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- Neslihan Serap Sengör, Özkan Karabacak, Ulrich Steinmetz
- ICANN
- 2008

A connectionist model of cortico-striato-thalamic loops unifying learning and action selection is proposed. The aim in proposing the connectionist model is to develop a simple model revealing the mechanisms behind the cognitive process of goal directed behaviour rather than merely obtaining a model of neural structures. In the proposed connectionist model,… (More)

- Fatihcan M. Atay, Özkan Karabacak
- SIAM J. Applied Dynamical Systems
- 2006

We consider networks of coupled scalar maps, with weighted connections which may include a time delay, and study the stability of equilibria with respect to the delays and connection structure. We prove that the largest eigenvalue of the graph Laplacian determines the effect of the connection topology on stability. The stability region in the parameter… (More)

- Peter Ashwin, Özkan Karabacak, Thomas Nowotny
- Journal of mathematical neuroscience
- 2011

We introduce a test for robustness of heteroclinic cycles that appear in neural microcircuits modeled as coupled dynamical cells. Robust heteroclinic cycles (RHCs) can appear as robust attractors in Lotka-Volterra-type winnerless competition (WLC) models as well as in more general coupled and/or symmetric systems. It has been previously suggested that RHCs… (More)

A model of cortex-basal ganglia-thalamus-cortex loop is presented. Even though the mentioned loop has been proposed to take part in different cognitive processes, the model exploits only the “action selection” function. The analysis of the model is based on the stability analysis of a non-linear dynamical system. Thus a biologically valid model of a… (More)

- Özkan Karabacak, Peter Ashwin
- J. Nonlinear Science
- 2010

We analyze an example system of four coupled phase oscillators and discover a novel phenomenon that we call a “heteroclinic ratchet”; a particular type of robust heteroclinic network on a torus where connections wind in only one direction. The coupling structure has only one symmetry, but there are a number of invariant subspaces and degenerate bifurcations… (More)

- Özkan Karabacak
- Systems & Control Letters
- 2013

- Özkan Karabacak, Neslihan Serap Sengör
- ICANN
- 2006

Based on a connectionist model of cortex-basal ganglia-thalamus loop recently proposed by authors a simple connectionist model realizing the Stroop effect is established. The connectionist model of cortex-basal gangliathalamus loop is a nonlinear dynamical system and the model is not only capable of revealing the action selection property of basal ganglia… (More)

- Özkan Karabacak
- 2008

We study an unusual but robust phenomenon that appears in an example system of four coupled phase oscillators. The coupling is preserved under only one symmetry, but there are a number of invariant subspaces and degenerate bifurcations forced by the coupling structure, and we investigate these. We show that the system can have a robust attractor that… (More)

- Özkan Karabacak, Neslihan Serap Sengör
- Int. J. Systems Science
- 2009

In this paper a sufficient condition on the minimum dwell time that guarantees the stability of switched linear systems is given. The proposed method interprets the stability of switched linear systems through the distance between the eigenvector sets of subsystem matrices. Thus, an explicit relation in view of stability is obtained between the family of… (More)

- Özkan Karabacak, Ferruh Ilhan, Isil Öner
- CDC
- 2014