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Dynamics and bifurcations of two coupled neural oscillators with different connection types

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Abstract

In this paper we present an oscillatory neural network composed of two coupled neural oscillators of the Wilson-Cowan type. Each of the oscillators describes the dynamics of average activities of excitatory and inhibitory populations of neurons. The network serves as a model for several possible network architectures. We study how the type and the strength of the connections between the oscillators affect the dynamics of the neural network. We investigate, separately from each other, four possible connection types (excitatory→excitatory, excitatory→inhibitory, inhibitory→excitatory, and inhibitory→inhibitory) and compute the corresponding bifurcation diagrams. In case of weak connections (small strength), the connection of populations of different types lead to periodicin-phase oscillations, while the connection of populations of the same type lead to periodicanti-phase oscillations. For intermediate connection strengths, the networks can enter quasiperiodic or chaotic regimes, and can also exhibit multistability. More generally, our analysis highlights the great diversity of the response of neural networks to a change of the connection strength, for different connection architectures. In the discussion, we address in particular the problem of information coding in the brain using quasiperiodic and chaotic oscillations. In modeling low levels of information processing, we propose that feature binding should be sought as a temporally coherent phase-locking of neural activity. This phase-locking is provided by one or more interacting convergent zones and does not require a central “top level” subcortical circuit (e.g. the septo-hippocampal system). We build a two layer model to show that although the application of a complex stimulus usually leads to different convergent zones with high frequency oscillations, it is nevertheless possible to synchronize these oscillations at a lower frequency level using envelope oscillations. This is interpreted as a feature binding of a complex stimulus.

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Authors and Affiliations

  1. Institute of Mathematical Problems in Biology, Russian Academy of Sciences, 142292, Pushchino, Moscow Region, Russia

    Galina N. Borisyuk, Roman M. Borisyuk & Alexander I. Khibnik

  2. Theory Center, Cornell University, 14853, Ithaca, NY, USA

    Alexander I. Khibnik

  3. Department of Computer Science, Katholieke Universiteit Leuven, B-3001, Leuven, Belgium

    Dirk Roose

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  1. Galina N. Borisyuk
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  2. Roman M. Borisyuk
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  3. Alexander I. Khibnik
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  4. Dirk Roose
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Borisyuk, G.N., Borisyuk, R.M., Khibnik, A.I. et al. Dynamics and bifurcations of two coupled neural oscillators with different connection types. Bltn Mathcal Biology 57, 809–840 (1995). https://doi.org/10.1007/BF02458296

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