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- Stephen Coombes
- School of Mathematical Sciences, University of NottinghamNottingham NG7 2RD, UK
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- Carlo Laing
- Institute of Information and Mathematical Sciences, Massey UniversityPrivate Bag 102 904 NSMC, Auckland 0745, New Zealand
説明
<jats:p> In this paper, we study the effect of two distinct discrete delays on the dynamics of a Wilson–Cowan neural network. This activity-based model describes the dynamics of synaptically interacting excitatory and inhibitory neuronal populations. We discuss the interpretation of the delays in the language of neurobiology and show how they can contribute to the generation of network rhythms. First, we focus on the use of linear stability theory to show how to destabilize a fixed point, leading to the onset of oscillatory behaviour. Next, we show for the choice of a Heaviside nonlinearity for the firing rate that such emergent oscillations can be either synchronous or anti-synchronous, depending on whether inhibition or excitation dominates the network architecture. To probe the behaviour of smooth (sigmoidal) nonlinear firing rates, we use a mixture of numerical bifurcation analysis and direct simulations, and uncover parameter windows that support chaotic behaviour. Finally, we comment on the role of delays in the generation of <jats:italic>bursting</jats:italic> oscillations, and discuss natural extensions of the work in this paper. </jats:p>
収録刊行物
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- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
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Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 367 (1891), 1117-1129, 2009-02-16
The Royal Society