ArticleTheory in biosciences = Theorie in den Biowissenschaften2024
Dynamics of neural fields with exponential temporal kernel.
Article in Theory in biosciences = Theorie in den Biowissenschaften, 2024. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 2 papers.
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2 citing papers in PubMed, 2 citations in OpenAlex.
- A Model-Based Approach to Neuronal Electrical Activity and Spatial Organization Through the Neuronal Actin Cytoskeleton.Methods and protocols · 2025Article
- Graph neural fields: A framework for spatiotemporal dynamical models on the human connectome.PLoS computational biology · 2021Article
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4 authors at 3 institutions in 3 countries.
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Abstract
We consider the standard neural field equation with an exponential temporal kernel. We analyze the time-independent (static) and time-dependent (dynamic) bifurcations of the equilibrium solution and the emerging spatiotemporal wave patterns. We show that an exponential temporal kernel does not allow static bifurcations such as saddle-node, pitchfork, and in particular, static Turing bifurcations. However, the exponential temporal kernel possesses the important property that it takes into account the finite memory of past activities of neurons, which Green's function does not. Through a dynamic bifurcation analysis, we give explicit bifurcation conditions. Hopf bifurcations lead to temporally non-constant, but spatially constant solutions, but Turing-Hopf bifurcations generate spatially and temporally non-constant solutions, in particular, traveling waves. Bifurcation parameters are the coefficient of the exponential temporal kernel, the transmission speed of neural signals, the time delay rate of synapses, and the ratio of excitatory to inhibitory synaptic weights.
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