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Dynamics of neural fields with exponential temporal kernel
Elham Shamsara1, Marius E Yamakou2, Fatihcan M Atay3
1Methods in Medical Informatics, Department of Computer Science, University of Tübingen, 72076, Tübingen, Germany.
Theory in Biosciences = Theorie in Den Biowissenschaften
|March 9, 2024
Summary
This study shows exponential temporal kernels in neural fields prevent static bifurcations but enable dynamic ones, like Turing-Hopf bifurcations, generating traveling waves and accounting for neural memory.
Area of Science:
- Computational neuroscience
- Mathematical biology
- Dynamical systems theory
Background:
- Neural field equations model large-scale brain activity.
- Temporal kernels shape neural signal integration over time.
- Understanding bifurcations reveals pattern formation mechanisms.
Purpose of the Study:
- Analyze bifurcations in neural fields with exponential temporal kernels.
- Investigate static and dynamic pattern formation.
- Characterize emergent spatiotemporal wave patterns.
Main Methods:
- Analysis of time-independent (static) bifurcations.
- Analysis of time-dependent (dynamic) bifurcations.
- Bifurcation analysis using parameters like kernel coefficient, transmission speed, synaptic delay, and excitation-inhibition ratio.
Main Results:
- Exponential temporal kernels preclude static bifurcations (saddle-node, pitchfork, Turing).
- These kernels capture finite neural memory, unlike Green's functions.
- Dynamic bifurcation analysis yields explicit conditions for Hopf and Turing-Hopf bifurcations.
- Turing-Hopf bifurcations generate spatially and temporally complex solutions, including traveling waves.
Conclusions:
- Exponential temporal kernels support dynamic pattern formation, crucial for neural computation.
- The model predicts traveling waves via Turing-Hopf bifurcations.
- Finite neural memory is a key feature enabled by this kernel type.
Keywords:
Bifurcation analysisExponential temporal kernelLeakageNeural fieldsSpatiotemporal patternsTransmission delaysMore Related Videos
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