Geodesic
Global bifurcations in a dynamical model of recurrent neural networks
Applications of Mathematics, Tome 68 (2023) no. 1, pp. 35-50.

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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.
DOI : 10.21136/AM.2022.0158-21
Classification : 34C23, 34C25, 34C37, 92B20
Keywords: saddle-node; Hopf; homoclinic; cycle fold bifurcation; Hopfield model 
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Windisch, Anita; Simon, Péter L. Global bifurcations in a dynamical model of recurrent neural networks. Applications of Mathematics, Tome 68 (2023) no. 1, pp. 35-50. doi : 10.21136/AM.2022.0158-21. http://geodesic.mathdoc.fr/articles/10.21136/AM.2022.0158-21/

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