Abstract
The dynamical behaviour of a continuous time recurrent neural network model with a special weight matrix is studied. The network contains several identical excitatory neurons and a single inhibitory one. This special construction enables us to reduce the dimension of the system and then fully characterize the local and global codimension-one bifurcations. It is shown that besides saddle-node and Andronov-Hopf bifurcations, homoclinic and cycle fold bifurcations may occur. These bifurcation curves divide the plane of weight parameters into nine domains. The phase portraits belonging to these domains are also characterized.
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This work was supported by the project “Integrated program for training new generation of researchers in the disciplinary fields of computer science”, No. EFOP-3.6.3-VEKOP-16-2017-00002. The project has been supported by the European Union and co-funded by the European Social Fund.
Péter L. Simon acknowledges support from Hungarian Scientific Research Fund, OTKA, (grant no. 115926) and from the Ministry of Innovation and Technology NRDI Office within the framework of the Artificial Intelligence National Laboratory Program. Open Access funding enabled and organized by Eötvös Loránd University.
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Windisch, A., Simon, P.L. Global bifurcations in a dynamical model of recurrent neural networks. Appl Math 68, 35–50 (2023). https://doi.org/10.21136/AM.2022.0158-21
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DOI: https://doi.org/10.21136/AM.2022.0158-21