using Measurements
Ozgun, Ali; Nesimoglu, Tayfun; Demir, Şimşek (2019-01-01)
In this paper, a new behavioural mixer model is introduced. In addition to amplitude nonlinearity; phase nonlinearity and memory effect of the mixer are modelled in a multi-box structure. Each nonlinearity source is modelled in distinct blocks of which cascade connections compose the behavioural mixer model. A test-bed has been constructed including a reference mixer and through measurements, amplitude and phase characteristics of the main tones and IMD products are modelled. The proposed behavioural model ...
Citation Formats
S. Çağ and M. Akhmet, “Bifurcation Analysis of Wilson-Cowan Model with Singular Impulses,” Discontinuity, Nonlinearity, and Complexity, pp. 161–172, 2021, Accessed: 00, 2021. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85101761651&origin=inward.