Bifurcaciones en sistemas de redes neuronales

Mauro Montealegre Cardenas; Jasmidt Vera Cuenca; Edgar Montealegre Cárdenas

doi:10.25054/22161325.1313

Bifurcations of neuronal networks systems

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Montealegre Cardenas, M., Vera Cuenca, J., & Montealegre Cárdenas, E. (2017). Bifurcations of neuronal networks systems. Ingeniería Y Región, 17, 21–32. https://doi.org/10.25054/22161325.1313

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Published: Jun 30, 2017

Doi

https://doi.org/10.25054/22161325.1313

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Vol. 17 (2017)

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Articles

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Mauro Montealegre Cardenas Surcolombiana University

Jasmidt Vera Cuenca Surcolombiana University

Edgar Montealegre Cárdenas Surcolombiana University

Abstract

This paper explores the concepts of dynamic systems that explain synergies in biological neural networks modeled with the Morris-Lecar equation, assuming that neurons or groups of neurons are oscillators, or not, at the cellular, neuronal synapses or network connectivity. For the fast-time subsystems, unique solutions and "Burstings" solutions are identified. In this dynamic system of hierarchical complexity, the parameters are the variables of the slow subsystem. In order to explain instability and transience, the generic bifurcation theory that characterizes mesoscopic aspects of network and phylogenetic connectivity over typical behavioral changes is used. This study is extended to models of recurrent artificial neural networks, in particular to the Hopfield model.

Keywords

Neural networks

singular solutions

"burstings" solutions

Morris-Lecar equation

Hopfield model

Bifurcations

mesoscopic level

hierarchical complexity

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Author Biographies / See

Mauro Montealegre Cardenas, Surcolombiana University

Research Group Dinusco

Jasmidt Vera Cuenca, Surcolombiana University

Research Group Dinusco

Edgar Montealegre Cárdenas, Surcolombiana University

Research Group Dinusco

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