Typical behaviors in co-evolving recurrent network of oscillatory neurons
We investigate the typical behaviors that emerge in a co-evolving recurrent network in which neurons and synaptic weights interact with each other. In general, the collective activities of neurons depend on the network structure of the synaptic connections. The neural connectivity, however, is adaptively modulated by plasticity in the synapses that depends on neural activity, and in turn the activity of neurons is affected by the adaptive connectivity. This mutual co-evolution of the neurons and synapses is believed to be essential in providing a neuronal basis for higher brain functions such as learning and memory. Because of the perceived importance of plasticity, the emergent behaviors under the synaptic plasticity have been studied in several conditions by a number of researchers. In a neural network which has dense recurrent connections, however, it is difficult to understand how the co-evolving mechanism affects the collective behavior of neurons, and it is still unclear what types of behavior the adaptive network can exhibit.
To investigate the fundamental properties possessed by the adaptive network, we present a simple mathematical model of the co-evolving network in which oscillatory neurons are the network nodes. The plasticity is incorporated by allowing the synaptic weights to develop in time according to the states of the pre- and post-synaptic neurons. This model can be characterized by a few parameters. Specifically, when and particularly the neurons are assumed to have the same firing rate, only two parameters are needed. As a result, we can systematically investigate the possible behaviors of our model for all ranges of model parameters, and we find three typical asymptotic behaviors, depending on the nature of the dynamics of the synaptic weights. When the dynamics of the weights is qualitatively similar to the Hebbian rule, a two-cluster state emerges, in which the activity of neurons converges to synchronized sub-groups. For another set of the model parameter values in which the synaptic dynamics become similar to spike-timing-dependent plasticity (temporal asymmetric rule), a coherent state with a fixed spike pattern emerges. In contrast to the two-cluster state, a sequential spike pattern of neurons is maintained with the synaptic connections organized through the co-evolving dynamics. For yet another set of parameter values, a chaotic state is realized when the dynamics of the synaptic weights and neurons are frustrated. In this case, the synaptic dynamics possesses an effect opposite to that of a Hebbian-like rule. According to this anti-Hebbian-like rule, a reciprocal destabilization of both the spike pattern and the network structure is observed. Moreover, we confirmed that Lyapunov exponents take positive values, and then we refer to this as a chaotic state.
In summary, we found that the model of the co-evolving network under investigation possesses three distinct types of dynamical behaviors. Because of its structural stability, our model will provide a framework for describing essential behaviors in adaptive recurrent networks.
Conference:
Computational and systems
neuroscience 2009, Salt Lake City, UT, United States, 26 Feb - 3 Mar, 2009.
Presentation Type:
Poster Presentation
Topic:
Poster Presentations
Citation:
(2009). Typical behaviors in co-evolving recurrent network of oscillatory neurons.
Front. Syst. Neurosci.
Conference Abstract:
Computational and systems
neuroscience 2009.
doi: 10.3389/conf.neuro.06.2009.03.005
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Received:
28 Jan 2009;
Published Online:
28 Jan 2009.