Dynamical behaviors of a class of recurrent neural networks with discontinuous neuron activations

Dynamical behaviors of a class of recurrent neural networks with discontinuous neuron activations. Li, L. & Huang, L. Applied Mathematical Modelling, 33(12):4326–4336, December, 2009. tex.ids: AMM-2009-Li-Dynamicala

Paper doi abstract bibtex

This paper investigates the dynamics of a class of recurrent neural networks where the neural activations are modeled by discontinuous functions. Without presuming the boundedness of activation functions, the sufﬁcient conditions to ensure the existence, uniqueness, global exponential stability and global convergence of state equilibrium point and output equilibrium point are derived, respectively. Furthermore, under certain conditions we prove that the system is convergent globally in ﬁnite time. The analysis in the paper is based on the properties of M-matrix, Lyapunov-like approach, and the theories of differential equations with discontinuous right-hand side as introduced by Filippov. The obtained results extend previous works on global stability of recurrent neural networks with not only Lipschitz continuous but also discontinuous neural activation functions.

@article{li_dynamical_2009,
	title = {Dynamical behaviors of a class of recurrent neural networks with discontinuous neuron activations},
	volume = {33},
	issn = {0307904X},
	url = {https://linkinghub.elsevier.com/retrieve/pii/S0307904X09000717},
	doi = {10.1016/j.apm.2009.03.014},
	abstract = {This paper investigates the dynamics of a class of recurrent neural networks where the neural activations are modeled by discontinuous functions. Without presuming the boundedness of activation functions, the sufﬁcient conditions to ensure the existence, uniqueness, global exponential stability and global convergence of state equilibrium point and output equilibrium point are derived, respectively. Furthermore, under certain conditions we prove that the system is convergent globally in ﬁnite time. The analysis in the paper is based on the properties of M-matrix, Lyapunov-like approach, and the theories of differential equations with discontinuous right-hand side as introduced by Filippov. The obtained results extend previous works on global stability of recurrent neural networks with not only Lipschitz continuous but also discontinuous neural activation functions.},
	language = {en},
	number = {12},
	urldate = {2022-01-19},
	journal = {Applied Mathematical Modelling},
	author = {Li, Liping and Huang, Lihong},
	month = dec,
	year = {2009},
	note = {tex.ids: AMM-2009-Li-Dynamicala},
	keywords = {/unread},
	pages = {4326--4336},
}

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